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		<title>分形维数</title>
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		<summary type="html">&lt;p&gt;Ilseyao2020：/* Self-similar sets自相似集合 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 ''X'' 的 Borel 子集上定义一个测度 μ，使得''μ''(''X'') &amp;gt; 0 和''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;''，对于某个常数 ''s'' &amp;gt; 0  和 ''X'' 中的每个球 ''B''(''x'', ''r'') 成立，则 dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s'' 。 部分逆向转换由弗洛斯曼引理定义。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; 是一个有限或可数的联合，则&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义得到验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 ''X'' 和''Y''是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets自相似集合==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合''E'' 是自相似的，如果它是集值ψ变换的不动点，即ψ(''E'') = ''E''，尽管下面给出了确切的定义。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''定理'''。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
是'''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;上的压缩常数''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'&amp;lt; 1的压缩映射。然后有一个唯一的非空紧集A &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
&lt;br /&gt;
这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The open set condition开集条件===&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集''A'' 的维数(在某些情况下) ，我们需要一个称为''开集条件''(OSC)的技术条件ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set ''V'' such that&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集''V''&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
&lt;br /&gt;
左边的集合是成对不相交的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
开集条件是保证图像子ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') 不重叠“太多”的分离条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
'''定理'''假设开集条件成立，并且每个ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 ''s'' ，其中  ''s'' 是 ''s'' &amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;的唯一解&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算谢尔宾斯基三角形的豪斯多夫维数(或者有时候叫做谢尔宾斯基垫圈)。考虑R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; 平面上的三个非共线点，''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;，''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;，''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;，让ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;是围绕着''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''膨胀比率的1/2。对应映射的唯一非空不动点是一个谢尔宾斯基垫圈，其维数''s''是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
取上述方程两边的自然对数，我们可以求出 ''s''，即: ''s'' = ln(3)/ln(2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 ''E''是一个映射的不动点&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
是自相似的，当且仅当&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 ''s''是''E''的豪斯多夫维数， ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' 表示 豪斯多夫测度。对于谢尔宾斯基垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
'''定理'''：在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
&lt;br /&gt;
==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
&lt;br /&gt;
==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
最后一站马斯特兰德&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
第50卷&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
第三期&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
&lt;br /&gt;
* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
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* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
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* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
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* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<title>分形维数</title>
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		<summary type="html">&lt;p&gt;Ilseyao2020：/* The open set condition开集条件 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 ''X'' 的 Borel 子集上定义一个测度 μ，使得''μ''(''X'') &amp;gt; 0 和''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;''，对于某个常数 ''s'' &amp;gt; 0  和 ''X'' 中的每个球 ''B''(''x'', ''r'') 成立，则 dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s'' 。 部分逆向转换由弗洛斯曼引理定义。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; 是一个有限或可数的联合，则&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义得到验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 ''X'' 和''Y''是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets自相似集合==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合''E'' 是自相似的，如果它是集值ψ变换的不动点，即ψ(''E'') = ''E''，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''块引定理'''。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
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are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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是'''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;上的压缩常数''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'&amp;lt; 1的压缩映射。然后有一个唯一的非空紧集A &lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集''A'' 的维数(在某些情况下) ，我们需要一个称为''开集条件''(OSC)的技术条件ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集''V''&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') 不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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'''定理'''假设开集条件成立，并且每个ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 ''s'' ，其中  ''s'' 是 ''s'' &amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算谢尔宾斯基三角形的豪斯多夫维数(或者有时候叫做谢尔宾斯基垫圈)。考虑R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; 平面上的三个非共线点，''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;，''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;，''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;，让ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;是围绕着''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''膨胀比率的1/2。对应映射的唯一非空不动点是一个谢尔宾斯基垫圈，其维数''s''是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 ''s''，即: ''s'' = ln(3)/ln(2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 ''E''是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的，当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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其中 ''s''是''E''的豪斯多夫维数， ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' 表示 豪斯多夫测度。对于谢尔宾斯基垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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'''定理'''：在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
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* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
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* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
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* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
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* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
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		<title>分形维数</title>
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		<updated>2020-08-17T06:10:21Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Self-similar sets */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 ''X'' 的 Borel 子集上定义一个测度 μ，使得''μ''(''X'') &amp;gt; 0 和''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;''，对于某个常数 ''s'' &amp;gt; 0  和 ''X'' 中的每个球 ''B''(''x'', ''r'') 成立，则 dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s'' 。 部分逆向转换由弗洛斯曼引理定义。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义得到验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 ''X'' 和''Y''是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets自相似集合==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合''E'' 是自相似的，如果它是集值ψ变换的不动点，即ψ(''E'') = ''E''，尽管下面给出了确切的定义。&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''块引定理'''。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
是'''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;上的压缩常数''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'&amp;lt; 1的压缩映射。然后有一个唯一的非空紧集A &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
&lt;br /&gt;
这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
&lt;br /&gt;
==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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 | last1=Marstrand&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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 | issue=3&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
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		<title>分形维数</title>
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		<updated>2020-08-17T06:03:43Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Behaviour under unions and products */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 ''X'' 的 Borel 子集上定义一个测度 μ，使得''μ''(''X'') &amp;gt; 0 和''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;''，对于某个常数 ''s'' &amp;gt; 0  和 ''X'' 中的每个球 ''B''(''x'', ''r'') 成立，则 dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s'' 。 部分逆向转换由弗洛斯曼引理定义。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; 是一个有限或可数的联合，则&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义得到验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 ''X'' 和''Y''是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
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are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集 v&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E5%88%86%E5%BD%A2%E7%BB%B4%E6%95%B0&amp;diff=12800</id>
		<title>分形维数</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E5%88%86%E5%BD%A2%E7%BB%B4%E6%95%B0&amp;diff=12800"/>
		<updated>2020-08-17T05:59:57Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 ''X'' 的 Borel 子集上定义一个测度 μ，使得''μ''(''X'') &amp;gt; 0 和''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;''，对于某个常数 ''s'' &amp;gt; 0  和 ''X'' 中的每个球 ''B''(''x'', ''r'') 成立，则 dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s'' 。 部分逆向转换由弗洛斯曼引理定义。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
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are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集 v&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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 | last1=Marstrand&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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 | issue=3&lt;br /&gt;
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 | issue=3&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
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		<title>分形维数</title>
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		<updated>2020-08-17T05:52:45Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
&lt;br /&gt;
非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
&lt;br /&gt;
The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
&lt;br /&gt;
The Hausdorff dimension of X is defined by&lt;br /&gt;
&lt;br /&gt;
X 的豪斯多夫维数定义为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
&lt;br /&gt;
[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
&lt;br /&gt;
[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
&lt;br /&gt;
* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
&lt;br /&gt;
* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
&lt;br /&gt;
[[大不列颠海岸&lt;br /&gt;
&lt;br /&gt;
* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
&lt;br /&gt;
==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
&lt;br /&gt;
Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
&lt;br /&gt;
设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
&lt;br /&gt;
=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
&lt;br /&gt;
If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
这可以直接从定义中验证。&lt;br /&gt;
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&lt;br /&gt;
If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
&lt;br /&gt;
块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
/ blockquote&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
&lt;br /&gt;
这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The open set condition开集条件===&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set ''V'' such that&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
&lt;br /&gt;
左边的集合是成对不相交的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
是自相似的当且仅当&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
&lt;br /&gt;
==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
&lt;br /&gt;
==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
最后一站马斯特兰德&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
第50卷&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
第三期&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
&lt;br /&gt;
* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
&lt;br /&gt;
==External links外部链接==&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Fractals]]&lt;br /&gt;
&lt;br /&gt;
Category:Fractals&lt;br /&gt;
&lt;br /&gt;
分类: 分形&lt;br /&gt;
&lt;br /&gt;
[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
&lt;br /&gt;
[[Category:Dimension theory]]&lt;br /&gt;
&lt;br /&gt;
Category:Dimension theory&lt;br /&gt;
&lt;br /&gt;
范畴: 维度理论&lt;br /&gt;
&lt;br /&gt;
&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
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		<title>分形维数</title>
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		<updated>2020-08-17T05:38:07Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hausdorff dimension and inductive dimension */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
&lt;br /&gt;
{{short description|Invariant}}&lt;br /&gt;
&lt;br /&gt;
[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
&lt;br /&gt;
In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
&lt;br /&gt;
换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
&lt;br /&gt;
===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
&lt;br /&gt;
The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
&lt;br /&gt;
The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
&lt;br /&gt;
豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
&lt;br /&gt;
The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
&lt;br /&gt;
The Hausdorff dimension of X is defined by&lt;br /&gt;
&lt;br /&gt;
X 的豪斯多夫维数定义为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
&lt;br /&gt;
==Examples实例==&lt;br /&gt;
&lt;br /&gt;
[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
&lt;br /&gt;
[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
&lt;br /&gt;
* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
&lt;br /&gt;
* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
&lt;br /&gt;
[[大不列颠海岸&lt;br /&gt;
&lt;br /&gt;
* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
&lt;br /&gt;
==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Hausdorff dimension and inductive dimension 豪斯多夫维数和归纳维数===&lt;br /&gt;
&lt;br /&gt;
Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
&lt;br /&gt;
设''X'' 是[[任意可分度量空间]]。对于''X'' 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'')。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
'''定理'''：假设''X'' 是非空的。那么&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中''Y''是度量空间同胚到 ''X''的范围。换句话说， ''X''和 ''Y''具有相同的基本点集，''Y''的度规''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; 的子拓扑等价于''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 [[Edward Szpilrajn]] (1907–1976)建立的,  参见 Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}第七章。&lt;br /&gt;
&lt;br /&gt;
=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数绝对大于豪斯多夫维数。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
&lt;br /&gt;
If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
这可以直接从定义中验证。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
&lt;br /&gt;
块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
/ blockquote&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
&lt;br /&gt;
这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The open set condition开集条件===&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set ''V'' such that&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
&lt;br /&gt;
左边的集合是成对不相交的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
是自相似的当且仅当&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
&lt;br /&gt;
==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
&lt;br /&gt;
==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
最后一站马斯特兰德&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
第50卷&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
第三期&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
&lt;br /&gt;
* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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		<title>分形维数</title>
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		<summary type="html">&lt;p&gt;Ilseyao2020：/* Examples实例 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
&lt;br /&gt;
For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
&lt;br /&gt;
对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
&lt;br /&gt;
==Formal definitions形式化定义==&lt;br /&gt;
&lt;br /&gt;
{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
&lt;br /&gt;
Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
&lt;br /&gt;
Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
&lt;br /&gt;
设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
&lt;br /&gt;
In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
&lt;br /&gt;
换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
&lt;br /&gt;
===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
&lt;br /&gt;
The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
&lt;br /&gt;
The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
&lt;br /&gt;
豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
&lt;br /&gt;
The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
&lt;br /&gt;
The Hausdorff dimension of X is defined by&lt;br /&gt;
&lt;br /&gt;
X 的豪斯多夫维数定义为&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
&lt;br /&gt;
等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
&lt;br /&gt;
[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
&lt;br /&gt;
[[Image:谢尔宾斯基三角形 deep.svg|thumb|250px|进一步的[[分形维数]]的例子，进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;的物体]]&lt;br /&gt;
&lt;br /&gt;
* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
*[[可数集]]拥有豪斯多夫维数0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=豪斯多夫维数, Its Properties, and Its Surprises |journal=The American Mathematical Monthly美国数学期刊 |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
*[[教育空间]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; 有豪斯多夫维数 ''n''，循环'''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; 拥有豪斯多夫维数1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
&lt;br /&gt;
* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。&lt;br /&gt;
* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
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[[大不列颠海岸&lt;br /&gt;
&lt;br /&gt;
* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。]]&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
&lt;br /&gt;
设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
定理：假设 x 是非空的。然后&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
&lt;br /&gt;
If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
这可以直接从定义中验证。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
&lt;br /&gt;
块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
/ blockquote&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
&lt;br /&gt;
这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===The open set condition开集条件===&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set ''V'' such that&lt;br /&gt;
&lt;br /&gt;
There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
&lt;br /&gt;
左边的集合是成对不相交的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
is self-similar if and only if the intersections&lt;br /&gt;
&lt;br /&gt;
是自相似的当且仅当&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
&lt;br /&gt;
==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
&lt;br /&gt;
==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
&lt;br /&gt;
最后一站马斯特兰德&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
第50卷&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
第三期&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
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* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
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* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
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* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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		<title>分形维数</title>
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		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hausdorff dimension豪斯多夫维数 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim &amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'')可定义为 ''d'' ∈ [0, ∞) 集的下确界，使得''X'' 的''d''-维 [[豪斯多夫测度]] 为零。这与 ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞)的集合的上确界相同，因此''X''的 d 维豪斯多夫测度是无限的(除非后一个集合 ''d'' 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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定理：假设 x 是非空的。然后&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
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are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集 v&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
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* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
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* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
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* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
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* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
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		<title>分形维数</title>
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		<updated>2020-08-17T05:06:02Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hausdorff content豪斯多夫集 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个建模是使用这个比例因子(3)和自相似物体的数量(4)来计算维度，设在第一次迭代后为 D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，&amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期假设的基础，一个点的豪斯多夫维数是零，一条线是一等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后人们删除这个基础线段用来保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 N=4，其中每个自相似拷贝的长度是原始线段的1/S = 1/3 。这个方程很容易求解为 D，产生出现在图形中的对数(或自然对数)的比率，并给出——在 Koch 和其他分形情况下——这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体X的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数''n''&amp;amp;nbsp;=&amp;amp;nbsp;1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它看起来像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 ''N'' (r) ，需要完全覆盖 ''X''。当 r 很小时，n (r)以1/''r'' 增长多项式。对于一个表现足够好的 ''X''，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时， N(r)增长为1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; 。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说， &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; 是数字集合 &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; 的下确界，使得在 i / math 中存在一些球集合 &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt;  i 包含 s，对于每个 ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 满足 i 中的和&amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt; (在这里，我们使用inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞ )的标准约定。&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学  &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;，我们定义了  ''S''的 ''d''维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{有一个面} S\text{ 球 } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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定理：假设 x 是非空的。然后&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
