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Moved page from wikipedia:en:Edge of chaos (history)
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。
{{for|the computer game|Independence War 2: Edge of Chaos}}
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior.<ref>{{cite news|last1=Schwartz|first1=K.|title=On the Edge of Chaos: Where Creativity Flourishes|url=https://ww2.kqed.org/mindshift/2014/05/06/on-the-edge-of-chaos-where-creativity-flourishes/|publisher=KOED|date=2014}}</ref>
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior.
[文件: shish-kebab-skewer-60458640。 加州大学洛杉矶分校塞梅尔神经科学和人类行为研究所的精神病学和心理学教授罗伯特 · 比尔德博士说: “真正具有创造性的变化和巨大的转变就发生在混沌的边缘。
]]
]]
]]
The '''edge of chaos''' is a transition space between [[Orderliness|order]] and [[Randomness|disorder]] that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.<ref>{{cite web|last1=Complexity Labs|title=Edge of Chaos|url=http://complexitylabs.io/edge-of-chaos/.|website=Complexity Labs|accessdate=August 24, 2016}}</ref>
The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
混沌的边缘是有序和无序之间的过渡空间，这种过渡空间被假设存在于各种各样的系统中。这个过渡区域是一个有界的不稳定区域，在有序和无序之间产生持续的动态相互作用。
Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as [[ecology]],<ref>{{cite journal|last1=Ranjit Kumar Upadhyay|title=Dynamics of an ecological model living on the edge of chaos|journal=Applied Mathematics and Computation|date=2009|volume= 210| issue = 2|pages=455–464|doi=10.1016/j.amc.2009.01.006}}</ref> [[business management]],<ref>{{cite web|last1=Deragon|first1=Jay|title=Managing On The Edge Of Chaos|url=http://www.relationship-economy.com/2012/08/managing-on-the-edge-of-chaos/|website=Relationship Economy}}</ref> [[psychology]],<ref>{{cite book|last1=Lawler|first1=E.|last2=Thye|first2=S.|last3=Yoon|first3=J.|title=Order on the Edge of Chaos Social Psychology and the Problem of Social Order|date=2015|publisher=[[Cambridge University Press]]|isbn=9781107433977}}</ref> [[political science]], and other domains of the [[social science]]. [[Physicists]] have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=et.|first2=al.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J. Phys. Chem. A|date=2009|doi=10.1021/jp804420g|bibcode=2009JPCA..113...19W|volume=113|issue=1|pages=19–22|pmid=19072712}}</ref>
Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as ecology, business management, psychology, political science, and other domains of the social science. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.
尽管混沌边缘的概念是抽象的和不直观的，但它在生态学、商业管理、心理学、政治科学和其他社会科学领域有许多应用。物理学家已经证明，对混沌边缘的适应几乎发生在所有具有反馈的系统中。
== History ==
{{Unreferenced section|date=March 2017}}
The phrase ''edge of chaos'' was coined by [[mathematician]] [[Doyne Farmer]] to describe the transition phenomenon discovered by [[computer scientist]] [[Christopher Langton]]. The phrase originally refers to an area in the range of a [[Variable (programming)|variable]], λ (lambda), which was varied while examining the behavior of a [[cellular automaton]] (CA). As λ varied, the behavior of the CA went through a [[phase transition]] of behaviors. Langton found a small area conducive to produce CAs capable of [[universal computation]]. At around the same time [[physicist]] [[James P. Crutchfield]] and others used the phrase ''onset of chaos'' to describe more or less the same concept.
