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The science of '''pattern formation''' deals with the visible, ([[statistically]]) orderly outcomes of [[self-organization]] and the common principles behind similar [[patterns in nature]].

The science of '''pattern formation''' deals with the visible, ([[statistically]]) orderly outcomes of [[self-organization]] and the common principles behind similar [[patterns in nature]].

斑图生成学关注自组织中可见的、统计有序的结果，以及自然界中相似斑图背后的共同原理。

斑图生成学关注自组织中可见的、统计有序的结果，以及自然界中相似斑图背后的共同原理。

In [[developmental biology]], pattern formation refers to the generation of complex organizations of [[cell fate determination|cell fates]] in space and time. Pattern formation is controlled by [[gene]]s. The role of genes in pattern formation is an aspect of [[morphogenesis]], the creation of diverse [[anatomy|anatomies]] from similar genes, now being explored in the science of [[evolutionary developmental biology]] or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning of [[embryo]]s from the [[model organism]] ''[[Drosophila melanogaster]]'' (a fruit fly), one of the first organisms to have its morphogenesis studied and in the [[eyespot (mimicry)|eyespots]] of butterflies, whose development is a variant of the standard (fruit fly) mechanism.

In [[developmental biology]], pattern formation refers to the generation of complex organizations of [[cell fate determination|cell fates]] in space and time. Pattern formation is controlled by [[gene]]s. The role of genes in pattern formation is an aspect of [[morphogenesis]], the creation of diverse [[anatomy|anatomies]] from similar genes, now being explored in the science of [[evolutionary developmental biology]] or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning of [[embryo]]s from the [[model organism]] ''[[Drosophila melanogaster]]'' (a fruit fly), one of the first organisms to have its morphogenesis studied and in the [[eyespot (mimicry)|eyespots]] of butterflies, whose development is a variant of the standard (fruit fly) mechanism.

在'''<font color="#ff8000"> 发育生物学 Developmental Biology</font>''' 中，斑图生成指的是'''细胞命运'''中复杂组织的产生过程。斑图生成由基因控制的。基因在斑图生成中所起的作用属于形态发生的一个方面，即由相似的基因演化出不同的生命结构，当下也属于演化发育生物学所探究的问题。模式生物黑腹果蝇（第一个应用到形态发生研究的物种）的胚胎的斑图生成过程和蝴蝶的眼点清楚地体现了这一机制，而后者的发育过程是标准（果蝇）机制的一种变体。

在'''<font color="#ff8000"> 发育生物学 Developmental Biology</font>''' 中，斑图生成指的是'''细胞命运'''中复杂组织的产生过程。斑图生成由基因控制的。基因在斑图生成中所起的作用属于形态发生的一个方面，即由相似的基因演化出不同的生命结构，当下也属于演化发育生物学所探究的问题。模式生物黑腹果蝇（第一个应用到形态发生研究的物种）的胚胎的斑图生成过程和蝴蝶的眼点清楚地体现了这一机制，而后者的发育过程是标准（果蝇）机制的一种变体。

Examples of pattern formation can be found in biology, chemistry, physics, and mathematics,<ref name=":2">Ball, 2009.</ref> and can readily be simulated with computer graphics, as described in turn below.

Examples of pattern formation can be found in biology, chemistry, physics, and mathematics,<ref name=":2">Ball, 2009.</ref> and can readily be simulated with computer graphics, as described in turn below.

在生物、化学、物理和数学<ref name=":2" /> 中都有斑图生成的实例，并且我们可以用'''<font color="#ff8000"> 计算机图形学 Computer Graphics</font>''' 轻松地来模拟，下面依次进行介绍。

在生物、化学、物理和数学<ref name=":2" /> 中都有斑图生成的实例，并且我们可以用'''<font color="#ff8000"> 计算机图形学 Computer Graphics</font>''' 轻松地来模拟，下面依次进行介绍。

Biological patterns such as [[animal markings]], the segmentation of animals, and [[phyllotaxis]] are formed in different ways.<ref name=":3">Ball, 2009. ''Shapes'', pp. 231–252.</ref>

Biological patterns such as [[animal markings]], the segmentation of animals, and [[phyllotaxis]] are formed in different ways.<ref name=":3">Ball, 2009. ''Shapes'', pp. 231–252.</ref>