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are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集 v&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
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* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
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| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
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* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
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* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
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* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
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		<title>分形维数</title>
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		<updated>2020-07-27T06:42:40Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Properties of Hausdorff dimension */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个[ Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个形式使用这个比例因子(3)和自相似物体的数量(4)来计算维度，d，在第一次迭代后为 d (log n) / (log s)(log 4) / (log 3)1.26。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，math  overline { mathbb { r } / math，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期声明的基础，一个点的豪斯多夫维数是零，一条线是一，等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后这个基础线段被删除以保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 n4，其中每个自相似拷贝的长度是原始线段的1 / s 1 / 3。这个方程很容易求解为 d，产生出现在图形中的对数(或自然对数)的比率，并给出ー在 Koch 和其他分形情况下ー这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体 x 的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数 n 1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它表现得像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 n (r) ，需要完全覆盖 x。当 r 很小时，n (r)以1 / r 增长多项式。对于一个表现足够好的 x，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时 n (r)增长为1 / r sup d / sup。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 c h ^ d (s) :  inf  Bigl  sum i r i ^ d:  text { there is a cover of } s  text { by balls with radii } r i 0 Bigr } . / math&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学 d  geq 0 / math，我们定义了 s 的 d 维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学函数 h ^ d (s) : lim { r  to 0} inf  Bigl  sum i r i ^ d:  text {有一个{ s  text  by balls with radii }0 r i r  Bigr }的封面。 数学&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension豪斯多夫维数特性==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
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Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
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定理：假设 x 是非空的。然后&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
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Moreover,&lt;br /&gt;
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Moreover,&lt;br /&gt;
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此外,&lt;br /&gt;
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:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
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(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
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where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
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These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
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这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension 豪斯多夫维数和闵可夫斯基维度===&lt;br /&gt;
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The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
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闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数绝对大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
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如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由弗洛斯曼引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
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如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
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如果 x 和 y 是非空度量空间，那么它们乘积的豪斯多夫维数满足&lt;br /&gt;
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:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
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(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
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这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
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Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
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&lt;br /&gt;
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:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
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为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
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有一个相对紧的开集 v&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
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定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
&lt;br /&gt;
 | last1=Marstrand&lt;br /&gt;
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 | last1=Marstrand&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
&lt;br /&gt;
首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
 | issue=3&lt;br /&gt;
&lt;br /&gt;
第三期&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
&lt;br /&gt;
10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
&lt;br /&gt;
* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
&lt;br /&gt;
==External links外部链接==&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
&lt;br /&gt;
[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10942</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10942"/>
		<updated>2020-07-20T11:53:36Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Complex systems modeling复杂系统建模 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑箱（现象学），白箱（力学，基于第一原理）和灰箱（现象学和力学模型的混合）。在黑箱模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑箱模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白箱模型是透明的，直接显示了潜在的机制。在动态系统白箱模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑箱方法，这些方法无法生成复杂动态系统的机械模型。灰箱模型是中间模型，结合了黑箱方法和白箱方法。&lt;br /&gt;
&lt;br /&gt;
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复杂系统白箱模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白箱模型的必要条件，但不是充分条件。白箱模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白箱建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白箱建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白箱模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白箱类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
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2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
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3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
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*细菌菌落优化&lt;br /&gt;
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*遗传算法&lt;br /&gt;
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*基因编程&lt;br /&gt;
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*群智能&lt;br /&gt;
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4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
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5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
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6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
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7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
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#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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30em | &lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
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7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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		<title>分形维数</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E5%88%86%E5%BD%A2%E7%BB%B4%E6%95%B0&amp;diff=10902"/>
		<updated>2020-07-20T00:53:03Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* References */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个[ Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个形式使用这个比例因子(3)和自相似物体的数量(4)来计算维度，d，在第一次迭代后为 d (log n) / (log s)(log 4) / (log 3)1.26。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，math  overline { mathbb { r } / math，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期声明的基础，一个点的豪斯多夫维数是零，一条线是一，等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后这个基础线段被删除以保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 n4，其中每个自相似拷贝的长度是原始线段的1 / s 1 / 3。这个方程很容易求解为 d，产生出现在图形中的对数(或自然对数)的比率，并给出ー在 Koch 和其他分形情况下ー这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体 x 的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数 n 1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它表现得像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 n (r) ，需要完全覆盖 x。当 r 很小时，n (r)以1 / r 增长多项式。对于一个表现足够好的 x，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时 n (r)增长为1 / r sup d / sup。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 c h ^ d (s) :  inf  Bigl  sum i r i ^ d:  text { there is a cover of } s  text { by balls with radii } r i 0 Bigr } . / math&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学 d  geq 0 / math，我们定义了 s 的 d 维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学函数 h ^ d (s) : lim { r  to 0} inf  Bigl  sum i r i ^ d:  text {有一个{ s  text  by balls with radii }0 r i r  Bigr }的封面。 数学&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
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coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
&lt;br /&gt;
设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
定理：假设 x 是非空的。然后&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension ===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数严格大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures ===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由霜人引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们产品的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是严格的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)讨论了这些事实。&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
==Self-similar sets==&lt;br /&gt;
&lt;br /&gt;
{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
&lt;br /&gt;
许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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&lt;br /&gt;
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where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
&lt;br /&gt;
The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References参考文献==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个[ Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个形式使用这个比例因子(3)和自相似物体的数量(4)来计算维度，d，在第一次迭代后为 d (log n) / (log s)(log 4) / (log 3)1.26。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，math  overline { mathbb { r } / math，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期声明的基础，一个点的豪斯多夫维数是零，一条线是一，等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后这个基础线段被删除以保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 n4，其中每个自相似拷贝的长度是原始线段的1 / s 1 / 3。这个方程很容易求解为 d，产生出现在图形中的对数(或自然对数)的比率，并给出ー在 Koch 和其他分形情况下ー这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体 x 的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数 n 1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它表现得像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 n (r) ，需要完全覆盖 x。当 r 很小时，n (r)以1 / r 增长多项式。对于一个表现足够好的 x，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时 n (r)增长为1 / r sup d / sup。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 c h ^ d (s) :  inf  Bigl  sum i r i ^ d:  text { there is a cover of } s  text { by balls with radii } r i 0 Bigr } . / math&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学 d  geq 0 / math，我们定义了 s 的 d 维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学函数 h ^ d (s) : lim { r  to 0} inf  Bigl  sum i r i ^ d:  text {有一个{ s  text  by balls with radii }0 r i r  Bigr }的封面。 数学&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
定理：假设 x 是非空的。然后&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension ===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数严格大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures ===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由霜人引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们产品的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是严格的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)讨论了这些事实。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
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* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links外部链接==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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		<title>分形维数</title>
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		<updated>2020-07-20T00:50:59Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* See also */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个[ Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个形式使用这个比例因子(3)和自相似物体的数量(4)来计算维度，d，在第一次迭代后为 d (log n) / (log s)(log 4) / (log 3)1.26。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，math  overline { mathbb { r } / math，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期声明的基础，一个点的豪斯多夫维数是零，一条线是一，等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后这个基础线段被删除以保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 n4，其中每个自相似拷贝的长度是原始线段的1 / s 1 / 3。这个方程很容易求解为 d，产生出现在图形中的对数(或自然对数)的比率，并给出ー在 Koch 和其他分形情况下ー这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体 x 的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数 n 1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它表现得像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 n (r) ，需要完全覆盖 x。当 r 很小时，n (r)以1 / r 增长多项式。对于一个表现足够好的 x，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时 n (r)增长为1 / r sup d / sup。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 c h ^ d (s) :  inf  Bigl  sum i r i ^ d:  text { there is a cover of } s  text { by balls with radii } r i 0 Bigr } . / math&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学 d  geq 0 / math，我们定义了 s 的 d 维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学函数 h ^ d (s) : lim { r  to 0} inf  Bigl  sum i r i ^ d:  text {有一个{ s  text  by balls with radii }0 r i r  Bigr }的封面。 数学&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
定理：假设 x 是非空的。然后&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension ===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数严格大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures ===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由霜人引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们产品的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是严格的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)讨论了这些事实。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
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我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
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Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
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取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
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其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
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==See also参阅==&lt;br /&gt;
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* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
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* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
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* [[Intrinsic dimension]]&lt;br /&gt;
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* [[Packing dimension]]&lt;br /&gt;
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* [[Fractal dimension]]&lt;br /&gt;
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==References==&lt;br /&gt;
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{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
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* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
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* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
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* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
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* {{cite journal&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
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 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
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第198-202页&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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 | last1=Mattila&lt;br /&gt;
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最后1个 Mattila&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
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 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
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| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
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* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
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*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
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==External links==&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
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		<title>分形维数</title>
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		<updated>2020-07-20T00:50:13Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* The open set condition */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。&lt;br /&gt;
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{{short description|Invariant}}&lt;br /&gt;
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[[File:KochFlake.svg|thumb|280px|Example of non-integer dimensions. The first four [[iteration]]s of the [[Koch snowflake|Koch curve]], where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.&amp;lt;ref name=CampbellAnnenberg15&amp;gt;MacGregor Campbell, 2013, &amp;quot;5.6 Scaling and the Hausdorff Dimension,&amp;quot; at ''Annenberg Learner:MATHematics illuminated'', see [http://www.learner.org/courses/mathilluminated/units/5/textbook/06.php], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, while the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3, for [[fractal]]s such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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Example of non-integer dimensions. The first four [[iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses this scale factor (3) and the number of self-similar objects (4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26. That is, while the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3, for fractals such as this, the object can have a non-integer dimension.]]&lt;br /&gt;
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非整数维度示例：前四个[ Koch 曲线的迭代，在每次迭代后，所有原始线段都被替换为四个，每个自相似的复制是原始线段长度的1 / 3。豪斯多夫维数的一个形式使用这个比例因子(3)和自相似物体的数量(4)来计算维度，d，在第一次迭代后为 d (log n) / (log s)(log 4) / (log 3)1.26。也就是说，当一个点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3时，对于像这样的分形，物体可以有一个非整数维度。&lt;br /&gt;
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In [[mathematics]], '''Hausdorff dimension''' is a measure of ''roughness'', or more specifically, [[fractal dimension]], that was first introduced in 1918 by [[mathematician]] [[Felix Hausdorff]].&amp;lt;ref&amp;gt;{{Cite journal |arxiv = 1101.1444|doi = 10.1214/11-STS370|title = Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data|journal = Statistical Science|volume = 27|issue = 2|pages = 247–277|year = 2012|last1 = Gneiting|first1 = Tilmann|last2 = Ševčíková|first2 = Hana|last3 = Percival|first3 = Donald B.}}&amp;lt;/ref&amp;gt; For instance, the Hausdorff dimension of a single [[point (geometry)|point]] is zero, of a [[line segment]] is 1, of a [[square]] is 2, and of a [[cube]] is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an [[integer]] agreeing with the usual sense of dimension, also known as the [[Inductive dimension|topological dimension]]. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of [[scaling (geometry)|scaling]] and [[self-similarity]], one is led to the conclusion that particular objects—including [[fractal]]s—have non-integer Hausdorff dimensions. Because of the significant technical advances made by [[Abram Samoilovitch Besicovitch]] allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the ''Hausdorff–Besicovitch dimension.''&lt;br /&gt;
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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or &amp;quot;rough&amp;quot; sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.&lt;br /&gt;
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在数学中，豪斯多夫维数是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a [[metric space]]. The dimension is drawn from the [[Extended real number line|extended real numbers]], &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, &amp;lt;math&amp;gt;\overline{\mathbb{R}}&amp;lt;/math&amp;gt;, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.&lt;br /&gt;
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更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，math  overline { mathbb { r } / math，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real [[vector space]]. That is, the Hausdorff dimension of an ''n''-dimensional [[inner product space]] equals ''n''. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that [[fractal|irregular sets]] can have noninteger Hausdorff dimensions. For instance, the [[Koch snowflake]] shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new [[equilateral]] triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4.&amp;lt;ref&amp;gt;Larry Riddle, 2014, &amp;quot;Classic Iterated Function Systems: Koch Snowflake&amp;quot;, Agnes Scott College e-Academy (online), see [http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm], accessed 5 March 2015.&amp;lt;/ref&amp;gt; That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S&amp;lt;sup&amp;gt;D&amp;lt;/sup&amp;gt;.&amp;lt;ref name=ClaytonSCTPLS96&amp;gt;Keith Clayton, 1996, &amp;quot;Fractals and the Fractal Dimension,&amp;quot; ''Basic Concepts in Nonlinear Dynamics and Chaos'' (workshop), Society for Chaos Theory in Psychology and the Life Sciences annual meeting, June 28, 1996, Berkeley, California, see [http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Workshop.html], accessed 5 March 2015.&amp;lt;/ref&amp;gt; This equation is easily solved for D, yielding the ratio of logarithms (or [[natural logarithm]]s) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.&lt;br /&gt;