The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
混沌的边缘这个短语是由数学家 Doyne Farmer 创造的，用来描述由计算机科学家克里斯托弗·兰顿发现的转变现象。这个短语最初指的是变量(lambda)范围内的一个区域，在检查一个细胞自动机(CA)的行为时，这个区域是不同的。不同的 CA 行为都经历了行为的相变。Langton 发现了一个很小的区域，有利于产生具有通用计算能力的 ca。大约在同一时期，物理学家詹姆斯 · p · 克拉奇菲尔德和其他人使用混沌开始这个短语来描述或多或少相同的概念。
In the sciences in general, the phrase has come to refer to a metaphor that some [[physics|physical]], [[biology|biological]], [[economics|economic]] and [[sociology|social]] [[system]]s operate in a region between order and either complete [[randomness]] or [[chaos theory|chaos]], where the [[complexity]] is maximal. The generality and significance of the idea, however, has since been called into question by [[Melanie Mitchell]] and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
在一般的科学中，这个短语已经变成了一个比喻，一些物理的、生物的、经济的和社会的系统运行在一个介于有序和完全随机或混乱之间的区域，其中复杂性是最大的。然而，这个想法的普遍性和重要性从那时起就受到了梅勒妮 · 米切尔和其他人的质疑。这个短语也被工商界借用，有时用得不恰当，而且用在远远超出该词原有含义范围的情况下。
[[Stuart Kauffman]] has studied [[mathematical model]]s of [[evolution|evolving]] systems in which the rate of evolution is maximized near the edge of chaos.
Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.
斯图尔特 · 考夫曼研究了进化系统的数学模型，其中进化速率在混沌边缘附近达到最大值。
==Adaptation==
[[Adaptation]] plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment.<ref>{{cite book|last1=Strogatz|first1=Steven|title=Nonlinear dynamics and Chaos|date=1994|publisher=[[Westview Press]]}}</ref> The most important instruments for the [[adaptation]] are the [[adaptive systems|self-adjusting parameters]] inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid [[chaos theory|chaos]]. The name for this phenomenon is ''"Adaptation to the edge of chaos"''.
Adaptation plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment. The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".
适应对所有生物体和系统都起着至关重要的作用。它们都在不断地改变自己的内在属性，以便更好地适应当前的环境。自适应最重要的手段是许多自然系统固有的自我调节参数。具有自调整参数的系统的显著特征是具有避免混沌的能力。这种现象的名称是“适应混沌的边缘”。
Adaptation to the edge of chaos refers to the idea that many [[complex adaptive systems]] seem to intuitively evolve toward a regime near the boundary between chaos and order.<ref>{{cite book|last1=Kauffman|first1=S.A.|title=The Origins of Order Self-Organization and Selection in Evolution|date=1993|publisher=[[Oxford University Press]]|location=New York|isbn=9780195079517}}</ref> Physics has shown that edge of chaos is the optimal settings for control of a system.<ref>{{cite journal|last1=Pierre|first1=D.|last2=et.|first2=al.|title=A theory for adaptation and competition applied to logistic map dynamics|journal=Physica D|date=1994|volume=75|issue=1–3|pages=343–360|bibcode=1994PhyD...75..343P|doi=10.1016/0167-2789(94)90292-5}}</ref> It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.<ref>{{cite journal|last1=Langton|first1=C.A.|title=Computation at the edge of chaos|journal=Physica D|date=1990|volume=42|issue=1–3|pages=12|doi=10.1016/0167-2789(90)90064-v|bibcode=1990PhyD...42...12L|url=https://zenodo.org/record/1258375}}</ref>
Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.
适应混沌的边缘是指这样的想法，许多复杂的自适应系统似乎直观地进化到一个制度接近混沌和秩序之间的边界。物理学已经表明，混沌边缘是系统控制的最佳设置。它也是一个可选的设置，可以影响物理系统执行基本功能的计算能力。
Because of the importance of [[adaptation]] in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of [[cellular automata]] rules which optimize the performance evolving with a [[genetic algorithm]].<ref>{{cite journal|last1=Packard|first1=N.H.|title=Adaptation toward the edge of chaos|journal=Dynamic Patterns in Complex Systems|date=1988|pages=293–301}}</ref><ref>{{cite journal|last1=Mitchell|first1=M.|last2=Hraber|first2=P.|last3=Crutchfield|first3=J.|title=Revisiting the edge of chaos: Evolving cellular automata to perform computations|journal=Complex Systems|date=1993|volume=7|issue=2|pages=89–130|arxiv=adap-org/9303003|bibcode=1993adap.org..3003M}}</ref> Another example of this phenomenon is the [[self-organized criticality]] in [[avalanche]] and earthquake models.<ref>{{cite journal|last1=Bak|first1=P.|last2=Tang|first2=C.|last3=Wiesenfeld|first3=K.|title=Self-organized criticality|journal=Phys Rev A|date=1988|volume=38|issue=1|pages=364–374|doi=10.1103/PhysRevA.38.364|bibcode=1988PhRvA..38..364B}}</ref>
Because of the importance of adaptation in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.
