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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.

In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. Pattern formation is controlled by genes. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse 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 embryos from the model organism Drosophila melanogaster (a fruit fly), one of the first organisms to have its morphogenesis studied and in the 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 fates in space and time. Pattern formation is controlled by genes. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse 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 embryos from the model organism Drosophila melanogaster (a fruit fly), one of the first organisms to have its morphogenesis studied and in the 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，模式形成指的是细胞命运在空间和时间上复杂组织的产生。模式的形成是由基因控制的。形态发生是由相似的基因创造出不同的解剖结构，基因在模式形成中的作用是形态发生的一个方面，目前演化发育生物学正在探讨这个问题。模式生物黑腹果蝇(一种果蝇)的胚胎前后图案和蝴蝶的眼点清楚地体现了其中的机制，后者的发育是标准(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在空间和时间上复杂组织的产生。斑图的生成是由基因控制的。形态发生是由相似的基因创造出不同的解剖结构，基因在斑图生成中的作用是形态发生的一个方面，目前演化发育生物学正在探讨这个问题。模式生物黑腹果蝇(一种果蝇)的胚胎前后图案和蝴蝶的眼点清楚地体现了其中的机制，后者的发育是标准(果蝇)机制的一种变体。

Examples of pattern formation can be found in biology, chemistry, physics, and mathematics, 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, and can readily be simulated with computer graphics, as described in turn below.

模式形成的例子可以在生物、化学、物理和数学中找到，并且可以很容易地用'''<font color="#ff8000"> 计算机图形学computer graphics</font>'''模拟，下面依次介绍。

斑图生成的例子可以在生物、化学、物理和数学中找到，并且可以很容易地用'''<font color="#ff8000"> 计算机图形学computer graphics</font>'''模拟，下面依次介绍。

In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. In this context, a field of cells is the group of cells whose fates are affected by responding to the same set positional information cues. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo.

In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. In this context, a field of cells is the group of cells whose fates are affected by responding to the same set positional information cues. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo.

在发育生物学中，模式形成描述了胚胎发育组织中最初的等效细胞呈现出复杂形态和功能的机制。'''<font color="#ff8000"> 胚胎发生Embryogenesis</font>'''，例如果蝇的胚胎发生，涉及到细胞命运的协调控制。模式的形成是遗传控制的，通常涉及一个场中的每个细胞沿着形态原梯度感知和响应其位置，然后通过细胞信号通路进行短距离的细胞间通信，以完善初始模式。在此背景下，'''<font color="#32CD32">细胞场 a field of cells</font>'''是指通过响应同一组位置信息线索而影响其命运的一组细胞。这个概念模型最早在20世纪60年代被描述为法旗模型。更一般地说，生物体的形态是由进化发育生物学的机制所决定的，如改变胚胎中特定发育事件的时间和位置。

在发育生物学中，斑图生成描述了胚胎发育组织中最初的等效细胞呈现出复杂形态和功能的机制。'''<font color="#ff8000"> 胚胎发生Embryogenesis</font>'''，例如果蝇的胚胎发生，涉及到细胞命运的协调控制。模式的形成是遗传控制的，通常涉及一个场中的每个细胞沿着形态原梯度感知和响应其位置，然后通过细胞信号通路进行短距离的细胞间通信，以完善初始模式。在此背景下，'''<font color="#32CD32">细胞场 a field of cells</font>'''是指通过响应同一组位置信息线索而影响其命运的一组细胞。这个概念模型最早在20世纪60年代被描述为法旗模型。更一般地说，生物体的形态是由进化发育生物学的机制所决定的，如改变胚胎中特定发育事件的时间和位置。

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。

生物系统中可能的斑图生成机制制包括阿兰 · 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。

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。

斑图生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。

Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.

Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.

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。

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，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。