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用数学术语来说，豪斯多夫维数概括了实向量空间维数的概念。也就是说，n 维内积空间的豪斯多夫维数等于 n。 这就是早期声明的基础，一个点的豪斯多夫维数是零，一条线是一，等等，不规则集可以有非整数的豪斯多夫维数。例如，右边所示的 Koch 雪花是由一个正三角形构成的; 在每次迭代中，它的组成线段被分成单位长度的3段，新创建的中间线段被用作一个指向外部的新正三角形的基础，然后这个基础线段被删除以保留单位长度4的迭代中的最终对象。也就是说，在第一次迭代之后，每个原始线段都被替换为 n4，其中每个自相似拷贝的长度是原始线段的1 / s 1 / 3。这个方程很容易求解为 d，产生出现在图形中的对数(或自然对数)的比率，并给出ー在 Koch 和其他分形情况下ー这些对象的非整数维数。&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or [[Minkowski–Bouligand dimension]].&lt;br /&gt;
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The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.&lt;br /&gt;
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豪斯多夫维数是更简单但通常等价的计盒维数或闵可夫斯基维数Minkowski-Bouligand的继承者。&lt;br /&gt;
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==Intuition概念==&lt;br /&gt;
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The intuitive concept of dimension of a geometric object ''X'' is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the [[cardinality]] of the [[real plane]] is equal to the cardinality of the [[real line]] (this can be seen by an [[Cantor's diagonal argument|argument]] involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a [[space-filling curve]] shows that one can even map the real line to the real plane [[Surjective function|surjectively]] (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and ''continuously'', so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.&lt;br /&gt;
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几何物体 x 的直观尺寸概念就是一个物体需要多少个独立参数才能找到一个独特的点。但是，任何由两个参数指定的点都可以由一个参数指定，因为实际平面的基数等于实际行的基数(这可以通过一个参数看到，该参数涉及交织两个数字的数字以产生一个编码相同信息的单个数字)。皮亚诺曲线的例子表明，一个人甚至可以完美和连续地映射实际线到真正的平面(把一个实数转换成一对实数，这样所有的数对都被覆盖)，由此一维物体完全填充了一个高维物体。&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called [[Lebesgue covering dimension]], explains why. This dimension is ''n'' if, in every covering of ''X'' by small open balls, there is at least one point where ''n''&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;''n''&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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Every space filling curve hits some points multiple times, and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is n if, in every covering of X by small open balls, there is at least one point where n&amp;amp;nbsp;+&amp;amp;nbsp;1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension&amp;amp;nbsp;n&amp;amp;nbsp;=&amp;amp;nbsp;1.&lt;br /&gt;
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每条空间填充曲线都会多次撞击某些点，且不存在连续的倒数。将两个维度以连续和连续可逆的方式映射到一个维度是不可能的。拓扑维度，也被称为拓朴维数，解释了为什么。这个维度是 n，如果在 x 的每个小开球覆盖中，至少有一个点 n + 1个球重叠。例如，当一个点覆盖一条具有短开区间的直线时，某些点必须被覆盖两次，给出维数 n 1。&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A [[fractal]] has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.&lt;br /&gt;
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但是，拓扑维度是对空间局部尺寸(点附近的尺寸)的一个非常粗略的度量。一条几乎是空间填充的曲线仍然可以有一维拓扑，即使它填充了一个区域的大部分面积。分形具有整数的拓扑维数，但就其所占空间的数量而言，它表现得像一个更高维的空间。&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the [[metric space|metric]]. Consider the number ''N''(''r'') of [[ball (mathematics)|balls]] of radius at most ''r'' required to cover ''X'' completely. When ''r'' is very small, ''N''(''r'') grows polynomially with 1/''r''. For a sufficiently well-behaved  ''X'', the Hausdorff dimension is the unique number ''d'' such that N(''r'') grows as 1/''r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt;'' as ''r'' approaches zero. More precisely, this defines the [[Minkowski–Bouligand dimension|box-counting dimension]], which equals the Hausdorff dimension when the value ''d'' is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved  X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/r&amp;lt;sup&amp;gt;d&amp;lt;/sup&amp;gt; as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.&lt;br /&gt;
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豪斯多夫维数测量一个空间的局部大小时，会考虑到点之间距离的度量。考虑半径最大为 r 的球数 n (r) ，需要完全覆盖 x。当 r 很小时，n (r)以1 / r 增长多项式。对于一个表现足够好的 x，豪斯多夫维数是唯一的数 d，这样当 r 趋近于零时 n (r)增长为1 / r sup d / sup。更确切地说，这定义了盒子计数维度，当值 d 是不足以覆盖空间的增长率和过度充裕的增长率之间的关键边界时，它等于豪斯多夫维数。&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But [[Benoit Mandelbrot]] observed that [[fractal]]s, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:&lt;br /&gt;
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对于光滑的形状，或者有少量棱角的形状，传统几何和科学的形状，豪斯多夫维数是一个整数，与拓扑维度一致。但是伯努·曼德布洛特观察到分形---- 具有非整数豪斯多夫维数的集合---- 在自然界中随处可见。他观察到，我们周围大多数粗糙形状的理想化不是光滑的理想化形状，而是分形理想化形状:&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot;&amp;gt;{{cite book   | last = Mandelbrot   | first = Benoît   | authorlink = Benoit Mandelbrot   | title = The Fractal Geometry of Nature   | publisher = W. H. Freeman   | series = Lecture notes in mathematics 1358   | year = 1982   | doi =    | isbn = 0-7167-1186-9   | url-access = registration   | url = https://archive.org/details/fractalgeometryo00beno   }}&amp;lt;/ref&amp;gt;&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;云不是球体，山不是锥体，海岸线不是圆圈，树皮不平滑，闪电也不是直线运动。 &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and [[Minkowski–Bouligand dimension|box-counting dimension]] coincide. The [[packing dimension]] is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well documented exceptions where all these dimensions differ.&lt;br /&gt;
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对于自然界中出现的分形，豪斯多夫维数和盒计数维数是一致的。封装尺寸是另一个类似的概念，它给出了许多形状相同的值，但是在所有这些尺寸不同的情况下，有很好的文档说明的例外。&lt;br /&gt;
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==Formal definitions形式化定义==&lt;br /&gt;
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{{unreferenced section|date=March 2015}}&lt;br /&gt;
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===Hausdorff content豪斯多夫集===&lt;br /&gt;
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Let ''X'' be a [[metric space]]. If ''S'' ⊂ ''X'' and ''d'' ∈ [0, ∞), the ''d''-dimensional '''unlimited Hausdorff content''' of ''S'' is defined by&lt;br /&gt;
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Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by&lt;br /&gt;
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设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i&amp;gt;0\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 c h ^ d (s) :  inf  Bigl  sum i r i ^ d:  text { there is a cover of } s  text { by balls with radii } r i 0 Bigr } . / math&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the [[infimum]] of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of [[ball (mathematics)|ball]]s &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering ''S'' with ''r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each ''i''&amp;amp;nbsp;∈&amp;amp;nbsp;''I'' that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that [[infimum|inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞]].)&lt;br /&gt;
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In other words, &amp;lt;math&amp;gt;C_H^d(S)&amp;lt;/math&amp;gt; is the infimum of the set of numbers &amp;lt;math&amp;gt;\delta \geq 0&amp;lt;/math&amp;gt; such that there is some (indexed) collection of balls &amp;lt;math&amp;gt;\{B(x_i,r_i):i\in I\}&amp;lt;/math&amp;gt; covering S with r&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 for each i&amp;amp;nbsp;∈&amp;amp;nbsp;I that satisfies &amp;lt;math&amp;gt;\sum_{i\in I} r_i^d&amp;lt;\delta &amp;lt;/math&amp;gt;. (Here, we use the standard convention that inf&amp;amp;nbsp;Ø&amp;amp;nbsp;=&amp;amp;nbsp;∞.)&lt;br /&gt;
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换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定&lt;br /&gt;
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===Hausdorff measurement豪斯多夫分形测量===&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of ''S'', we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the ''d''-dimensional Hausdorff outer measure of ''S'' as&lt;br /&gt;
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The Hausdorff outer measure is different from the unbounded Hausdorf content in that rather than considering all possible coverings of S, we see what happens when the sizes of the balls go to zero. This is  for &amp;lt;math&amp;gt;d \geq 0 &amp;lt;/math&amp;gt;, we define the d-dimensional Hausdorff outer measure of S as&lt;br /&gt;
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豪斯多夫外测度不同于无界的豪斯多夫，因为我们不考虑 s 的所有可能，我们看到当球的大小为零时会发生什么。这是为了数学 d  geq 0 / math，我们定义了 s 的 d 维豪斯多夫Hausdorff 外测度为&lt;br /&gt;
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:&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \mathcal{H}^d(S):=\lim_{r \to 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii } 0 &amp;lt; r_i &amp;lt; r\Bigr\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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数学函数 h ^ d (s) : lim { r  to 0} inf  Bigl  sum i r i ^ d:  text {有一个{ s  text  by balls with radii }0 r i r  Bigr }的封面。 数学&lt;br /&gt;
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===Hausdorff dimension豪斯多夫维数===&lt;br /&gt;
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The '''Hausdorff dimension''' of ''X'' is defined by&lt;br /&gt;
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The Hausdorff dimension of X is defined by&lt;br /&gt;
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X 的豪斯多夫维数定义为&lt;br /&gt;
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:&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt;\dim_{\operatorname{H}}(X):=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.&amp;lt;/math&amp;gt;&lt;br /&gt;
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Math  operatorname { h }(x) :  inf  ge 0:  mathcal { h } ^ d (x)0} . / math&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(''X'') may be defined as the [[infimum]] of the set of ''d'' ∈ [0, ∞) such that the ''d''-dimensional [[Hausdorff measure]] of ''X'' is zero. This is the same as the supremum of the set of ''d''&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the ''d''-dimensional Hausdorff measure of ''X'' is infinite (except that when this latter set of numbers ''d'' is empty the Hausdorff dimension is zero).&lt;br /&gt;
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Equivalently, dim&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt;(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d&amp;amp;nbsp;∈&amp;amp;nbsp;[0,&amp;amp;nbsp;∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).&lt;br /&gt;
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等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。&lt;br /&gt;
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==Examples实例==&lt;br /&gt;
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[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.&amp;lt;ref name=ClaytonSCTPLS96/&amp;gt;]]&lt;br /&gt;
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Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]&lt;br /&gt;
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进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]&lt;br /&gt;
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* [[Countable set]]s have Hausdorff dimension 0.&amp;lt;ref name=&amp;quot;schleicher&amp;quot;&amp;gt;{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* The [[Euclidean space]] ℝ&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; has Hausdorff dimension ''n'', and the circle '''S'''&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt; has Hausdorff dimension 1.&amp;lt;ref name=&amp;quot;schleicher&amp;quot; /&amp;gt;&lt;br /&gt;
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* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt; For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3)&amp;amp;nbsp;≈&amp;amp;nbsp;0.63.&amp;lt;ref&amp;gt;{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&amp;lt;/ref&amp;gt; The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of&amp;amp;nbsp;1/2; this yields a Hausdorff dimension of ln(3)/ln(2)&amp;amp;nbsp;≈&amp;amp;nbsp;1.58.&amp;lt;ref name=CampbellAnnenberg15/&amp;gt; These Hausdorff dimensions are related to the &amp;quot;critical exponent&amp;quot; of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].&lt;br /&gt;
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* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.&lt;br /&gt;
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* The trajectory of [[Brownian motion]] in dimension 2 and above is conjectured to be Hausdorff dimension 2.&amp;lt;ref&amp;gt;{{cite book | last=Morters | first=Peres | title= Brownian Motion | publisher=[[Cambridge University Press]] | year=2010 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[image:Great Britain Hausdorff.svg|thumb|250px|Estimating the Hausdorff dimension of the [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|coast of Great Britain]]]]&lt;br /&gt;
&lt;br /&gt;
coast of Great Britain]]&lt;br /&gt;
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大不列颠海岸]&lt;br /&gt;
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* 刘易斯·弗赖伊·理查森[[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].&amp;lt;ref name=&amp;quot;mandelbrot&amp;quot; /&amp;gt;&lt;br /&gt;
*刘易斯·弗赖伊·理查森（Lewis Fry Richardson）已经通过豪斯多夫维数去测量了很多海岸线。它的结果涵盖从1.02的南非海岸线到1.25的大英帝国西海岸模型。&lt;br /&gt;
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==Properties of Hausdorff dimension==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
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=== Hausdorff dimension and inductive dimension ===&lt;br /&gt;
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Let ''X'' be an arbitrary [[Separable space|separable]] metric space. There is a [[topology|topological]] notion of [[inductive dimension]] for ''X'' which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(''X'').&lt;br /&gt;
&lt;br /&gt;
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dim&amp;lt;sub&amp;gt;ind&amp;lt;/sub&amp;gt;(X).&lt;br /&gt;
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设 x 是任意可分度量空间。对于 x 有一个递归定义的归纳维数拓扑概念。它总是一个整数(或 + ∞) ，并且表示 dim sub ind / sub (x)。&lt;br /&gt;
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'''Theorem'''. Suppose ''X'' is non-empty. Then &lt;br /&gt;
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Theorem. Suppose X is non-empty. Then &lt;br /&gt;
&lt;br /&gt;
定理：假设 x 是非空的。然后&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).数学&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
Moreover,&lt;br /&gt;
&lt;br /&gt;
此外,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(y) dim { operatorname { Haus }(y) dim { operatorname { ind }(x) ，/ math&lt;br /&gt;
&lt;br /&gt;
where ''Y'' ranges over metric spaces [[homeomorphic]] to ''X''. In other words, ''X'' and ''Y'' have the same underlying set of points and the metric ''d''&amp;lt;sub&amp;gt;''Y''&amp;lt;/sub&amp;gt; of ''Y'' is topologically equivalent to ''d''&amp;lt;sub&amp;gt;''X''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric d&amp;lt;sub&amp;gt;Y&amp;lt;/sub&amp;gt; of Y is topologically equivalent to d&amp;lt;sub&amp;gt;X&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
其中 y 是度量空间同胚到 x 的范围。换句话说，x 和 y 具有相同的基本点集，y 的度规 d 子 y / 子拓扑等价于 d 子 x / 子。&lt;br /&gt;
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&lt;br /&gt;
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These results were originally established by [[Edward Szpilrajn]] (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.{{full citation needed|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.&lt;br /&gt;
&lt;br /&gt;
这些结果最初是由 Edward Szpilrajn (1907-1976)建立的，例如，见 Hurewicz 和 Wallman，第七章。&lt;br /&gt;
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=== Hausdorff dimension and Minkowski dimension ===&lt;br /&gt;
&lt;br /&gt;
The [[Minkowski dimension]] is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of [[rational number|rational]] points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.&lt;br /&gt;
&lt;br /&gt;
闵可夫斯基维度与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，Minkowski 维数为1。还有一些紧集的 Minkowski 维数严格大于豪斯多夫维数。&lt;br /&gt;
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=== Hausdorff dimensions and Frostman measures ===&lt;br /&gt;
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If there is a [[measure (mathematics)|measure]] μ defined on [[Borel measure|Borel]] subsets of a metric space ''X'' such that ''μ''(''X'') &amp;gt; 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' holds for some constant ''s'' &amp;gt; 0 and for every ball ''B''(''x'', ''r'') in ''X'', then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(''X'') ≥ ''s''. A partial converse is provided by [[Frostman's lemma]].{{citation needed|date=March 2015}}&amp;lt;ref&amp;gt;This Wikipedia article also discusses further useful characterizations of the Hausdorff dimension.{{clarify|date=March 2015}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) &amp;gt; 0 and μ(B(x, r)) ≤ r&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; holds for some constant s &amp;gt; 0 and for every ball B(x, r) in X, then dim&amp;lt;sub&amp;gt;Haus&amp;lt;/sub&amp;gt;(X) ≥ s. A partial converse is provided by Frostman's lemma.&lt;br /&gt;
&lt;br /&gt;
如果在度量空间 x 的 Borel 子集上定义一个测度，使得(x)0和(b (x，r))≤ rsup s / sup 对于某个常数 s0和 x 中的每个球 b (x，r)成立，则 dim sub Haus / sub (x)≥ s。 部分逆向由霜人引理提供。&lt;br /&gt;
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=== Behaviour under unions and products ===&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;X=\bigcup_{i\in I}X_i&amp;lt;/math&amp;gt; is a finite or countable union, then&lt;br /&gt;
&lt;br /&gt;
如果 math x x i / math 是一个有限或可数的联合，则&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x) sup { i }{ operatorname { Haus }(xi) . / math&lt;br /&gt;
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&lt;br /&gt;
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This can be verified directly from the definition.&lt;br /&gt;
&lt;br /&gt;
This can be verified directly from the definition.&lt;br /&gt;
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这可以直接从定义中验证。&lt;br /&gt;
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If ''X'' and ''Y'' are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&amp;lt;ref&amp;gt;{{cite journal |author=Marstrand, J. M. |title=The dimension of Cartesian product sets |journal=Proc. Cambridge Philos. Soc. |volume=50 |issue=3 |pages=198–202 |year=1954 |doi=10.1017/S0305004100029236 |bibcode = 1954PCPS...50..198M }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies&lt;br /&gt;
&lt;br /&gt;
如果 x 和 y 是非空度量空间，那么它们产品的豪斯多夫维数满足&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(x 乘以 y) ge  dim { operatorname { Haus }(x) +  dim { operatorname { Haus }(y) . / math&lt;br /&gt;
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&lt;br /&gt;
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This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1.&amp;lt;ref&amp;gt;{{cite book  | last = Falconer  | first = Kenneth J.  | title = Fractal geometry. Mathematical foundations and applications  | publisher = John Wiley &amp;amp; Sons, Inc., Hoboken, New Jersey  | year = 2003  | doi =   | isbn = }}&amp;lt;/ref&amp;gt; In the opposite direction, it is known that when ''X'' and ''Y'' are Borel subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt;, the Hausdorff dimension of ''X'' × ''Y'' is bounded from above by the Hausdorff dimension of ''X'' plus the [[packing dimension|upper packing dimension]] of ''Y''. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt;, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).&lt;br /&gt;
&lt;br /&gt;
这种不平等可以是严格的。有可能找到两个维数为0的集合，其乘积的维数为1。在相反的方向上，我们知道当 x 和 y 是 r sup n / sup 的 Borel 子集时，x y 的豪斯多夫维数从上面以 x 的豪斯多夫维数加上 y 的填充维数为界。Mattila (1995)讨论了这些事实。&lt;br /&gt;
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==Self-similar sets==&lt;br /&gt;
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{{refimprove section|date=March 2015}}&lt;br /&gt;
&lt;br /&gt;
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set ''E'' is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(''E'') = ''E'', although the exact definition is given below.&lt;br /&gt;
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Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.&lt;br /&gt;
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许多由自相似条件定义的集合具有可以显式确定的维数。粗略地说，集合 e 是自相似的，如果它是集值变换的不动点，即(e) e，尽管下面给出了确切的定义。&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;'''Theorem'''. Suppose&lt;br /&gt;
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&amp;lt;blockquote&amp;gt;Theorem. Suppose&lt;br /&gt;
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块引定理。假设&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Math  psi i:  mathbf { r } ^ n  right tarrow  mathbf { r } ^ n， quad i 1， ldots，m / math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
are [[Contraction mapping|contractive]] mappings on '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with contraction constant ''r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt;'' &amp;lt; 1. Then there is a unique ''non-empty'' compact set ''A'' such that&lt;br /&gt;
&lt;br /&gt;
are contractive mappings on R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with contraction constant r&amp;lt;sub&amp;gt;j&amp;lt;/sub&amp;gt; &amp;lt; 1. Then there is a unique non-empty compact set A such that&lt;br /&gt;
&lt;br /&gt;
Rsup n / sup 上的压缩常数 r 子 j / 子1的压缩映射。然后有一个唯一的非空紧集&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; A = \bigcup_{i=1}^m \psi_i (A). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
数学 a  bigcup { i 1} ^ m  psi i (a)。数学&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
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/ blockquote&lt;br /&gt;
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The theorem follows from [[Stefan Banach]]'s [[Contractive mapping theorem|contractive mapping fixed point theorem]] applied to the complete metric space of non-empty compact subsets of '''R'''&amp;lt;sup&amp;gt;''n''&amp;lt;/sup&amp;gt; with the [[Hausdorff distance]].&amp;lt;ref&amp;gt;{{cite book |author=Falconer, K. J. |title=The Geometry of Fractal Sets |publisher=Cambridge University Press |location=Cambridge, UK |year=1985 |isbn=0-521-25694-1 |chapter=Theorem 8.3}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of R&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; with the Hausdorff distance.&lt;br /&gt;
