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第100行：
第100行： − 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。+ 第116行：
第116行： − 细菌菌落在菌落生长过程中表现出多种多样的形式。产生的形状取决于生长条件。特别是强调(培养基的硬度，缺乏营养等)增加了产生模式的复杂性。其他有机体，如粘菌显示了显着的模式所造成的动态化学信号。+ − 第146行：
第145行： − 植被模式，如虎灌木和冷杉波形成的原因不同。在尼日尔等干旱国家，植物生长受到降雨的限制，虎灌木由干旱斜坡上的带状灌木组成。每一条粗略的水平植被带都可以从其上方的裸露地带吸收雨水。+ 第166行：
第165行： − 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。+ 第202行：
第201行： − 在20世纪80年代，Lugiato 和 Lefever 发展了一个光在光学腔中传播的模型，该模型通过利用非线性效应形成图案。+ 第212行：
第211行： − B nard 细胞，激光，条纹或卷云的形成。冰柱上的涟漪。十字架上的搓板图案。凝固过程中的树枝晶、液晶。孤子。+ 第239行：
第238行： + 第256行：
第256行： − 图案类似于[[反应扩散模型，使用锐化和模糊]]+ 第263行：
第263行： + 第284行：
第285行： − 一个流行的 Photoshop 插件 KPT 6，包含了一个叫做 KPT reaction 的过滤器。基于提供的种子图像，反应产生反应扩散样式的图案。+ 第294行：
第295行： − 在数字图像处理中，只需一点点耐心，通过在图形编辑器中反复锐化和模糊图像，就可以达到类似于“ KPT 反应”的效果。如果使用其他过滤器，如浮雕或边缘检测，可以实现不同类型的效果。+ 第304行：
第305行： − 计算机经常被用来模拟导致图案形成的生物、物理或化学过程，它们可以以一种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为模拟所研究的现象而设计的实际数学方程。+
无编辑摘要
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.
细菌菌落在菌落生长过程中形成的形态种类繁多。所形成的形状取决于生长条件。特别是，压力（培养基的硬度、营养物质的缺乏等）增强了所产生的模式的复杂性。其他生物，如粘液霉菌，则显示出由化学信号动态引起的显著模式。
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..
虎灌木和冷杉波等植被模式形成的原因不同。在尼日尔等干旱国家，植物生长受到降雨的限制，虎灌木由干旱斜坡上的带状灌木组成。每一条大致水平的植被带都可以从紧靠其上方的裸露地带吸收雨水。
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.
20世纪80年代，卢贾托Lugiato和勒弗Lefever开发了一个光在光学腔中传播的模型，该模型通过利用非线性效应形成图案。
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.
贝纳尔细胞，激光，云层形成的条状或卷状。冰柱上的涟漪 泥路上的洗衣板图案。凝固中的树枝状，液晶。孤子
{{further|Gradient pattern analysis}}
{{further|Gradient pattern analysis}}
{{进一步|梯度模式分析}}
Pattern resembling a [[reaction–diffusion model, produced using sharpen and blur]]
Pattern resembling a [[reaction–diffusion model, produced using sharpen and blur]]
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}}
{{进一步|细胞自动机}}
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.
一个流行的Photoshop插件，KPT6，包括一个名为“KPT反应”的过滤器。反应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 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.
利用数字图像处理中的'''<font color="#ff8000"> 卷积函数convolution functions</font>'''，只要稍有耐心，在图形编辑器中反复对图像进行锐化和模糊处理，就能达到类似 "KPT反应 "的效果。如果使用其他滤镜，如浮雕或边缘检测，可以实现不同类型的效果。
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.
计算机经常被用来模拟导致模式形成的生物、物理或化学过程，并能以真实的方式显示结果。使用反应-扩散或MClone等模型进行计算，是根据科学家设计的实际数学方程来模拟所研究的现象。