由于适应在许多自然系统中的重要性，对混沌边缘的适应在许多科学研究中占有突出的地位。物理学家证明了元胞自动机规则种群对混沌和有序边界状态的适应性，该规则通过遗传算法优化性能演化。这种现象的另一个例子是雪崩和地震模型中的自组织临界性。
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.<ref>{{cite journal|last1=Melby|first1=P.|last2=et.|first2=al.|title=Adaptation to the edge of chaos in the self-adjusting logistic map.|journal=Phys. Rev. Lett.|date=2000|doi=10.1103/PhysRevLett.84.5991|arxiv=nlin/0007006|bibcode=2000PhRvL..84.5991M|volume=84|issue=26|pages=5991–5993|pmid=10991106}}</ref> Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.<ref>{{cite journal|last1=Bayam|first1=M.|last2=et.|first2=al.|title=Conserved quantities and adaptation to the edge of chaos|journal=Physical Review E|date=2006|volume=73|issue=5|pages=056210|doi=10.1103/PhysRevE.73.056210|bibcode=2006PhRvE..73e6210B}}</ref>
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos. Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.
混沌动力学最简单的模型是逻辑斯谛映射。自调整逻辑映射动力学表现出对混沌边缘的适应性。理论分析允许预测系统演化的边界附近窄参数区域的位置。
==See also==
* [[Self-organized criticality]]
==References==
{{Reflist}}
*{{cite journal|author=Christopher G. Langton|title=Computation at the edge of chaos|journal=Physica D|volume=42|pages=12|year=1990|url=http://www.romanpoet.org/223/langton.edgeofchaos.pdf|doi=10.1016/0167-2789(90)90064-V|bibcode=1990PhyD...42...12L}}
*{{cite book|author=J. P. Crutchfield and K. Young|chapter=Computation at the Onset of Chaos|title=Entropy, Complexity, and the Physics of Information|editor=W. Zurek|series=SFI Studies in the Sciences of Complexity, VIII|publisher=[[Addison-Wesley]]|location=Reading, Massachusetts|year=1990|pages=223–269|chapter-url=http://csc.ucdavis.edu/~cmg/papers/CompOnset.pdf}}
*{{cite journal | last1 = Mitchell | first1 = Melanie | last2 = Hraber | first2 = Peter T. | last3 = Crutchfield | first3 = James P. | year = 1993 | title = Revisiting the edge of chaos: Evolving cellular automata to perform computations | url = http://web.cecs.pdx.edu/~mm/rev-edge.pdf | journal = Complex Systems | volume = 7 | issue = | pages = 89–130 }}
* Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. ''[http://web.cecs.pdx.edu/~mm/dyn-comp-edge.pdf Dynamics, Computation, and the "Edge of Chaos": A Re-Examination]''
*''Origins of Order: Self-Organization and Selection in Evolution'' by Stuart Kauffman
* {{Cite journal|last1=Mora |first1=Thierry |last2=Bialek |first2=William |year= 2010|title=Are biological systems poised at criticality? |journal=Journal of Statistical Physics |volume=144 |issue=2 |pages=268–302 |arxiv= 1012.2242|doi=10.1007/s10955-011-0229-4 |bibcode=2011JSP...144..268M }}
== External links ==
* [http://bactra.org/notebooks/edge-of-chaos.html "The Edge of Chaos"] – a criticism of the idea's prevalence.