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这个定理来源于 Stefan Banach 的压缩映射不动点定理，该定理应用于 r sup n / sup 的非空紧子集的完备空间豪斯多夫距离。&lt;br /&gt;
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===The open set condition开集条件===&lt;br /&gt;
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To determine the dimension of the self-similar set ''A'' (in certain cases), we need a technical condition called the ''open set condition'' (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
为了确定自相似集 a 的维数(在某些情况下) ，我们需要一个称为开集条件(OSC)的技术条件。&lt;br /&gt;
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There is a relatively compact open set ''V'' such that&lt;br /&gt;
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There is a relatively compact open set V such that&lt;br /&gt;
&lt;br /&gt;
有一个相对紧的开集 v&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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:&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \bigcup_{i=1}^m\psi_i (V) \subseteq V, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学大杯{ i } ^ m  psi (v) subseteq v，/ math&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
where the sets in union on the left are pairwise [[disjoint sets|disjoint]].&lt;br /&gt;
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where the sets in union on the left are pairwise disjoint.&lt;br /&gt;
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左边的集合是成对不相交的。&lt;br /&gt;
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The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt;(''V'') do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
The open set condition is a separation condition that ensures the images ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;(V) do not overlap &amp;quot;too much&amp;quot;.&lt;br /&gt;
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开集条件是保证图像子 i / 子(v)不重叠“太多”的分离条件。&lt;br /&gt;
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&lt;br /&gt;
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'''Theorem'''. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an [[isometry]] and a [[dilation (metric space)|dilation]] around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is ''s'' where ''s'' is the unique solution of&amp;lt;ref&amp;gt;{{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Theorem. Suppose the open set condition holds and each ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
定理。假设开集条件成立，并且每个子 i / sub 是一个相似量，这是一个等距和围绕某一点的膨胀的合成。那么唯一的不动点是一个集合，它的豪斯多夫维数是 s，其中 s 是 s 的唯一解&lt;br /&gt;
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:&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;math&amp;gt; \sum_{i=1}^m r_i^s = 1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学1 ^ m r i ^ s 1。数学&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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The contraction coefficient of a similitude is the magnitude of the dilation.&lt;br /&gt;
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相似物的收缩系数就是膨胀的大小。&lt;br /&gt;
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We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three [[non-collinear points]] ''a''&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, ''a''&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane '''R'''&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;''i''&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around ''a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;''. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension ''s'' is the unique solution of&lt;br /&gt;
&lt;br /&gt;
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, a&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; in the plane R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and let ψ&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt; be the dilation of ratio 1/2 around a&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of&lt;br /&gt;
&lt;br /&gt;
我们可以使用这个定理来计算豪斯多夫维数谢尔宾斯基三角形的密封圈(或者有时候叫做 Sierpinski 垫圈)。考虑平面上的三个非共线点，一个子1 / 子，一个子2 / 子，一个子3 / 子。对应映射的唯一非空不动点是一个 Sierpinski 垫片，其维数 s 是对应映射的唯一解&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; \left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s+\left(\frac{1}{2}\right)^s = 3 \left(\frac{1}{2}\right)^s =1. &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学左(压缩{1}{2}右) ^ s + 左(压缩{1}右) ^ s + 左(压缩{1}右) ^ s 3左(压缩{1}右) ^ s 1。数学&lt;br /&gt;
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Taking [[natural logarithm]]s of both sides of the above equation, we can solve for ''s'', that is: ''s'' = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set ''E'' which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
Taking natural logarithms of both sides of the above equation, we can solve for s, that is: s = ln(3)/ln(2).  The Sierpinski gasket is self-similar and satisfies the OSC. In general a set E which is a fixed point of a mapping&lt;br /&gt;
&lt;br /&gt;
取上述方程两边的自然对数，我们可以求出 s，即: s ln (3) / ln (2)。该密封垫具有自相似性，满足 OSC 要求。一般来说，集合 e 是一个映射的不动点&lt;br /&gt;
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: &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 &amp;lt;math&amp;gt; A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 a 映射 / 压缩 / 压缩 / 压缩&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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is self-similar if and only if the intersections&lt;br /&gt;
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是自相似的当且仅当&lt;br /&gt;
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:&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; H^s\left(\psi_i(E) \cap \psi_j(E)\right) =0, &amp;lt;/math&amp;gt;&lt;br /&gt;
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数学 h ^ s 左( psi i (e) cap  psi j (e)右)0，/ math&lt;br /&gt;
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where ''s'' is the Hausdorff dimension of ''E'' and ''H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt;'' denotes [[Hausdorff measure]]. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
where s is the Hausdorff dimension of E and H&amp;lt;sup&amp;gt;s&amp;lt;/sup&amp;gt; denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:&lt;br /&gt;
&lt;br /&gt;
其中 s 是 e 的豪斯多夫维数，h sup s / sup 表示 Hausdorff 测度。对于 Sierpinski 垫圈(交叉点就是点)来说，这一点很明显，但更普遍的情况是:&lt;br /&gt;
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'''Theorem'''. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
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Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.&lt;br /&gt;
&lt;br /&gt;
定理。在与前一定理相同的条件下，其唯一不动点是自相似的。&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
* [[List of fractals by Hausdorff dimension]] Examples of deterministic fractals, random and natural fractals.&lt;br /&gt;
&lt;br /&gt;
* [[Assouad dimension]], another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls&lt;br /&gt;
&lt;br /&gt;
* [[Intrinsic dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Packing dimension]]&lt;br /&gt;
&lt;br /&gt;
* [[Fractal dimension]]&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
{{reflist}}&lt;br /&gt;
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==Further reading拓展阅读==&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Dodson |first1=M. Maurice |title=Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot |volume=72 |issue=1 |pages=305–347 |last2=Kristensen |first2=Simon |chapter=Hausdorff Dimension and Diophantine Approximation |date=June 12, 2003 |arxiv=math/0305399 |bibcode = 2003math......5399D |doi=10.1090/pspum/072.1/2112110|series=Proceedings of Symposia in Pure Mathematics |isbn=9780821836378 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite book |last1=Hurewicz |first1=Witold |authorlink1=Witold Hurewicz |last2=Wallman |first2=Henry |authorlink2=Henry Wallman |title=Dimension Theory |url=https://archive.org/details/in.ernet.dli.2015.84609 |publisher=Princeton University Press |year=1948 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=E. Szpilrajn |authorlink=Edward Marczewski |title=La dimension et la mesure |journal=Fundamenta Mathematicae |volume=28 |pages=81–9 |year=1937 }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal&lt;br /&gt;
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 | last1=Marstrand&lt;br /&gt;
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 | last1=Marstrand&lt;br /&gt;
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最后一站马斯特兰德&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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 | first1=J. M. | title=The dimension of cartesian product sets | year=1954 | journal=Proc. Cambridge Philos. Soc.&lt;br /&gt;
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首先1 j。笛卡儿积集的尺寸 | 1954年 | 期刊 Proc。Cambridge Philos.Soc.&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
&lt;br /&gt;
 | volume=50&lt;br /&gt;
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第50卷&lt;br /&gt;
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 | issue=3&lt;br /&gt;
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 | issue=3&lt;br /&gt;
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第三期&lt;br /&gt;
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 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
 | pages=198–202&lt;br /&gt;
&lt;br /&gt;
第198-202页&lt;br /&gt;
&lt;br /&gt;
 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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 | doi=10.1017/S0305004100029236|bibcode = 1954PCPS...50..198M }}&lt;br /&gt;
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10.1017 / S0305004100029236 | bibcode 1954PCPS... 50. . 198 m }&lt;br /&gt;
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* {{Cite book&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
 | last1=Mattila&lt;br /&gt;
&lt;br /&gt;
最后1个 Mattila&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=[[Cambridge University Press]]&lt;br /&gt;
&lt;br /&gt;
 | first1=Pertti | author1-link=Pertti Mattila| title=Geometry of sets and measures in Euclidean spaces | publisher=Cambridge University Press&lt;br /&gt;
&lt;br /&gt;
| first1 Pertti | author1-link Pertti Mattila | title 欧几里德空间中集合和度量的几何 | 出版商剑桥大学出版社&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
 | isbn=978-0-521-65595-8 | year=1995}}&lt;br /&gt;
&lt;br /&gt;
| isbn 978-0-521-65595-8 | year 1995}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=A. S. Besicovitch |authorlink=A. S. Besicovitch |title=On Linear Sets of Points of Fractional Dimensions |journal=[[Mathematische Annalen]] |volume=101 |year=1929 | doi=10.1007/BF01454831| issue=1 |pages= 161–193}}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author1=A. S. Besicovitch |authorlink1=A. S. Besicovitch |author2=H. D. Ursell |authorlink2=H. D. Ursell |title=Sets of Fractional Dimensions |journal=Journal of the London Mathematical Society |volume=12 |year=1937 | issue=1 | doi=10.1112/jlms/s1-12.45.18  | pages=18–25 }}&amp;lt;br/&amp;gt;Several selections from this volume are reprinted in {{cite book |author=Edgar, Gerald A. |title=Classics on fractals |publisher=Addison-Wesley |location=Boston |year=1993 |isbn=0-201-58701-7}} See chapters 9,10,11&lt;br /&gt;
&lt;br /&gt;
* {{cite journal |author=F. Hausdorff |authorlink=F. Hausdorff |title=Dimension und äußeres Maß |journal=Mathematische Annalen |volume=79 |issue=1–2 |pages=157–179 |date=March 1919 |doi=10.1007/BF01457179|hdl=10338.dmlcz/100363 |url=http://dml.cz/bitstream/handle/10338.dmlcz/100363/CzechMathJ_09-1959-3_5.pdf }}&lt;br /&gt;
&lt;br /&gt;
* {{cite journal | last=Hutchinson | first=John E. | title=Fractals and self similarity | journal=Indiana Univ. Math. J. | volume=30 | year=1981 | pages=713–747 | doi=10.1512/iumj.1981.30.30055 | issue=5 | doi-access=free }}&lt;br /&gt;
&lt;br /&gt;
*{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_dimension Hausdorff dimension] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
&lt;br /&gt;
* [https://www.encyclopediaofmath.org/index.php/Hausdorff_measure Hausdorff measure] at [https://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]&lt;br /&gt;
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{{DEFAULTSORT:Hausdorff Dimension}}&lt;br /&gt;
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[[Category:Fractals]]&lt;br /&gt;
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Category:Fractals&lt;br /&gt;
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分类: 分形&lt;br /&gt;
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[[Category:Metric geometry]]&lt;br /&gt;
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Category:Metric geometry&lt;br /&gt;
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分类: 米制几何&lt;br /&gt;
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[[Category:Dimension theory]]&lt;br /&gt;
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Category:Dimension theory&lt;br /&gt;
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范畴: 维度理论&lt;br /&gt;
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&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Hausdorff dimension]]. Its edit history can be viewed at [[分形维数/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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		<title>人工生命</title>
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		<updated>2020-07-19T16:07:18Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* External links 外部链接 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
&lt;br /&gt;
Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{引文&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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2卡尔米科夫&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
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| first2 Vyacheslav l.&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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参考资料&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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参考资料&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
&lt;br /&gt;
外部链接&lt;br /&gt;
&lt;br /&gt;
*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10896</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10896"/>
		<updated>2020-07-19T16:05:41Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* See also 另请参阅 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
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[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
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Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
参考资料&lt;br /&gt;
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&amp;lt;!-- Format copied from the page on AI:&lt;br /&gt;
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&amp;lt;!-- Format copied from the page on AI:&lt;br /&gt;
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! -- 从 AI 页面复制的格式:&lt;br /&gt;
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  See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for a&lt;br /&gt;
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  See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for a&lt;br /&gt;
&lt;br /&gt;
参见《 http://en.wikipedia.org/wiki/wikipedia:footnotes&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
讨论不同的引用方法和如何产生&lt;br /&gt;
&lt;br /&gt;
  footnotes using the &amp;lt;ref&amp;gt;, &amp;lt;/ref&amp;gt; and  &amp;lt;reference /&amp;gt; tags&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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==External links==&lt;br /&gt;
&lt;br /&gt;
==External links 外部链接==&lt;br /&gt;
&lt;br /&gt;
外部链接&lt;br /&gt;
&lt;br /&gt;
*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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类别: 科学建模&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10895</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10895"/>
		<updated>2020-07-19T16:03:55Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* References */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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&lt;br /&gt;
|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10894</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10894"/>
		<updated>2020-07-19T16:01:26Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* See also */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
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&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
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&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
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&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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30em | &lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10893</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10893"/>
		<updated>2020-07-19T16:00:29Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Criticism 批评 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
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2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
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3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
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*细菌菌落优化&lt;br /&gt;
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*遗传算法&lt;br /&gt;
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*基因编程&lt;br /&gt;
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*群智能&lt;br /&gt;
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4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
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5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
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6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
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7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
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#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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30em | &lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10892</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10892"/>
		<updated>2020-07-19T15:58:55Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Criticism */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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生物理论学学报&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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第63卷&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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第1-19页&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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2015年&lt;br /&gt;
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 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
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 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
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25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
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7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10891</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10891"/>
		<updated>2020-07-19T15:57:18Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* History */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10889</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10889"/>
		<updated>2020-07-19T15:56:23Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Related subjects 相关主题 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
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[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
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Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
&lt;br /&gt;
*遗传算法&lt;br /&gt;
&lt;br /&gt;
*基因编程&lt;br /&gt;
&lt;br /&gt;
*群智能&lt;br /&gt;
&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Webots}}&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
参考资料&lt;br /&gt;
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&amp;lt;!-- Format copied from the page on AI:&lt;br /&gt;
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  See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for a&lt;br /&gt;
&lt;br /&gt;
参见《 http://en.wikipedia.org/wiki/wikipedia:footnotes&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
讨论不同的引用方法和如何产生&lt;br /&gt;
&lt;br /&gt;
  footnotes using the &amp;lt;ref&amp;gt;, &amp;lt;/ref&amp;gt; and  &amp;lt;reference /&amp;gt; tags&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10887</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10887"/>
		<updated>2020-07-19T15:55:05Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Related subjects */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects 相关主题 ==&lt;br /&gt;
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1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
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#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10886</id>
		<title>人工生命</title>
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		<updated>2020-07-19T15:54:23Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Open problems 开放性问题 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
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[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects ==&lt;br /&gt;
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== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
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7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10885</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10885"/>
		<updated>2020-07-19T15:53:38Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）= */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）==&lt;br /&gt;
&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
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&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10881</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10881"/>
		<updated>2020-07-19T15:52:21Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）= */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{引文&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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2卡尔米科夫&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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生物理论学学报&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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第63卷&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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第1-19页&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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2015年&lt;br /&gt;