动物标记、动物分节和叶序等生物学斑图是以不同的方式形成的。<ref name=":3" />

动物标记、动物分节和叶序等生物学斑图是以不同的方式形成的。<ref name=":3" />

Possible mechanisms of pattern formation in biological systems include the classical [[reaction–diffusion]] model proposed by [[Alan Turing]]<ref name=":7">S. Kondo, T. Miura, "Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation", Science 24 Sep 2010: Vol. 329, Issue 5999, pp. 1616-1620 DOI: 10.1126/science.1179047</ref> and the more recently found [[elastic instability]] mechanism which is thought to be responsible for the fold patterns on the [[cerebral cortex]] of higher animals, among other things.<ref name="Mercker">{{cite journal |last1=Mercker |first1=M |last2=Brinkmann |first2=F |last3=Marciniak-Czochra |first3=A |last4=Richter |first4=T |title=Beyond Turing: mechanochemical pattern formation in biological tissues. |journal=Biology Direct |date=4 May 2016 |volume=11 |pages=22 |doi=10.1186/s13062-016-0124-7 |pmid=27145826|pmc=4857296 }}</ref><ref name=":8">Tallinen et al. Nature Physics 12, 588–593 (2016) doi:10.1038/nphys3632</ref>

Possible mechanisms of pattern formation in biological systems include the classical [[reaction–diffusion]] model proposed by [[Alan Turing]]<ref name=":7">S. Kondo, T. Miura, "Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation", Science 24 Sep 2010: Vol. 329, Issue 5999, pp. 1616-1620 DOI: 10.1126/science.1179047</ref> and the more recently found [[elastic instability]] mechanism which is thought to be responsible for the fold patterns on the [[cerebral cortex]] of higher animals, among other things.<ref name="Mercker">{{cite journal |last1=Mercker |first1=M |last2=Brinkmann |first2=F |last3=Marciniak-Czochra |first3=A |last4=Richter |first4=T |title=Beyond Turing: mechanochemical pattern formation in biological tissues. |journal=Biology Direct |date=4 May 2016 |volume=11 |pages=22 |doi=10.1186/s13062-016-0124-7 |pmid=27145826|pmc=4857296 }}</ref><ref name=":8">Tallinen et al. Nature Physics 12, 588–593 (2016) doi:10.1038/nphys3632</ref>

生物系统中可能存在的斑图生成机制包括：'''阿兰 · 图灵 Alan Turing''' 提出的经典'''反应—扩散 Reaction–Diffusion'''模型<ref name=":7" /> 和最近发现的弹性不稳定机制，后者被认为是高等动物大脑皮层上褶皱模式等形成的原因。<ref name="Mercker" /><ref name=":8" />

生物系统中可能存在的斑图生成机制包括：'''阿兰 · 图灵 Alan Turing''' 提出的经典'''反应—扩散 Reaction–Diffusion'''模型<ref name=":7" /> 和最近发现的弹性不稳定机制，后者被认为是高等动物大脑皮层上褶皱模式等形成的原因。<ref name="Mercker" /><ref name=":8" />

In the 1980s [[Lugiato–Lefever equation|Lugiato and Lefever]] developed a model of light propagation in an optical cavity that results in pattern formation by the exploitation of nonlinear effects.

In the 1980s [[Lugiato–Lefever equation|Lugiato and Lefever]] developed a model of light propagation in an optical cavity that results in pattern formation by the exploitation of nonlinear effects.

20世纪80年代，'''卢贾托 Lugiato'''和'''勒弗 Lefever'''开发了一个光在光学谐振腔中传播的模型，该模型通过利用非线性效应形成斑图。

20世纪80年代，'''卢贾托 Lugiato'''和'''勒弗 Lefever'''开发了一个光在光学谐振腔中传播的模型，该模型通过利用非线性效应形成斑图。

[[Bénard cell]]s, [[laser]], [[cloud|cloud formation]]s in stripes or rolls. Ripples in icicles. Washboard patterns on dirtroads. [[dendrite (crystal)|Dendrites]] in [[freezing|solidification]], [[liquid crystal]]s. [[Soliton]]s.

[[Bénard cell]]s, [[laser]], [[cloud|cloud formation]]s in stripes or rolls. Ripples in icicles. Washboard patterns on dirtroads. [[dendrite (crystal)|Dendrites]] in [[freezing|solidification]], [[liquid crystal]]s. [[Soliton]]s.

Bénard cells, laser, cloud formations in stripes or rolls. Ripples in icicles. Washboard patterns on dirtroads. Dendrites in solidification, liquid crystals. Solitons.

如'''伯纳德涡流 Bénard Cells'''、激光、条状云或卷状云、冰柱上的涟漪、泥路上的洗衣板等图案以及凝固中的树突、液晶，'''孤子 Solitons'''等。

 

'''Rayleigh-Bénard convection''' is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as '''Bénard cells'''. Bénard–Rayleigh convection is one of the most commonly studied convection phenomena because of its analytical and experimental accessibility. The convection patterns are the most carefully examined example of self-organizing nonlinear systems.

'''Rayleigh-Bénard convection''' is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as '''Bénard cells'''. Bénard–Rayleigh convection is one of the most commonly studied convection phenomena because of its analytical and experimental accessibility. The convection patterns are the most carefully examined example of self-organizing nonlinear systems.

[[Sphere packing]]s and coverings. Mathematics underlies the other pattern formation mechanisms listed.