{{Chaos theory}}
[[Category:Chaos theory]]
Category:Chaos theory
范畴: 混沌理论
[[Category:Self-organization]]
Category:Self-organization
类别: 自我组织
<noinclude>
<small>This page was moved from [[wikipedia:en:Edge of chaos]]. Its edit history can be viewed at [[混沌边缘/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{for|the computer game|Independence War 2: Edge of Chaos}}
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior.<ref>{{cite news|last1=Schwartz|first1=K.|title=On the Edge of Chaos: Where Creativity Flourishes|url=https://ww2.kqed.org/mindshift/2014/05/06/on-the-edge-of-chaos-where-creativity-flourishes/|publisher=KOED|date=2014}}</ref>
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior.
[文件: shish-kebab-skewer-60458640。 加州大学洛杉矶分校塞梅尔神经科学和人类行为研究所的精神病学和心理学教授罗伯特 · 比尔德博士说: “真正具有创造性的变化和巨大的转变就发生在混沌的边缘。
]]
]]
]]
The '''edge of chaos''' is a transition space between [[Orderliness|order]] and [[Randomness|disorder]] that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.<ref>{{cite web|last1=Complexity Labs|title=Edge of Chaos|url=http://complexitylabs.io/edge-of-chaos/.|website=Complexity Labs|accessdate=August 24, 2016}}</ref>
The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
混沌的边缘是有序和无序之间的过渡空间，这种过渡空间被假设存在于各种各样的系统中。这个过渡区域是一个有界的不稳定区域，在有序和无序之间产生持续的动态相互作用。
Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as [[ecology]],<ref>{{cite journal|last1=Ranjit Kumar Upadhyay|title=Dynamics of an ecological model living on the edge of chaos|journal=Applied Mathematics and Computation|date=2009|volume= 210| issue = 2|pages=455–464|doi=10.1016/j.amc.2009.01.006}}</ref> [[business management]],<ref>{{cite web|last1=Deragon|first1=Jay|title=Managing On The Edge Of Chaos|url=http://www.relationship-economy.com/2012/08/managing-on-the-edge-of-chaos/|website=Relationship Economy}}</ref> [[psychology]],<ref>{{cite book|last1=Lawler|first1=E.|last2=Thye|first2=S.|last3=Yoon|first3=J.|title=Order on the Edge of Chaos Social Psychology and the Problem of Social Order|date=2015|publisher=[[Cambridge University Press]]|isbn=9781107433977}}</ref> [[political science]], and other domains of the [[social science]]. [[Physicists]] have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=et.|first2=al.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J. Phys. Chem. A|date=2009|doi=10.1021/jp804420g|bibcode=2009JPCA..113...19W|volume=113|issue=1|pages=19–22|pmid=19072712}}</ref>
Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as ecology, business management, psychology, political science, and other domains of the social science. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.
尽管混沌边缘的概念是抽象的和不直观的，但它在生态学、商业管理、心理学、政治科学和其他社会科学领域有许多应用。物理学家已经证明，对混沌边缘的适应几乎发生在所有具有反馈的系统中。
== History ==
{{Unreferenced section|date=March 2017}}
The phrase ''edge of chaos'' was coined by [[mathematician]] [[Doyne Farmer]] to describe the transition phenomenon discovered by [[computer scientist]] [[Christopher Langton]]. The phrase originally refers to an area in the range of a [[Variable (programming)|variable]], λ (lambda), which was varied while examining the behavior of a [[cellular automaton]] (CA). As λ varied, the behavior of the CA went through a [[phase transition]] of behaviors. Langton found a small area conducive to produce CAs capable of [[universal computation]]. At around the same time [[physicist]] [[James P. Crutchfield]] and others used the phrase ''onset of chaos'' to describe more or less the same concept.