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 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
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 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
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10.1007 / s10441-015-9257-9&lt;br /&gt;
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 | pmid = 25980478&lt;br /&gt;
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 | pmid = 25980478&lt;br /&gt;
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25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10880</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10880"/>
		<updated>2020-07-19T15:51:28Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Biochemical-based (&amp;quot;wet&amp;quot;) */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
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&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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外部链接&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10879</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10879"/>
		<updated>2020-07-19T15:50:50Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Hardware-based (&amp;quot;hard&amp;quot;) */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
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&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
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[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
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基于硬件(“硬件”)&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
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Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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开放性问题&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
参考资料&lt;br /&gt;
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  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
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讨论不同的引用方法和如何产生&lt;br /&gt;
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  footnotes using the &amp;lt;ref&amp;gt;, &amp;lt;/ref&amp;gt; and  &amp;lt;reference /&amp;gt; tags&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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类别: 科学建模&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10878</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10878"/>
		<updated>2020-07-19T15:50:10Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Complex systems modeling复杂系统建模 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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&lt;br /&gt;
|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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&lt;br /&gt;
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&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10876</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10876"/>
		<updated>2020-07-19T15:49:26Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Complex systems modeling */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10873</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10873"/>
		<updated>2020-07-19T15:48:25Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Overview 概述 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
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&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
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&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10871</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10871"/>
		<updated>2020-07-19T15:46:00Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Open problems */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{引文&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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2卡尔米科夫&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
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| first2 Vyacheslav l.&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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生物理论学学报&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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第63卷&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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第1-19页&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10868</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10868"/>
		<updated>2020-07-19T15:42:21Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Techniques */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
*人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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外部链接&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10866</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10866"/>
		<updated>2020-07-19T15:40:38Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Philosophy 哲学讨论 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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*强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
*弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
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2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
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 | journal = PeerJ&lt;br /&gt;
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 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
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第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
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第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
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 | pmc = 4451025&lt;br /&gt;
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4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
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} / ref &lt;br /&gt;
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黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
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复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
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[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
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Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
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==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
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基于硬件(“硬件”)&lt;br /&gt;
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{{Further|Robot}}&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
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Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
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硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
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==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
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生物化学为基础(“湿”)&lt;br /&gt;
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{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
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Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems ==&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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开放性问题&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
参考资料&lt;br /&gt;
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  See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for a&lt;br /&gt;
&lt;br /&gt;
参见《 http://en.wikipedia.org/wiki/wikipedia:footnotes&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
  discussion of different citation methods and how to generate&lt;br /&gt;
&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10864</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10864"/>
		<updated>2020-07-19T15:36:24Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Techniques */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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&lt;br /&gt;
|-&lt;br /&gt;
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&lt;br /&gt;
| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
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Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems ==&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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开放性问题&lt;br /&gt;
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;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects ==&lt;br /&gt;
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== Related subjects 相关主题 ==&lt;br /&gt;
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1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
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#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
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#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
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7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10862</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10862"/>
		<updated>2020-07-19T15:33:57Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Software-based (&amp;quot;soft&amp;quot;) */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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生物理论学学报&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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第63卷&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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第1-19页&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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 | year = 2015&lt;br /&gt;
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2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
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 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
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 | doi = 10.7717/peerj.948&lt;br /&gt;
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10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
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 | pmid = 26038717&lt;br /&gt;
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26038717&lt;br /&gt;
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 | pmc = 4451025&lt;br /&gt;
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 | pmc = 4451025&lt;br /&gt;
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4451025&lt;br /&gt;
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 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
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&lt;br /&gt;
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Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems ==&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
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&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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==References==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10861</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10861"/>
		<updated>2020-07-19T15:32:42Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Overview 概述 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
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复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{{Citation&lt;br /&gt;
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{引文&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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2卡尔米科夫&lt;br /&gt;
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 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
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用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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 | journal = Acta Biotheoretica&lt;br /&gt;
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生物理论学学报&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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| volume = 63&lt;br /&gt;
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第63卷&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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 | issue = 2&lt;br /&gt;
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第二期&lt;br /&gt;
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 | pages = 1–19&lt;br /&gt;
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2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10859</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10859"/>
		<updated>2020-07-19T15:30:21Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Notable simulators */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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| Neurokernel神经核 ||Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014|| 进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
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基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
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基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
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30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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外部链接&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10858</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10858"/>
		<updated>2020-07-19T15:28:43Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Notable simulators */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名!!驱动源!!开始年份!!结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| [[Avida]]阿维达 || executable DNA || 1993 || ongoing进行中&lt;br /&gt;
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| Biogenesis生物起源 || executable DNA可执行 DNA || 2006 || ongoing进行中&lt;br /&gt;
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|Neurokernel神经核|Geppetto盖佩托（http://www.geppetto.org/）模拟平台||2014||进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] 生物|| neural net/simulated biochemistry神经网络 / 模拟生物化学 || 1996-2001 || Fandom still active to this day, some abortive attempts at new products狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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&lt;br /&gt;
====Program-based程序模拟====&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
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对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Bioethics}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Complex adaptive system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Darwin machine}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Emergence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Life simulation game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|List of emerging technologies}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Simulated reality}}&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Social simulation}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Soda Constructor}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Swarm intelligence}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Universal Darwinism}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
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}}&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10855</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10855"/>
		<updated>2020-07-19T15:22:05Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Notable simulators */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行DNA executable DNA || 1993 &lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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|生物起源 ||可执行 DNA | 2006 || 正在进行&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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| 格培多&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|ongoing&lt;br /&gt;
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正在进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
&lt;br /&gt;
| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
&lt;br /&gt;
生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net神经网络 || 2005 || ongoing 进行中&lt;br /&gt;
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| Darwinbots达尔文机器人 || 可执行的 DNAexecutable DNA || 2003 || ongoing进行中&lt;br /&gt;
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| DigiHive || executable DNA可执行 DNA || 2006 || ongoing 进行中&lt;br /&gt;
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| DOSE || executable DNA可执行 DNA || 2012 || ongoing正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map模糊认知地图 || 2009 || ongoing 进行中&lt;br /&gt;
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| [[Framsticks]] 荧光棒|| executable DNA可执行 DNA || 1996 || ongoing进行中&lt;br /&gt;
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| Geb盖布 || neural net神经网络 || 1997 || ongoing进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[OpenWorm]] || Geppetto盖佩托（http://www.geppetto.org/）模拟平台 || 2011 || ongoing进行中&lt;br /&gt;
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| [[Polyworld]]多元世界 || neural net神经网络 || 1990 || ongoing&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life原始生命 || executable DNA可执行 DNA || 1994 || 2003&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots脚本机器人 || executable DNA可执行 DNA || 2010 || ongoing 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]]技术圈 || modules模组 || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation计算机模拟)|Tierra]] 铁拉|| executable DNA可执行 DNA || 1991 || 2004&lt;br /&gt;
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|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]]3D虚拟生物进化 || neural net神经网络 || 2008 || NA&lt;br /&gt;
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|}&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
&lt;br /&gt;
====Program-based====&lt;br /&gt;
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&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
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3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
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4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
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5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
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6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10853</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10853"/>
		<updated>2020-07-19T14:53:05Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Notable simulators */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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{{Redirect-distinguish|ALife|Alife (disambiguation){{!}}Alife}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
&lt;br /&gt;
       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
&lt;br /&gt;
==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
&lt;br /&gt;
This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
&lt;br /&gt;
下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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{ | class“ wikitable sortable”&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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语言 / 社会模拟 | 1996 | 进行中&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
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可执行 DNA 1993年 正在进行中&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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生物起源 | 可执行 DNA | 2006 | | 正在进行&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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| 格培多&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|ongoing&lt;br /&gt;
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|ongoing&lt;br /&gt;
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正在进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
&lt;br /&gt;
生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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2005年正在进行中&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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可执行 DNA 2006年正在进行&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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可执行 DNA | 2012 | | 正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
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可执行 DNA | 1996 | 正在进行&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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1997年正在进行&lt;br /&gt;
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| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
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| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
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2011年3月11日&lt;br /&gt;
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| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
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| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
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多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
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| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
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| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
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| TechnoSphere || modules || 1995 ||&lt;br /&gt;
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1995年&lt;br /&gt;
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| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
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| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
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可执行 DNA | 1991 | 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
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| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
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3 d 虚拟生物进化神经网络&lt;br /&gt;