[[Sphere packing]]s and coverings. Mathematics underlies the other pattern formation mechanisms listed.

例如最密堆积（球填充）和覆盖。数学是其他斑图生成机制的基础。

例如最密堆积（球填充）和覆盖。数学是其他斑图生成机制的基础。

{{进一步|细胞自动机}}

{{进一步|细胞自动机}}

Some types of [[finite-state machine|automata]] have been used to generate organic-looking [[texture (computer graphics)|textures]] for more realistic [[Shader|shading]] of [[3D modeling|3d objects]].<ref>Greg Turk, [http://www.cc.gatech.edu/~turk/reaction_diffusion/reaction_diffusion.html Reaction–Diffusion]</ref><ref>{{cite journal|title=Reaction–Diffusion Textures|author1=Andrew Witkin |author2=Michael Kassy |url=https://www.cs.cmu.edu/~aw/pdf/texture.pdf|doi=10.1145/122718.122750|journal=Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques|year=1991|pages=299–308|isbn=0897914368 }}</ref>

Some types of [[finite-state machine|automata]] have been used to generate organic-looking [[texture (computer graphics)|textures]] for more realistic [[Shader|shading]] of [[3D modeling|3d objects]].<ref name=":16">Greg Turk, [http://www.cc.gatech.edu/~turk/reaction_diffusion/reaction_diffusion.html Reaction–Diffusion]</ref><ref name=":17">Andrew Witkin; Michael Kassy (1991). "Reaction–Diffusion Textures" (PDF). ''Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques'': 299–308. doi:10.1145/122718.122750. ISBN <bdi>0897914368</bdi>. S2CID 207162368.</ref>

 

一些类型的自动机已经用来生成类似有机外观的纹理，为三维物体提供更真实的阴影效果。

一些类型的自动机已经用来生成类似有机外观的纹理，为三维物体提供更真实的阴影效果。<ref name=":16" /><ref name=":17" />

A popular Photoshop plugin, [[Kai's Power Tools|KPT 6]], included a filter called 'KPT reaction'. Reaction produced [[reaction–diffusion system|reaction–diffusion]] style patterns based on the supplied seed image.

A popular Photoshop plugin, [[Kai's Power Tools|KPT 6]], included a filter called 'KPT reaction'. Reaction produced [[reaction–diffusion system|reaction–diffusion]] style patterns based on the supplied seed image.

KPT6是流行的Photoshop插件，包一个名为“KPT反应”的过滤器。反应该根据提供的种子图像产生反应-扩散风格的图案。

 

KPT6是流行的Photoshop插件，，包一个名为“KPT反应”的过滤器。反应该根据提供的种子图像产生反应-扩散风格的图案。

A similar effect to the 'KPT reaction' can be achieved with [[convolution]] functions in [[digital image processing]], with a little patience, by repeatedly [[unsharp masking|sharpening]] and [[box blur|blurring]] an image in a graphics editor. If other filters are used, such as [[image embossing|emboss]] or [[edge detection]], different types of effects can be achieved.

A similar effect to the 'KPT reaction' can be achieved with [[convolution]] functions in [[digital image processing]], with a little patience, by repeatedly [[unsharp masking|sharpening]] and [[box blur|blurring]] an image in a graphics editor. If other filters are used, such as [[image embossing|emboss]] or [[edge detection]], different types of effects can be achieved.

在数字图像处理中，只要有一点耐心，通过在图形编辑器中反复锐化和模糊图像，就可以用卷积函数实现类似于“KPT反应”的效果。如果使用其他滤波器，如浮雕或边缘检测，可以实现不同类型的效果。

在数字图像处理中，只要有一点耐心，通过在图形编辑器中反复锐化和模糊图像，就可以用卷积函数实现类似于“KPT反应”的效果。如果使用其他滤波器，如浮雕或边缘检测，可以实现不同类型的效果。

Computers are often used to [[computer simulation|simulate]] the biological, physical or chemical processes that lead to pattern formation, and they can display the results in a realistic way. Calculations using models like [[reaction–diffusion]] or [[MClone]] are based on the actual mathematical equations designed by the scientists to model the studied phenomena.

Computers are often used to [[computer simulation|simulate]] the biological, physical or chemical processes that lead to pattern formation, and they can display the results in a realistic way. Calculations using models like [[reaction–diffusion]] or [[MClone]] are based on the actual mathematical equations designed by the scientists to model the studied phenomena.

计算机经常被用来模拟导致斑图生成的生物、物理或化学过程，它们可以以逼真的方式显示结果。使用反应—扩散或MClone等模型的计算是基于科学家们为模拟研究现象而设计的实际数学方程。

计算机经常被用来模拟导致斑图生成的生物、物理或化学过程，它们可以以逼真的方式显示结果。使用反应—扩散或MClone等模型的计算是基于科学家们为模拟研究现象而设计的实际数学方程。