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Possible mechanisms of pattern formation in biological systems include the classical reaction–diffusion model proposed by Alan Turing 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.

Possible mechanisms of pattern formation in biological systems include the classical reaction–diffusion model proposed by Alan Turing 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.

生物系统中模式形成的可能机制包括阿兰 · 图灵提出的经典反应扩散模型和最近发现的弹性不稳定机制，该机制被认为对高等动物大脑皮层的折叠模式负有责任。

生物系统中可能的模式形成机制制包括阿兰 · 图灵Alan Turing提出的经典反应扩散模型和最近发现的弹性不稳定机制，该机制被认为是高等动物大脑皮层上褶皱模式的原因，等等。

Bacterial colonies show a large variety of patterns formed during colony growth. The resulting shapes depend on the growth conditions. In particular, stresses (hardness of the culture medium, lack of nutrients, etc.) enhance the complexity of the resulting patterns. Other organisms such as slime moulds display remarkable patterns caused by the dynamics of chemical signaling.

Bacterial colonies show a large variety of patterns formed during colony growth. The resulting shapes depend on the growth conditions. In particular, stresses (hardness of the culture medium, lack of nutrients, etc.) enhance the complexity of the resulting patterns. Other organisms such as slime moulds display remarkable patterns caused by the dynamics of chemical signaling.

 

Vegetation patterns such as tiger bush and fir waves form for different reasons. Tiger bush consists of stripes of bushes on arid slopes in countries such as Niger where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation absorbs rainwater from the bare zone immediately above it..

Vegetation patterns such as tiger bush and fir waves form for different reasons. Tiger bush consists of stripes of bushes on arid slopes in countries such as Niger where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation absorbs rainwater from the bare zone immediately above it..

Pattern formation has been well studied in chemistry and chemical engineering, including both temperature and concentration patterns. The Brusselator model developed by Ilya Prigogine and collaborators is one such example that exhibits Turing instability. Pattern formation in chemical systems often involve oscillatory chemical kinetics or autocatalytic reactions such as Belousov–Zhabotinsky reaction or Briggs–Rauscher reaction. In industrial applications such as chemical reactors, pattern formation can lead to temperature hot spots which can reduce the yield or create hazardous safety problems such as a thermal runaway. The emergence of pattern formation can be studied by mathematical modeling and simulation of the underlying reaction-diffusion system.

Pattern formation has been well studied in chemistry and chemical engineering, including both temperature and concentration patterns. The Brusselator model developed by Ilya Prigogine and collaborators is one such example that exhibits Turing instability. Pattern formation in chemical systems often involve oscillatory chemical kinetics or autocatalytic reactions such as Belousov–Zhabotinsky reaction or Briggs–Rauscher reaction. In industrial applications such as chemical reactors, pattern formation can lead to temperature hot spots which can reduce the yield or create hazardous safety problems such as a thermal runaway. The emergence of pattern formation can be studied by mathematical modeling and simulation of the underlying reaction-diffusion system.

模式的形成已经在化学和化学工程中得到了很好的研究，包括温度和浓度模式。由 Ilya Prigogine 和他的合作者发展的 Brusselator 模型就是这样一个展示图灵不稳定性的例子。化学体系中图形的形成通常涉及振荡化学动力学或自催化反应，如 Belousov-Zhabotinsky 反应或 Briggs-Rauscher 反应。在工业应用中，如化学反应堆，图案的形成可能导致温度热点，这可能降低产量或造成危险的安全问题，如热失控。模式形成的出现可以用潜在的反应扩散系统的数学建模与模拟来研究。

模式的形成已经在化学和化学工程中得到了很好研究，包括温度和浓度模式。由伊利亚·普里戈吉因Ilya Prigogine和其合作者开发的Brusselator模型就是这样一个表现出图灵不稳定性的例子。化学体系中的模式形成通常涉及'''<font color="#ff8000"> 振荡化学动力学oscillatory chemical kinetics</font>'''或'''<font color="#ff8000"> 自催化反应autocatalytic reactions</font>'''，如Belousov-Zhabotinsky反应或Briggs-Rauscher反应。在工业应用中，如化学反应堆，模式形成可能导致温度热点，这可能降低产量或造成危险的安全问题，如热失控。模式形成的出现可以用潜在的反应扩散系统的数学建模与模拟来研究。

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

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

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

{{further|Gradient pattern analysis}}

{{further|Gradient pattern analysis}}

Pattern resembling a [[reaction–diffusion model, produced using sharpen and blur]]

Pattern resembling a [[reaction–diffusion model, produced using sharpen and blur]]

图案类似于[[反应扩散模型，使用锐化和模糊]]

类似[[反应-扩散模型，使用锐化和模糊技术制作]]的图案。

{{further|Cellular automaton}}

{{further|Cellular automaton}}

A popular Photoshop plugin, KPT 6, included a filter called 'KPT reaction'. Reaction produced reaction–diffusion style patterns based on the supplied seed image.

A popular Photoshop plugin, KPT 6, included a filter called 'KPT reaction'. Reaction produced reaction–diffusion style patterns based on the supplied seed image.

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

Computers are often used to 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 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.