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|}&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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====Program-based====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based====&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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基于模块的&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
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====Parameter-based基于参数的模拟====&lt;br /&gt;
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基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based====&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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基于神经网络的&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
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第一个列夫 v。&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
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 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
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#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
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2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10851</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10851"/>
		<updated>2020-07-19T14:43:38Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Philosophy */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
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可执行 DNA 1993年 正在进行中&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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1997年正在进行&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
2011年3月11日&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
&lt;br /&gt;
多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
&lt;br /&gt;
| TechnoSphere || modules || 1995 ||&lt;br /&gt;
&lt;br /&gt;
1995年&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
可执行 DNA | 1991 | 2004&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
3 d 虚拟生物进化神经网络&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
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&lt;br /&gt;
====Program-based程序模拟====&lt;br /&gt;
&lt;br /&gt;
====Program-based====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based====&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
基于模块的&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
单个模块被添加到一个生物上。这些模块直接通过硬编码进入模拟(腿 a 型增加速度和新陈代谢) ，或者间接通过生物模块之间的紧急互动(腿 a 型上下移动频率为 x，与其他腿交互创造运动)来修改生物的行为和特征。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
====Neural net–based====&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
基于神经网络的&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
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Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
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基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
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2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems ==&lt;br /&gt;
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== Open problems 开放性问题==&lt;br /&gt;
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开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
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生命是如何从无生命中产生的？&lt;br /&gt;
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生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
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生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
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*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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;How is life related to mind, machines, and culture?&lt;br /&gt;
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How is life related to mind, machines, and culture?&lt;br /&gt;
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生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
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*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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*Establish ethical principles for artificial life.&lt;br /&gt;
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== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
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*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
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*Bacterial colony optimization&lt;br /&gt;
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#*[[Genetic algorithm]]&lt;br /&gt;
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*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:Logical_deterministic_individual-based_cellular_automata_model_of_interspecific_competition_for_a_single_limited_resource%E5%8D%95%E4%B8%AA%E6%9C%89%E9%99%90%E8%B5%84%E6%BA%90%E7%9A%84%E7%A7%8D%E9%97%B4%E7%AB%9E%E4%BA%89%E7%9A%84%E9%80%BB%E8%BE%91%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%9F%BA%E4%BA%8E%E4%B8%AA%E4%BD%93%E7%9A%84%E7%BB%86%E8%83%9E%E8%87%AA%E5%8A%A8%E6%9C%BA%E6%A8%A1%E5%9E%8B.png&amp;diff=10850</id>
		<title>文件:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource单个有限资源的种间竞争的逻辑确定性基于个体的细胞自动机模型.png</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:Logical_deterministic_individual-based_cellular_automata_model_of_interspecific_competition_for_a_single_limited_resource%E5%8D%95%E4%B8%AA%E6%9C%89%E9%99%90%E8%B5%84%E6%BA%90%E7%9A%84%E7%A7%8D%E9%97%B4%E7%AB%9E%E4%BA%89%E7%9A%84%E9%80%BB%E8%BE%91%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%9F%BA%E4%BA%8E%E4%B8%AA%E4%BD%93%E7%9A%84%E7%BB%86%E8%83%9E%E8%87%AA%E5%8A%A8%E6%9C%BA%E6%A8%A1%E5%9E%8B.png&amp;diff=10850"/>
		<updated>2020-07-19T14:29:49Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：&lt;/p&gt;
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		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10846</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10846"/>
		<updated>2020-07-19T14:11:38Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* External links */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
&lt;br /&gt;
       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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{ | class“ wikitable sortable”&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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语言 / 社会模拟 | 1996 | 进行中&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
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可执行 DNA 1993年 正在进行中&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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生物起源 | 可执行 DNA | 2006 | | 正在进行&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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| 格培多&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
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|ongoing&lt;br /&gt;
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|ongoing&lt;br /&gt;
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正在进行中&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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2005年正在进行中&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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可执行 DNA 2006年正在进行&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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可执行 DNA | 2012 | | 正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
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可执行 DNA | 1996 | 正在进行&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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1997年正在进行&lt;br /&gt;
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| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
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| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
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2011年3月11日&lt;br /&gt;
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| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
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| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
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多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
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| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
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| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
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| TechnoSphere || modules || 1995 ||&lt;br /&gt;
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1995年&lt;br /&gt;
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| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
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| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
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可执行 DNA | 1991 | 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
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| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
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3 d 虚拟生物进化神经网络&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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====Program-based====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
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====Module-based====&lt;br /&gt;
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====Module-based基于模块的模拟====&lt;br /&gt;
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基于模块的&lt;br /&gt;
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Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
单个模块被添加到一个生物上。这些模块直接通过硬编码进入模拟(腿 a 型增加速度和新陈代谢) ，或者间接通过生物模块之间的紧急互动(腿 a 型上下移动频率为 x，与其他腿交互创造运动)来修改生物的行为和特征。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
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基于参数的&lt;br /&gt;
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Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
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生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
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====Neural net–based====&lt;br /&gt;
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====Neural net–based基于神经网络的模拟====&lt;br /&gt;
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基于神经网络的&lt;br /&gt;
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These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
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这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
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===Complex systems modeling===&lt;br /&gt;
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===Complex systems modeling复杂系统建模===&lt;br /&gt;
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复杂的系统建模&lt;br /&gt;
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Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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 | last = Kalmykov&lt;br /&gt;
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最后的卡尔米科夫&lt;br /&gt;
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 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
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#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
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&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
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#*[[Genetic programming]]&lt;br /&gt;
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*Genetic programming&lt;br /&gt;
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#*[[Swarm intelligence]]&lt;br /&gt;
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*Swarm intelligence&lt;br /&gt;
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#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
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&amp;lt;!--*Simulated reality&lt;br /&gt;
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! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
&lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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{{Reflist}}&lt;br /&gt;
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==External links==&lt;br /&gt;
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==External links 外部链接==&lt;br /&gt;
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外部链接&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
	</entry>
	<entry>
		<id>https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10844</id>
		<title>人工生命</title>
		<link rel="alternate" type="text/html" href="https://wiki.swarma.org/index.php?title=%E4%BA%BA%E5%B7%A5%E7%94%9F%E5%91%BD&amp;diff=10844"/>
		<updated>2020-07-19T14:04:36Z</updated>

		<summary type="html">&lt;p&gt;Ilseyao2020：/* Referencescan参考资料 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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== Philosophy ==&lt;br /&gt;
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哲学讨论&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
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&lt;br /&gt;
| Geb || neural net || 1997 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Geb || neural net || 1997 || ongoing&lt;br /&gt;
&lt;br /&gt;
1997年正在进行&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
2011年3月11日&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
&lt;br /&gt;
多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
&lt;br /&gt;
| TechnoSphere || modules || 1995 ||&lt;br /&gt;
&lt;br /&gt;
1995年&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
可执行 DNA | 1991 | 2004&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
3 d 虚拟生物进化神经网络&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
====Program-based程序模拟====&lt;br /&gt;
&lt;br /&gt;
====Program-based====&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based====&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
基于模块的&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
单个模块被添加到一个生物上。这些模块直接通过硬编码进入模拟(腿 a 型增加速度和新陈代谢) ，或者间接通过生物模块之间的紧急互动(腿 a 型上下移动频率为 x，与其他腿交互创造运动)来修改生物的行为和特征。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
====Neural net–based====&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
基于神经网络的&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
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In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
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== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
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*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
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*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
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*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
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*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
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*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
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What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
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*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
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*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
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*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
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&lt;br /&gt;
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*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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*{{annotated link|Multi-agent system}}&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
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&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
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*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月&lt;br /&gt;
&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
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8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
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9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利，第1节&lt;br /&gt;
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10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
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11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
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12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
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13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
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14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
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15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
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16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
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17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
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18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
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19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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		<title>人工生命</title>
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		<summary type="html">&lt;p&gt;Ilseyao2020：/* Referencescan参考资料 */&lt;/p&gt;
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
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3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
&lt;br /&gt;
==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
&lt;br /&gt;
=== Techniques ===&lt;br /&gt;
&lt;br /&gt;
*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
&lt;br /&gt;
=== Notable simulators ===&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
&lt;br /&gt;
This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
&lt;br /&gt;
下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
&lt;br /&gt;
{ | class“ wikitable sortable”&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
&lt;br /&gt;
! Name !! Driven By !! Started !! Ended&lt;br /&gt;
&lt;br /&gt;
!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
&lt;br /&gt;
| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
&lt;br /&gt;
语言 / 社会模拟 | 1996 | 进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
&lt;br /&gt;
可执行 DNA 1993年 正在进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
&lt;br /&gt;
生物起源 | 可执行 DNA | 2006 | | 正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
&lt;br /&gt;
|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Neurokernel&lt;br /&gt;
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|Geppetto&lt;br /&gt;
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|Geppetto&lt;br /&gt;
&lt;br /&gt;
| 格培多&lt;br /&gt;
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|2014&lt;br /&gt;
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|2014&lt;br /&gt;
&lt;br /&gt;
|2014&lt;br /&gt;
&lt;br /&gt;
|ongoing&lt;br /&gt;
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|ongoing&lt;br /&gt;
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正在进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
&lt;br /&gt;
| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
&lt;br /&gt;
生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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2005年正在进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
&lt;br /&gt;
| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
&lt;br /&gt;
可执行 DNA 2006年正在进行&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
&lt;br /&gt;
| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
&lt;br /&gt;
可执行 DNA | 2012 | | 正在进行&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
&lt;br /&gt;
| EcoSim || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
&lt;br /&gt;
| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
&lt;br /&gt;
| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
&lt;br /&gt;
可执行 DNA | 1996 | 正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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1997年正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
&lt;br /&gt;
2011年3月11日&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
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| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
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多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
&lt;br /&gt;
原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
&lt;br /&gt;
| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
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| TechnoSphere || modules || 1995 ||&lt;br /&gt;
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1995年&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
&lt;br /&gt;
可执行 DNA | 1991 | 2004&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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|-&lt;br /&gt;
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| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
&lt;br /&gt;
3 d 虚拟生物进化神经网络&lt;br /&gt;
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|}&lt;br /&gt;
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|}&lt;br /&gt;
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|}&lt;br /&gt;
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&lt;br /&gt;
====Program-based程序模拟====&lt;br /&gt;
&lt;br /&gt;
====Program-based====&lt;br /&gt;
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&lt;br /&gt;
{{Further|programming game}}&lt;br /&gt;
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&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based====&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
基于模块的&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
单个模块被添加到一个生物上。这些模块直接通过硬编码进入模拟(腿 a 型增加速度和新陈代谢) ，或者间接通过生物模块之间的紧急互动(腿 a 型上下移动频率为 x，与其他腿交互创造运动)来修改生物的行为和特征。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
====Neural net–based====&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
基于神经网络的&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
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#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
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#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
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#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
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Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
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== History ==&lt;br /&gt;