The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
混沌的边缘这个短语是由数学家 Doyne Farmer 创造的，用来描述由计算机科学家克里斯托弗·兰顿发现的转变现象。这个短语最初指的是变量(lambda)范围内的一个区域，在检查一个细胞自动机(CA)的行为时，这个区域是不同的。不同的 CA 行为都经历了行为的相变。Langton 发现了一个很小的区域，有利于产生具有通用计算能力的 ca。大约在同一时期，物理学家詹姆斯 · p · 克拉奇菲尔德和其他人使用混沌开始这个短语来描述或多或少相同的概念。
In the sciences in general, the phrase has come to refer to a metaphor that some [[physics|physical]], [[biology|biological]], [[economics|economic]] and [[sociology|social]] [[system]]s operate in a region between order and either complete [[randomness]] or [[chaos theory|chaos]], where the [[complexity]] is maximal. The generality and significance of the idea, however, has since been called into question by [[Melanie Mitchell]] and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
在一般的科学中，这个短语已经变成了一个比喻，一些物理的、生物的、经济的和社会的系统运行在一个介于有序和完全随机或混乱之间的区域，其中复杂性是最大的。然而，这个想法的普遍性和重要性从那时起就受到了梅勒妮 · 米切尔和其他人的质疑。这个短语也被工商界借用，有时用得不恰当，而且用在远远超出该词原有含义范围的情况下。
[[Stuart Kauffman]] has studied [[mathematical model]]s of [[evolution|evolving]] systems in which the rate of evolution is maximized near the edge of chaos.
Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.
斯图尔特 · 考夫曼研究了进化系统的数学模型，其中进化速率在混沌边缘附近达到最大值。
==Adaptation==
[[Adaptation]] plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment.<ref>{{cite book|last1=Strogatz|first1=Steven|title=Nonlinear dynamics and Chaos|date=1994|publisher=[[Westview Press]]}}</ref> The most important instruments for the [[adaptation]] are the [[adaptive systems|self-adjusting parameters]] inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid [[chaos theory|chaos]]. The name for this phenomenon is ''"Adaptation to the edge of chaos"''.
Adaptation plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment. The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".
适应对所有生物体和系统都起着至关重要的作用。它们都在不断地改变自己的内在属性，以便更好地适应当前的环境。自适应最重要的手段是许多自然系统固有的自我调节参数。具有自调整参数的系统的显著特征是具有避免混沌的能力。这种现象的名称是“适应混沌的边缘”。
Adaptation to the edge of chaos refers to the idea that many [[complex adaptive systems]] seem to intuitively evolve toward a regime near the boundary between chaos and order.<ref>{{cite book|last1=Kauffman|first1=S.A.|title=The Origins of Order Self-Organization and Selection in Evolution|date=1993|publisher=[[Oxford University Press]]|location=New York|isbn=9780195079517}}</ref> Physics has shown that edge of chaos is the optimal settings for control of a system.<ref>{{cite journal|last1=Pierre|first1=D.|last2=et.|first2=al.|title=A theory for adaptation and competition applied to logistic map dynamics|journal=Physica D|date=1994|volume=75|issue=1–3|pages=343–360|bibcode=1994PhyD...75..343P|doi=10.1016/0167-2789(94)90292-5}}</ref> It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.<ref>{{cite journal|last1=Langton|first1=C.A.|title=Computation at the edge of chaos|journal=Physica D|date=1990|volume=42|issue=1–3|pages=12|doi=10.1016/0167-2789(90)90064-v|bibcode=1990PhyD...42...12L|url=https://zenodo.org/record/1258375}}</ref>
Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.
适应混沌的边缘是指这样的想法，许多复杂的自适应系统似乎直观地进化到一个制度接近混沌和秩序之间的边界。物理学已经表明，混沌边缘是系统控制的最佳设置。它也是一个可选的设置，可以影响物理系统执行基本功能的计算能力。
Because of the importance of [[adaptation]] in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of [[cellular automata]] rules which optimize the performance evolving with a [[genetic algorithm]].<ref>{{cite journal|last1=Packard|first1=N.H.|title=Adaptation toward the edge of chaos|journal=Dynamic Patterns in Complex Systems|date=1988|pages=293–301}}</ref><ref>{{cite journal|last1=Mitchell|first1=M.|last2=Hraber|first2=P.|last3=Crutchfield|first3=J.|title=Revisiting the edge of chaos: Evolving cellular automata to perform computations|journal=Complex Systems|date=1993|volume=7|issue=2|pages=89–130|arxiv=adap-org/9303003|bibcode=1993adap.org..3003M}}</ref> Another example of this phenomenon is the [[self-organized criticality]] in [[avalanche]] and earthquake models.<ref>{{cite journal|last1=Bak|first1=P.|last2=Tang|first2=C.|last3=Wiesenfeld|first3=K.|title=Self-organized criticality|journal=Phys Rev A|date=1988|volume=38|issue=1|pages=364–374|doi=10.1103/PhysRevA.38.364|bibcode=1988PhRvA..38..364B}}</ref>
Because of the importance of adaptation in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.