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== History 历史==&lt;br /&gt;
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历史&lt;br /&gt;
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{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
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== Criticism ==&lt;br /&gt;
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== Criticism 批评==&lt;br /&gt;
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Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
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人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
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== See also ==&lt;br /&gt;
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== See also 另请参阅==&lt;br /&gt;
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参见&lt;br /&gt;
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{{Portal|Systems science}}&lt;br /&gt;
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人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
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*{{annotated link|Artificial consciousness}}&lt;br /&gt;
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*{{annotated link|Player Project}}&lt;br /&gt;
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==References==&lt;br /&gt;
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==Referencescan参考资料==&lt;br /&gt;
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1.     “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
2.     认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
3.    “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月。10。&lt;br /&gt;
4.    马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
5.     Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
6.     Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
7.     兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
8.     Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
9.     参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利。。，第1节&lt;br /&gt;
10.    参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
11.    雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
12.    Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
13.   跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
14.    Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
15.    弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
16.    “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
17.    “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
18.    “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
19.    Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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		<author><name>Ilseyao2020</name></author>
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&lt;div&gt;此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{short description|A field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations}}&lt;br /&gt;
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{{About|a field of research|artificially created life forms|Synthetic life|the journal|Artificial Life (journal)}}&lt;br /&gt;
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'''Artificial life''' (often abbreviated '''ALife''' or '''A-Life''') is a field of study wherein researchers examine [[system]]s related to natural [[life]], its processes, and its evolution, through the use of [[simulation]]s with [[computer models]], [[robotics]], and [[biochemistry]].&amp;lt;ref&amp;gt;{{cite web|url=http://dictionary.reference.com/browse/artificial%20life|title=Dictionary.com definition|accessdate=2007-01-19}}&amp;lt;/ref&amp;gt; The discipline was named by [[Christopher Langton]], an American theoretical biologist, in 1986.&amp;lt;ref&amp;gt;[https://books.google.com/books?id=-wt1aZrGXLYC&amp;amp;pg=PA37&amp;amp;cd=1#v=onepage The MIT Encyclopedia of the Cognitive Sciences], The MIT Press, p.37. {{ISBN|978-0-262-73144-7}}&amp;lt;/ref&amp;gt; In 1987 Langton organized the first conference on the field, in [[Los Alamos, New Mexico]].&amp;lt;ref&amp;gt;{{cite magazine |title=The Game Industry's Dr. Frankenstein |magazine=[[Next Generation (magazine)|Next Generation]]|issue=35|publisher=[[Imagine Media]] |date=November 1997|page=10}}&amp;lt;/ref&amp;gt; There are three main kinds of alife,&amp;lt;ref&amp;gt;{{cite web |url=http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|title=Artificial life: organization, adaptation and complexity from the bottom up|author=Mark A. Bedau |date=November 2003|accessdate=2007-01-19|publisher=Trends in Cognitive Sciences|archive-url=https://web.archive.org/web/20081202185445/http://www.reed.edu/~mab/publications/papers/BedauTICS03.pdf|archive-date=2008-12-02|url-status=dead}}&amp;lt;/ref&amp;gt; named for their approaches: ''soft'',&amp;lt;ref&amp;gt;{{cite book|title=Artificial Life Models in Software |author=Maciej Komosinski and [[Andrew Adamatzky]]|year=2009|publisher=Springer |location=New York|isbn=978-1-84882-284-9|url=https://www.springer.com/computer/mathematics/book/978-1-84882-284-9}}&amp;lt;/ref&amp;gt; from [[software]]; ''hard'',&amp;lt;ref&amp;gt;{{cite book |title=Artificial Life Models in Hardware|author=[[Andrew Adamatzky]] and Maciej Komosinski|year=2009|publisher=Springer|location=New York|isbn=978-1-84882-529-1 |url=https://www.springer.com/computer/hardware/book/978-1-84882-529-1}}&amp;lt;/ref&amp;gt; from [[computer hardware|hardware]]; and ''[[wet artificial life|wet]]'', from biochemistry. Artificial life researchers study traditional [[biology]] by trying to recreate aspects of biological phenomena.&amp;lt;ref&amp;gt;{{cite web|url=http://zooland.alife.org/|title=What is Artificial Life?|first=Christopher|last=Langton|accessdate=2007-01-19 |archiveurl=https://web.archive.org/web/20070117220840/http://zooland.alife.org/|archivedate=2007-01-17|url-status=dead}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;Aguilar, W., Santamaría-Bonfil, G., Froese, T., and Gershenson, C. (2014). The past, present, and future of artificial life. Frontiers in Robotics and AI, 1(8). https://dx.doi.org/10.3389/frobt.2014.00008&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987 Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.&lt;br /&gt;
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人工生命（经常被缩写为ALife或者A-Life）是在电脑系统中，通过仿真模型、机器技术和生物化学方式，模拟生命系统来研究生命的过程及其演变的领域。这个概念由美国理论生物学家克里斯托弗·兰顿Christopher Langton于1986年提出。1987年，兰顿第一次在新墨西哥州的洛斯阿拉莫斯 Los Alamos, New Mexico举行了该领域的第一次会议。&lt;br /&gt;
从研究方法的角度，可将人工生命研究分为三类：&lt;br /&gt;
1、软件模拟&lt;br /&gt;
2、硬件模拟&lt;br /&gt;
3、基于生物化学的研究&lt;br /&gt;
人工生命研究者尝试通过重现生命现象的各个方面来研究传统的生物学。&lt;br /&gt;
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[[File:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|250px|A [[Braitenberg vehicle]] simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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A [[Braitenberg vehicle simulation, programmed in breve, an artificial life simulator]]&lt;br /&gt;
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用breve来编程的人工生命模拟 Braitenberg仿真小车&lt;br /&gt;
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== Overview 概述 ==&lt;br /&gt;
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== Overview 概述==&lt;br /&gt;
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概述&lt;br /&gt;
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Artificial life studies the fundamental processes of [[living system]]s in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include [[Evolutionary algorithm|evolutionary dynamics]], [[Emergence|emergent properties of collective systems]], [[Biomimetics|biomimicry]], as well as related issues about the [[Philosophy of biology|philosophy of the nature of life]] and the use of lifelike properties in artistic works.&lt;br /&gt;
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Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems.  These topics are broad, but often include evolutionary dynamics, emergent properties of collective systems, biomimicry, as well as related issues about the philosophy of the nature of life and the use of lifelike properties in artistic works.&lt;br /&gt;
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人工生命研究人工环境中生命系统的基本过程，借此对定义此类系统的复杂信息进行更深入的理解。该研究角度涵盖深广，但通常会包括进化动力学、集体系统的涌现特性、仿生学、对生命本质哲学研究的相关内容，以及艺术作品中逼真的生物描绘。&lt;br /&gt;
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== Philosophy 哲学讨论==&lt;br /&gt;
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== Philosophy ==&lt;br /&gt;
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哲学讨论&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&amp;lt;ref&amp;gt;See Langton, C. G. 1992. [http://www.probelog.com/texts/Langton_al.pdf Artificial Life] {{webarchive |url=https://web.archive.org/web/20070311225322/http://www.probelog.com/texts/Langton_al.pdf |date=March 11, 2007 }}. Addison-Wesley. ., section 1&amp;lt;/ref&amp;gt;&lt;br /&gt;
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The modeling philosophy of artificial life strongly differs from traditional modeling by studying not only &amp;quot;life-as-we-know-it&amp;quot; but also &amp;quot;life-as-it-might-be&amp;quot;.&lt;br /&gt;
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人工生命的建模哲学，与传统的建模相比有显著差异，它不仅是研究我们“所知的生命”，而且去“研究生命可能的样子”。&lt;br /&gt;
人造生活的建模哲学与传统建模有很大不同，不仅研究“我们知道的生活”，而且研究“可能生存的生活”。&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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A traditional model of a biological system will focus on capturing its most important parameters. In contrast, an alife modeling approach will generally seek to decipher the most simple and general principles underlying life and implement them in a simulation. The simulation then offers the possibility to analyse new and different lifelike systems.&lt;br /&gt;
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传统的生物学模型可能会集中捕捉某生物最重要的决定因素，与之相比，人工生命模型建模方法想要破译隐藏在生命体中最简单、最通用的规则和原理，并在模拟中实现它们。仿真为分析各种新出现的似生系统提供了可能性。 &lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&amp;lt;ref&amp;gt;See Red'ko, V. G. 1999. [http://pespmc1.vub.ac.be/MATHME.html Mathematical Modeling of Evolution]. in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels). For the importance of ALife modeling from a cosmic perspective, see also Vidal, C. 2008.[https://arxiv.org/abs/0803.1087 The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis]. In Death And Anti-Death, ed. Charles Tandy, 6: Thirty Years After Kurt Gödel (1906-1978) p. 285-318. Ria University Press.)&amp;lt;/ref&amp;gt;&lt;br /&gt;
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Vladimir Georgievich Red'ko proposed to generalize this distinction to the modeling of any process, leading to the more general distinction of &amp;quot;processes-as-we-know-them&amp;quot; and &amp;quot;processes-as-they-could-be&amp;quot;.&lt;br /&gt;
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Vladimir Georgievich Red'ko建议将这一本质区别推广至任意过程的建模中，从而概括出“我们所知的过程”与“他们可能是的过程”更加广义的区别。&lt;br /&gt;
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At present, the commonly accepted [[Life#Definitions|definition of life]] does not consider any current alife simulations or [[software]] to be alive, and they do not constitute part of the evolutionary process of any [[ecosystem]]. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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At present, the commonly accepted definition of life does not consider any current alife simulations or software to be alive, and they do not constitute part of the evolutionary process of any ecosystem. However, different opinions about artificial life's potential have arisen:&lt;br /&gt;
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近年来，学界普遍认为，任何系统或者软件都不能真正实现生命仿真，他们并不能构成生态系统进化过程的一部分。然而，有关人工生命潜力出现了不同的观点：&lt;br /&gt;
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* The ''strong alife'' (cf. [[philosophy of artificial intelligence#Strong AI vs. weak AI|Strong AI]]) position states that &amp;quot;life is a process which can be abstracted away from any particular medium&amp;quot; ([[John von Neumann]]) {{citation needed|date=April 2018|reason=There seems to be no original source for this quote, and in fact if you restrict a web search to pages that don't contain the phrase artificial life, there are only a handful left.}}. Notably, [[Thomas S. Ray|Tom Ray]] declared that his program [[Tierra (computer simulation)|Tierra]] is not simulating life in a computer but synthesizing it.&amp;lt;ref&amp;gt;{{cite journal|last1=Ray|first1=Thomas|authorlink1=Thomas S. Ray|editor1-last=Taylor|editor1-first=C. C.|editor2-last=Farmer|editor2-first=J. D.|editor3-last=Rasmussen|editor3-first=S|title=An approach to the synthesis of life|journal=Artificial Life II, Santa Fe Institute Studies in the Sciences of Complexity|date=1991|volume=XI|pages=371–408|url=http://life.ou.edu/pubs/alife2/tierra.tex|language=English|quote=The intent of this work is to synthesize rather than simulate life.|archiveurl=https://web.archive.org/web/20150711051305/http://life.ou.edu/pubs/alife2/tierra.tex|archivedate=2015-07-11|accessdate=24 January 2016|url-status=live}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
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* The ''weak alife'' position denies the possibility of generating a &amp;quot;living process&amp;quot; outside of a chemical solution. Its researchers try instead to simulate life processes to understand the underlying mechanics of biological phenomena.&lt;br /&gt;
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       强人工生命模拟方向认为（参见强AI），“生命是可以从任何特定的介质抽离的过程”（约翰·冯·诺伊曼）[ 引证需要 ]。值得注意的是，汤姆·雷（Tom Ray）宣布，他的程序Tierra不是模拟在计算机中的生活，而是对其进行综合。&lt;br /&gt;
·       弱人工生命模拟方向否认在化学溶液之外存在“活过程”的可能，研究人员转而尝试模拟生命过程，以了解生物现象的潜在机理。&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)软件模拟人工生命==&lt;br /&gt;
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==Software-based (&amp;quot;soft&amp;quot;)==&lt;br /&gt;
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软件模拟人工生命&lt;br /&gt;
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=== Techniques 技术===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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=== Techniques ===&lt;br /&gt;
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*[[cellular automaton|Cellular automata]] were used in the early days of artificial life, and are still often used for ease of [[scalability]] and [[parallelization]].  Alife and cellular automata share a closely tied history.&lt;br /&gt;
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*[[Artificial neural network]]s are sometimes used to model the brain of an agent.  Although traditionally more of an [[artificial intelligence]] technique, neural nets can be important for simulating [[population dynamics]] of organisms that can ''learn''.  The symbiosis between learning and evolution is central to theories about the development of instincts in organisms with higher neurological complexity, as in, for instance, the [[Baldwin effect]].&lt;br /&gt;
    元胞自动机最早用于人工智能研究，至今仍常用于简化可扩展性和并行化的研究。人工生命与细胞自动机在早期有着相当紧密的联系。&lt;br /&gt;
·       人工神经网络有时被用来代替大脑建模。尽管传统上它更多地是一种人工智能技术，但是神经网络对于模拟可以学习的生物的种群动态非常重要。学习与进化之间的共生关系是对具有更高神经系统复杂性的生物（例如鲍德温效应）本能发展研究的核心。&lt;br /&gt;
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=== Notable simulators 著名的模拟器===&lt;br /&gt;
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=== Notable simulators ===&lt;br /&gt;
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This is a list of artificial life/[[digital organism]] simulators, organized by the method of creature definition.&lt;br /&gt;
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This is a list of artificial life/digital organism simulators, organized by the method of creature definition.&lt;br /&gt;
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下表列出了按照生物定义方法整理的人工生命/ 数字生物模拟器。&lt;br /&gt;
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{| class=&amp;quot;wikitable sortable&amp;quot;&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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! Name !! Driven By !! Started !! Ended&lt;br /&gt;
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!姓名! ！驱动源！开始年份! ！结束年份&lt;br /&gt;
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| ApeSDK（以前为Noble Ape）ApeSDK (formerly Noble Ape) || 语言/社会模拟language/social simulation || 1996 ||进行中 ongoing&lt;br /&gt;
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| ApeSDK (formerly Noble Ape) || language/social simulation || 1996 || ongoing&lt;br /&gt;
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| [[Avida]] || executable DNA || 1993 || ongoing&lt;br /&gt;
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| Avida 阿维达|| 可执行  DNA executable DNA || 1993 || 正在进行中ongoing&lt;br /&gt;
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可执行 DNA 1993年 正在进行中&lt;br /&gt;
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| Biogenesis || executable DNA || 2006 || ongoing&lt;br /&gt;
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| [[Creatures (artificial life program)|Creatures]] || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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| Creatures || neural net/simulated biochemistry || 1996-2001 || Fandom still active to this day, some abortive attempts at new products&lt;br /&gt;
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生物 | 神经网络 / 模拟生物化学 | 1996-2001 | 狂热者一直活跃到今天，对新产品进行了一些失败的尝试&lt;br /&gt;
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| Critterding || neural net || 2005 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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| Darwinbots || executable DNA || 2003 || ongoing&lt;br /&gt;
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达尔文机器人可执行的 DNA 正在进行中&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DigiHive || executable DNA || 2006 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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| DOSE || executable DNA || 2012 || ongoing&lt;br /&gt;
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可执行 DNA | 2012 | | 正在进行&lt;br /&gt;
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| [[EcoSim]] || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim || Fuzzy Cognitive Map || 2009 || ongoing&lt;br /&gt;
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| EcoSim | | 模糊认知地图 | | 2009 | | 正在进行中&lt;br /&gt;
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| [[Framsticks]] || executable DNA || 1996 || ongoing&lt;br /&gt;
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| Framsticks || executable DNA || 1996 || ongoing&lt;br /&gt;
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可执行 DNA | 1996 | 正在进行&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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| Geb || neural net || 1997 || ongoing&lt;br /&gt;
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1997年正在进行&lt;br /&gt;
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| [[OpenWorm]] || Geppetto || 2011 || ongoing&lt;br /&gt;
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| OpenWorm || Geppetto || 2011 || ongoing&lt;br /&gt;
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2011年3月11日&lt;br /&gt;
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| [[Polyworld]] || neural net || 1990 || ongoing&lt;br /&gt;
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| Polyworld || neural net || 1990 || ongoing&lt;br /&gt;
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多元世界 | 神经网 | 1990 | | 正在进行&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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| Primordial Life || executable DNA || 1994 || 2003&lt;br /&gt;
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原始生命 | 可执行 DNA | 1994 | 2003&lt;br /&gt;
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| ScriptBots || executable DNA || 2010 || ongoing&lt;br /&gt;
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| ScriptBots | | 可执行 DNA | | 2010 | | | 持续&lt;br /&gt;
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| [[TechnoSphere]] || modules || 1995 ||&lt;br /&gt;
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| [[Tierra (computer simulation)|Tierra]] || executable DNA || 1991 || 2004&lt;br /&gt;
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| Tierra || executable DNA || 1991 || 2004&lt;br /&gt;
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| [[3D Virtual Creature Evolution]] || neural net || 2008 || NA&lt;br /&gt;
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| 3D Virtual Creature Evolution || neural net || 2008 || NA&lt;br /&gt;
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3 d 虚拟生物进化神经网络&lt;br /&gt;
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====Program-based程序模拟====&lt;br /&gt;
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====Program-based====&lt;br /&gt;
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{{Further|programming game}}&lt;br /&gt;
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Program-based simulations contain organisms with a complex DNA language, usually [[Turing complete]].  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing [[self-replication]]. Mutations are generally implemented as random changes to the code. Use of [[cellular automata]] is common but not required. Another example could be an [[artificial intelligence]] and [[Multi-agent system|multi-agent system/program]].&lt;br /&gt;
&lt;br /&gt;
Program-based simulations contain organisms with a complex DNA language, usually Turing complete.  This language is more often in the form of a computer program than actual biological DNA.  Assembly derivatives are the most common languages used. An organism &amp;quot;lives&amp;quot; when its code is executed, and there are usually various methods allowing self-replication. Mutations are generally implemented as random changes to the code. Use of cellular automata is common but not required. Another example could be an artificial intelligence and multi-agent system/program.&lt;br /&gt;
&lt;br /&gt;
基于程序的模拟包含具有复杂DNA语言（通常为图灵完整）的生物。这种语言通常是计算机程序的形式，而不是实际的生物DNA。汇编派生词是最常用的语言。生物体在执行其代码时会“存活”，通常有多种方法可以进行自我复制。变异通常是通过随机更改代码来实现的。元胞自动机是常见工具，但不是唯一的。也有人用人工智能和多线程系统/程序来进行研究。&lt;br /&gt;
&lt;br /&gt;
====Module-based====&lt;br /&gt;
&lt;br /&gt;
====Module-based基于模块的模拟====&lt;br /&gt;
&lt;br /&gt;
基于模块的&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
Individual modules are added to a creature.  These modules modify the creature's behaviors and characteristics either directly, by hard coding into the simulation (leg type A increases speed and metabolism), or indirectly, through the emergent interactions between a creature's modules (leg type A moves up and down with a frequency of X, which interacts with other legs to create motion).  Generally these are simulators which emphasize user creation and accessibility over mutation and evolution.&lt;br /&gt;
&lt;br /&gt;
单个模块被添加到一个生物上。这些模块直接通过硬编码进入模拟(腿 a 型增加速度和新陈代谢) ，或者间接通过生物模块之间的紧急互动(腿 a 型上下移动频率为 x，与其他腿交互创造运动)来修改生物的行为和特征。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
基于模块的模拟是将单个模块添加到一个生物中。这些模块或者通过硬编码模拟（例如腿类型A加快速度和新陈代谢）直接修改生物的行为和特征，或者通过生物模块之间的紧急交互作用间接地修改动物的行为和特征（例如A型腿以频率X上下移动，与其他腿部互动以产生运动）。一般来说，这些模拟器强调的是用户创造和可访问性，而不是突变和进化。&lt;br /&gt;
&lt;br /&gt;
====Parameter-based====&lt;br /&gt;
&lt;br /&gt;
====Parameter-based基于参数的模拟====&lt;br /&gt;
&lt;br /&gt;
基于参数的&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other ''finite'' parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
Organisms are generally constructed with pre-defined and fixed behaviors that are controlled by various parameters that mutate.  That is, each organism contains a collection of numbers or other finite parameters. Each parameter controls one or several aspects of an organism in a well-defined way.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
生物体通常是由一系列预先定义的固定行为来构建的，这些行为受各种变异参数控制。也就是说，每个生物体都是一个包含数字或其他有限参数的集合。每个参数都明确地控制生物体的一个或多个方面。&lt;br /&gt;
&lt;br /&gt;
====Neural net–based====&lt;br /&gt;
&lt;br /&gt;
====Neural net–based基于神经网络的模拟====&lt;br /&gt;
&lt;br /&gt;
基于神经网络的&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
These simulations have creatures that learn and grow using neural nets or a close derivative.  Emphasis is often, although not always, more on learning than on natural selection.&lt;br /&gt;
&lt;br /&gt;
这些模拟让生物通过神经网络或近似衍生物进行学习和成长。通常强调的是学习，而不是自然选择，尽管并不总是如此。&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling===&lt;br /&gt;
&lt;br /&gt;
===Complex systems modeling复杂系统建模===&lt;br /&gt;
&lt;br /&gt;
复杂的系统建模&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: [[black-box]] (phenomenological), [[White box (software engineering)|white-box]] (mechanistic, based on the [[first principles]]) and [[Grey box model|grey-box]] (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. Solution&amp;quot;&amp;gt;&lt;br /&gt;
&lt;br /&gt;
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{{Citation&lt;br /&gt;
&lt;br /&gt;
{引文&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
 | title = A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata&lt;br /&gt;
&lt;br /&gt;
用逻辑确定性细胞自动机解决生物多样性悖论&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
 | journal = Acta Biotheoretica&lt;br /&gt;
&lt;br /&gt;
生物理论学学报&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
| volume = 63&lt;br /&gt;
&lt;br /&gt;
第63卷&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
 | issue = 2&lt;br /&gt;
&lt;br /&gt;
第二期&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
 | pages = 1–19&lt;br /&gt;
&lt;br /&gt;
第1-19页&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.1007/s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
10.1007 / s10441-015-9257-9&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
 | pmid = 25980478&lt;br /&gt;
&lt;br /&gt;
25980478&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot;&amp;gt;{{Citation&lt;br /&gt;
&lt;br /&gt;
} / ref name&amp;quot;kalmykov lev v，kalmykov vyacheslav l. white-box model&amp;quot;{ Citation&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last = Kalmykov&lt;br /&gt;
&lt;br /&gt;
最后的卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
 | first = Lev V.&lt;br /&gt;
&lt;br /&gt;
第一个列夫 v。&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
 | last2 = Kalmykov&lt;br /&gt;
&lt;br /&gt;
2卡尔米科夫&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
 | first2 = Vyacheslav L.&lt;br /&gt;
&lt;br /&gt;
| first2 Vyacheslav l.&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
 | title = A white-box model of S-shaped and double S-shaped single-species population growth&lt;br /&gt;
&lt;br /&gt;
S 形和双 s 形单种群增长的白盒模型&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
 | journal = PeerJ&lt;br /&gt;
&lt;br /&gt;
2012年3月24日&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
 | volume = 3:e948&lt;br /&gt;
&lt;br /&gt;
第三卷，第948集&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
| pages = e948&lt;br /&gt;
&lt;br /&gt;
第九季，第48集&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
 | year = 2015&lt;br /&gt;
&lt;br /&gt;
2015年&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
 | doi = 10.7717/peerj.948&lt;br /&gt;
&lt;br /&gt;
10.7717 / peerj. 948&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
 | pmid = 26038717&lt;br /&gt;
&lt;br /&gt;
26038717&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
 | pmc = 4451025&lt;br /&gt;
&lt;br /&gt;
4451025&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&amp;lt;ref name=&amp;quot;Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
 }}&amp;lt;/ref&amp;gt; In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers  use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.&lt;br /&gt;
&lt;br /&gt;
} / ref &lt;br /&gt;
&lt;br /&gt;
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。&lt;br /&gt;
&lt;br /&gt;
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]&lt;br /&gt;
&lt;br /&gt;
Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource&lt;br /&gt;
&lt;br /&gt;
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Hardware-based (&amp;quot;hard&amp;quot;)硬件模拟（”硬“）===&lt;br /&gt;
&lt;br /&gt;
基于硬件(“硬件”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Robot}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of ''robots'', that is, [[automation|automatically]] guided [[machine]]s able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
Hardware-based artificial life mainly consist of robots, that is, automatically guided machines able to do tasks on their own.&lt;br /&gt;
&lt;br /&gt;
硬件模拟人工生命主要由机器人组成，即能够自动完成任务的自动引导机器。&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)==&lt;br /&gt;
&lt;br /&gt;
==Biochemical-based (&amp;quot;wet&amp;quot;)基于生物化学的研究（“湿的”）==&lt;br /&gt;
&lt;br /&gt;
生物化学为基础(“湿”)&lt;br /&gt;
&lt;br /&gt;
{{Further|Synthetic biology}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of [[synthetic biology]]. It involves e.g. the creation of [[synthetic DNA]]. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;[[wetware (brain)|wetware]]&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
Biochemical-based life is studied in the field of synthetic biology. It involves e.g. the creation of synthetic DNA. The term &amp;quot;wet&amp;quot; is an extension of the term &amp;quot;wetware&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
基于生化的人工生命研究，是在合成生物学领域研究。它涉及合成DNA的创建，“生化”是“湿件 ”的延伸。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new [[Synthetic biology#Synthetic life|synthetic]] (possibly [[Artificial life#Biochemical-based (&amp;quot;wet&amp;quot;)|artificial]]) form of [[wikt:viability|viable]] [[life]], a variant of the [[bacteria]] ''[[Escherichia coli]]'', by reducing the natural number of 64 [[codon]]s in the bacterial [[genome]] to 59 codons instead, in order to encode 20 [[amino acid]]s.&amp;lt;ref name=&amp;quot;NYT-20190515&amp;quot;&amp;gt;{{cite news |last=Zimmer |first=Carl |authorlink=Carl Zimmer |title=Scientists Created Bacteria With a Synthetic Genome. Is This Artificial Life? - In a milestone for synthetic biology, colonies of E. coli thrive with DNA constructed from scratch by humans, not nature. |url=https://www.nytimes.com/2019/05/15/science/synthetic-genome-bacteria.html |date=15 May 2019 |work=[[The New York Times]] |accessdate=16 May 2019 }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;NAT-20190515&amp;quot;&amp;gt;{{cite journal |author=Fredens, Julius |display-authors=et al. |title=Total synthesis of Escherichia coli with a recoded genome |date=15 May 2019 |journal=[[Nature (journal)|Nature]] |doi=10.1038/s41586-019-1192-5 |pmid=31092918 |pmc=7039709 |volume=569 |issue=7757 |pages=514–518 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 59 codons instead, in order to encode 20 amino acids.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2019年5月，研究人员在一个具有里程碑意义的报告中提出将细菌基因组中64个密码子的天然数量减少到59个密码子，并编入20 个氨基酸，创造了一种新的、可以生长的合成（可能是人工的）生命，一种大肠杆菌的变体。&lt;br /&gt;
&lt;br /&gt;
== Open problems ==&lt;br /&gt;
&lt;br /&gt;
== Open problems 开放性问题==&lt;br /&gt;
&lt;br /&gt;
开放性问题&lt;br /&gt;
&lt;br /&gt;
;How does life arise from the nonliving?&amp;lt;ref&amp;gt;{{cite web|url=http://libarynth.org/open_problems_in_alife|title=Libarynth|accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{cite web|url=http://authors.library.caltech.edu/13564/1/BEDal00.pdf|title=Caltech |accessdate=2015-05-11}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
How does life arise from the nonliving?&lt;br /&gt;
&lt;br /&gt;
生命是如何从无生命中产生的？&lt;br /&gt;
&lt;br /&gt;
生命是如何从非生命中产生的？&lt;br /&gt;
*在体外产生一种分子原生物。&lt;br /&gt;
*在计算机模拟中实现向生命的过渡。&lt;br /&gt;
*确定是否可以根本上存在独特的活组织。&lt;br /&gt;
*模拟整个生命周期中的单细胞生物。&lt;br /&gt;
*解释规则和符号是如何通过生命系统中的物理动力学生成的。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Generate a molecular proto-organism [[in vitro]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Achieve the transition to life in an [[artificial chemistry]] [[in silico]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine whether fundamentally novel living organizations can exist.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Simulate a [[unicellular organism]] over its entire life cycle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Explain how rules and symbols are generated from physical dynamics in living systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
What are the potentials and limits of living systems?&lt;br /&gt;
&lt;br /&gt;
生命系统的潜力和限制是什么？&lt;br /&gt;
确定生活的无限发展中不可避免的事情。&lt;br /&gt;
*确定从特定响应系统到通用响应系统的演进过渡的最低条件。&lt;br /&gt;
*创建一个正式框架，以综合各种规模的动态层次结构。&lt;br /&gt;
*确定操纵生物体和生态系统的进化后果的可预测性。&lt;br /&gt;
*为不断发展的系统发展一套有关信息处理、信息流和信息生成的理论。&lt;br /&gt;
&lt;br /&gt;
*Determine what is inevitable in the open-ended [[evolution of life]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine minimal conditions for evolutionary transitions from specific to generic response systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Create a formal framework for synthesizing dynamical hierarchies at all scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Develop a theory of [[information processing]], [[Information flow (information theory)|information flow]], and information generation for evolving systems.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
;How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
How is life related to mind, machines, and culture?&lt;br /&gt;
&lt;br /&gt;
生命是如何与思想、机器和文化联系起来的？&lt;br /&gt;
*演示人工生命系统中智能和思维的出现。&lt;br /&gt;
*评估机器对生命的下一个重大进化的影响。&lt;br /&gt;
*提供文化和生物进化之间相互作用的定量模型。&lt;br /&gt;
*建立人工生命伦理。&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Demonstrate the emergence of intelligence and mind in an artificial living system.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Evaluate the influence of machines on the next major evolutionary transition of life.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Provide a quantitative model of the interplay between cultural and biological evolution.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*Establish ethical principles for artificial life.&lt;br /&gt;
&lt;br /&gt;
== Related subjects ==&lt;br /&gt;
&lt;br /&gt;
== Related subjects 相关主题 ==&lt;br /&gt;
&lt;br /&gt;
1.    人工智能传统上是使用自上而下的方法，而人工生命通常是自下而上的。&lt;br /&gt;
2.    人工化学最初是生命界中抽象化学反应过程的一种方法。&lt;br /&gt;
3.    进化算法是弱生命原理应用于优化问题的实际应用。已经设计出许多优化算法，这些算法借鉴或密切反映了生命技术。主要区别在于通过解决问题的能力而不是寻找食物、繁殖或避免死亡的能力来明确定义agent的适用性。人们经常使用以下与进化算法密切相关的方法：&lt;br /&gt;
*蚁群优化&lt;br /&gt;
*细菌菌落优化&lt;br /&gt;
*遗传算法&lt;br /&gt;
*基因编程&lt;br /&gt;
*群智能&lt;br /&gt;
4.    多主体系统 –多主体系统是由环境中多个交互的智能主体组成的计算机化系统。&lt;br /&gt;
5.    进化艺术使用人工生命中的技术和方法来创造新的艺术形式。&lt;br /&gt;
6.    进化音乐也使用类似的技术，但其领域主要应用于音乐而非视觉艺术。&lt;br /&gt;
7.    生物产生和生命起源有时也采用人工生命的方法。&lt;br /&gt;
&lt;br /&gt;
#[[Artificial intelligence]] has traditionally used a [[Top-down and bottom-up design|top down]] approach, while alife generally works from the bottom up.&amp;lt;ref&amp;gt;{{cite web |url=http://lggwg.com/wolff/aicg99/stern.html |title=AI Beyond Computer Games |accessdate=2008-07-04 |archiveurl=https://web.archive.org/web/20080701040911/http://www.lggwg.com/wolff/aicg99/stern.html |archivedate=2008-07-01 |url-status=dead }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Artificial intelligence has traditionally used a top down approach, while alife generally works from the bottom up.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Artificial chemistry]] started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
Artificial chemistry started as a method within the alife community to abstract the processes of chemical reactions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary algorithm]]s are a practical application of the weak alife principle applied to [[optimization problem]]s.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death.{{Citation needed|date=August 2007}} The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
Evolutionary algorithms are a practical application of the weak alife principle applied to optimization problems.  Many optimization algorithms have been crafted which borrow from or closely mirror alife techniques. The primary difference lies in explicitly defining the fitness of an agent by its ability to solve a problem, instead of its ability to find food, reproduce, or avoid death. The following is a list of evolutionary algorithms closely related to and used in alife:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Ant colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Ant colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Bacterial colony optimization]]&lt;br /&gt;
&lt;br /&gt;
*Bacterial colony optimization&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic algorithm]]&lt;br /&gt;
&lt;br /&gt;
*Genetic algorithm&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Genetic programming]]&lt;br /&gt;
&lt;br /&gt;
*Genetic programming&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#*[[Swarm intelligence]]&lt;br /&gt;
&lt;br /&gt;
*Swarm intelligence&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Multi-agent system]] – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
Multi-agent system – A multi-agent system is a computerized system composed of multiple interacting intelligent agents within an environment.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary art]] uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary art uses techniques and methods from artificial life to create new forms of art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Evolutionary music]] uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
Evolutionary music uses similar techniques, but applied to music instead of visual art.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
#[[Abiogenesis]] and the origin of life sometimes employ alife [[methodology|methodologies]] as well.&lt;br /&gt;
&lt;br /&gt;
Abiogenesis and the origin of life sometimes employ alife methodologies as well.&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
== History 历史==&lt;br /&gt;
&lt;br /&gt;
历史&lt;br /&gt;
&lt;br /&gt;
{{Main|History of artificial life}}&lt;br /&gt;
Main article: History of artificial life&lt;br /&gt;
主要文章：人造生命史&lt;br /&gt;
&lt;br /&gt;
== Criticism ==&lt;br /&gt;
&lt;br /&gt;
== Criticism 批评==&lt;br /&gt;
&lt;br /&gt;
批评&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. [[John Maynard Smith]] criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&amp;lt;ref&amp;gt;Horgan, J. 1995. [http://www2.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm From Complexity to Perplexity]. Scientific American. p107&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Alife has had a controversial history. John Maynard Smith criticized certain artificial life work in 1994 as &amp;quot;fact-free science&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
人造生命产生之初，就伴随着争议。约翰·梅纳德·史密斯John Maynard Smith在1994年批评某些人工生命研究，称他们为“无事实的科学”。&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
== See also 另请参阅==&lt;br /&gt;
&lt;br /&gt;
参见&lt;br /&gt;
&lt;br /&gt;
{{Portal|Systems science}}&lt;br /&gt;
&lt;br /&gt;
人工意识  –认知科学领域&lt;br /&gt;
*人工智能的应用&lt;br /&gt;
*自主机器人&lt;br /&gt;
*生物伦理学&lt;br /&gt;
*杂的自适应系统&lt;br /&gt;
*达尔文机&lt;br /&gt;
*数字形态&lt;br /&gt;
*出现  -复杂系统中的现象，其中相互作用产生的效果无法从子系统直接预测&lt;br /&gt;
*人生模拟游戏&lt;br /&gt;
*新兴技术清单&lt;br /&gt;
*数学和理论生物学&lt;br /&gt;
*多代理系统&lt;br /&gt;
*人工智能  概述– 人工智能概述和主题指南&lt;br /&gt;
*玩家专案&lt;br /&gt;
*模拟现实&lt;br /&gt;
*社会模拟&lt;br /&gt;
*苏打水构造&lt;br /&gt;
*群智能&lt;br /&gt;
*合成生活&lt;br /&gt;
*普遍达尔文主义  –试图将达尔文进化论的应用扩展到其他领域&lt;br /&gt;
*韦伯茨&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{cmn|colwidth=30em|&lt;br /&gt;
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{{cmn|colwidth=30em|&lt;br /&gt;
&lt;br /&gt;
30em | &lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Artificial consciousness}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Applications of artificial intelligence}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Autonomous robot}}&lt;br /&gt;
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*{{annotated link|Bioethics}}&lt;br /&gt;
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*{{annotated link|Complex adaptive system}}&lt;br /&gt;
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*{{annotated link|Darwin machine}}&lt;br /&gt;
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*{{annotated link|Digital morphogenesis}}&lt;br /&gt;
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*{{annotated link|Emergence}}&lt;br /&gt;
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*{{annotated link|Life simulation game}}&lt;br /&gt;
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*{{annotated link|List of emerging technologies}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Mathematical and theoretical biology}}&lt;br /&gt;
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&lt;br /&gt;
*{{annotated link|Multi-agent system}}&lt;br /&gt;
&lt;br /&gt;
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*{{annotated link|Outline of artificial intelligence}}&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
*{{annotated link|Player Project}}&lt;br /&gt;
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*{{annotated link|Simulated reality}}&lt;br /&gt;
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*{{annotated link|Social simulation}}&lt;br /&gt;
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*{{annotated link|Soda Constructor}}&lt;br /&gt;
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*{{annotated link|Swarm intelligence}}&lt;br /&gt;
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*{{annotated link|Synthetic life}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*[[Simulated reality]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--*Simulated reality&lt;br /&gt;
&lt;br /&gt;
! -- * 模拟现实&lt;br /&gt;
&lt;br /&gt;
*[[Artificial consciousness]] Do not uncomment.  See talk page --&amp;gt;&lt;br /&gt;
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*{{annotated link|Universal Darwinism}}&lt;br /&gt;
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*{{annotated link|Webots}}&lt;br /&gt;
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}}&lt;br /&gt;
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==References==&lt;br /&gt;
&lt;br /&gt;
==Referencescan参考资料==&lt;br /&gt;
&lt;br /&gt;
1.    ^ “ Dictionary.com定义” 。检索2007-01-19。&lt;br /&gt;
2.    ^ 认知科学的MIT百科全书，MIT出版社，第37页。书号978-0-262-73144-7&lt;br /&gt;
3.    ^ “游戏产业的科学怪人博士”。下一代。第35号。想象媒体。1997年11月。10。&lt;br /&gt;
4.    ^ 马克·贝道（2003年11月）。“人工生活：自下而上的组织，适应和复杂性” （PDF）。认知科学的趋势。（原始内容存档于（PDF） 2008-12-02）。检索2007-01-19。&lt;br /&gt;
5.    ^ Maciej Komosinski和Andrew Adamatzky（2009）。软件中的人工生命模型。纽约：施普林格。书号 978-1-84882-284-9。&lt;br /&gt;
6.    ^ Andrew Adamatzky和Maciej Komosinski（2009）。硬件中的人工生命模型。纽约：施普林格。书号 978-1-84882-529-1。&lt;br /&gt;
7.    ^ 兰顿，克里斯托弗。“什么是人工生命？” 。（原始内容存档于2007-01-17）。检索2007-01-19。&lt;br /&gt;
8.    ^ Aguilar，W.，Santamaría-Bonfil，G.，Froese，T.，and Gershenson，C.（2014年）。人造生活的过去，现在和未来。机器人与人工智能前沿，1（8）。https://dx.doi.org/10.3389/frobt.2014.00008&lt;br /&gt;
9.    ^ 参见Langton，CG1992。《人造生命》， 存档于2007年 3月11日，在 Wayback Machine上。艾迪生-韦斯利。。，第1节&lt;br /&gt;
10.   ^ 参见Red'ko，VG1999。进化的数学模型。见：F. Heylighen，C。Joslyn和V. Turchin（编辑）：Principia Cybernetica网站（Principia Cybernetica，布鲁塞尔）。有关从宇宙角度看ALife建模的重要性，另请参见Vidal，C.2008。《科学模拟的未来：从人工生命到人工宇宙发生》。在《死亡与反死》中，编辑。查尔斯·坦迪（Charles Tandy），《 6：库尔特·哥德尔（KurtGödel）诞辰三十年》（1906-1978）285-318。里亚大学出版社。）&lt;br /&gt;
11.   ^ 雷，托马斯（1991）。泰勒，CC；农夫，法学博士；Rasmussen，S（编辑）。“一种综合生活的方法”。人工生命II，圣达菲研究所，复杂性科学研究。十一：371–408。（原始内容存档于2015-07-11）。于2016 年1月24日检索。这项工作的目的是合成而不是模拟生活。&lt;br /&gt;
12.   ^ Kalmykov，列弗五；Kalmykov，Vyacheslav L.（2015），“通过逻辑确定性细胞自动机解决生物多样性悖论的方法”，生物理论学报，63（2）：1–19，doi：10.1007 / s10441-015-9257-9，PMID 25980478 &lt;br /&gt;
13.   ^ 跳到：a b Kalmykov，列弗五世；Kalmykov，Vyacheslav L.（2015），“ S形和双S形单物种种群增长的白盒模型”，PeerJ，3：e948：e948，doi：10.7717 / peerj.948，PMC  4451025，PMID  26038717&lt;br /&gt;
14.   ^ Zimmer，Carl（2019年5月15日）。“科学家用合成的基因组创造了细菌。这是人工生命吗？-在合成生物学的一个里程碑中，大肠杆菌的菌落以人类而非自然的方式从头开始构建的DNA蓬勃发展。”。纽约时报。检索2019年5月16日。&lt;br /&gt;
15.   ^ 弗雷登斯，朱利叶斯等。（2019年5月15日）。“具有编码基因组的大肠杆菌的全面合成”。大自然。569：514–518。doi：10.1038 / s41586-019-1192-5。PMID  31092918 。检索2019年5月16日。&lt;br /&gt;
16.   ^ “ Libarynth” 。检索2015-05-11。&lt;br /&gt;
17.   ^ “ Caltech” （PDF）。检索2015-05-11。&lt;br /&gt;
18.   ^ “在计算机游戏之外的AI”。（原始内容存档于2008-07-01）。检索2008-07-04。&lt;br /&gt;
19.   ^ Horgan，J. 1995.从复杂到困惑。科学美国人。107&lt;br /&gt;
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*{{DMOZ|Computers/Artificial_Life}}&lt;br /&gt;
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*[http://alife.org/ International Society of Artificial Life]&lt;br /&gt;
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*[http://www.mitpressjournals.org/loi/artl ''Artificial Life''] journal, at MIT Press Journal&lt;br /&gt;
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*[http://www.envirtech.com/artificial-life-lab.html The Artificial Life Lab], a virtual environment lab&lt;br /&gt;
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{{Computer science}}&lt;br /&gt;
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{{DEFAULTSORT:Artificial Life}}&lt;br /&gt;
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[[Category:Artificial life| ]]&lt;br /&gt;
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&amp;lt;small&amp;gt;This page was moved from [[wikipedia:en:Artificial life]]. Its edit history can be viewed at [[人工生命/edithistory]]&amp;lt;/small&amp;gt;&amp;lt;/noinclude&amp;gt;&lt;br /&gt;
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[[Category:待整理页面]]&lt;/div&gt;</summary>
		<author><name>Ilseyao2020</name></author>
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