由于适应在许多自然系统中的重要性，对混沌边缘的适应在许多科学研究中占有突出的地位。物理学家证明了元胞自动机规则种群对混沌和有序边界状态的适应性，该规则通过遗传算法优化性能演化。这种现象的另一个例子是雪崩和地震模型中的自组织临界性。
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.<ref>{{cite journal|last1=Melby|first1=P.|last2=et.|first2=al.|title=Adaptation to the edge of chaos in the self-adjusting logistic map.|journal=Phys. Rev. Lett.|date=2000|doi=10.1103/PhysRevLett.84.5991|arxiv=nlin/0007006|bibcode=2000PhRvL..84.5991M|volume=84|issue=26|pages=5991–5993|pmid=10991106}}</ref> Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.<ref>{{cite journal|last1=Bayam|first1=M.|last2=et.|first2=al.|title=Conserved quantities and adaptation to the edge of chaos|journal=Physical Review E|date=2006|volume=73|issue=5|pages=056210|doi=10.1103/PhysRevE.73.056210|bibcode=2006PhRvE..73e6210B}}</ref>
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos. Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.
混沌动力学最简单的模型是逻辑斯谛映射。自调整逻辑映射动力学表现出对混沌边缘的适应性。理论分析允许预测系统演化的边界附近窄参数区域的位置。
==See also==
* [[Self-organized criticality]]
==References==
{{Reflist}}
*{{cite journal|author=Christopher G. Langton|title=Computation at the edge of chaos|journal=Physica D|volume=42|pages=12|year=1990|url=http://www.romanpoet.org/223/langton.edgeofchaos.pdf|doi=10.1016/0167-2789(90)90064-V|bibcode=1990PhyD...42...12L}}
*{{cite book|author=J. P. Crutchfield and K. Young|chapter=Computation at the Onset of Chaos|title=Entropy, Complexity, and the Physics of Information|editor=W. Zurek|series=SFI Studies in the Sciences of Complexity, VIII|publisher=[[Addison-Wesley]]|location=Reading, Massachusetts|year=1990|pages=223–269|chapter-url=http://csc.ucdavis.edu/~cmg/papers/CompOnset.pdf}}
*{{cite journal | last1 = Mitchell | first1 = Melanie | last2 = Hraber | first2 = Peter T. | last3 = Crutchfield | first3 = James P. | year = 1993 | title = Revisiting the edge of chaos: Evolving cellular automata to perform computations | url = http://web.cecs.pdx.edu/~mm/rev-edge.pdf | journal = Complex Systems | volume = 7 | issue = | pages = 89–130 }}
* Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. ''[http://web.cecs.pdx.edu/~mm/dyn-comp-edge.pdf Dynamics, Computation, and the "Edge of Chaos": A Re-Examination]''
*''Origins of Order: Self-Organization and Selection in Evolution'' by Stuart Kauffman
* {{Cite journal|last1=Mora |first1=Thierry |last2=Bialek |first2=William |year= 2010|title=Are biological systems poised at criticality? |journal=Journal of Statistical Physics |volume=144 |issue=2 |pages=268–302 |arxiv= 1012.2242|doi=10.1007/s10955-011-0229-4 |bibcode=2011JSP...144..268M }}
== External links ==
* [http://bactra.org/notebooks/edge-of-chaos.html "The Edge of Chaos"] – a criticism of the idea's prevalence.
{{Chaos theory}}
[[Category:Chaos theory]]
Category:Chaos theory
范畴: 混沌理论
[[Category:Self-organization]]
Category:Self-organization
类别: 自我组织
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<small>This page was moved from [[wikipedia:en:Edge of chaos]]. Its edit history can be viewed at [[混沌边缘/edithistory]]</small></noinclude>
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