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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.

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.

--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+可补充：

--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+可补充：

一个能出现复杂现象的系统往往具有很大的自由度数目，由于非线性的存在，导致在高维相空间中存在一个有很多大于零的Lyapunov特征指数的奇怪吸引子。在这样的奇怪吸引子中存在数目巨大的有序成分和各种各样反映为物理空间有结构、时间上为混沌的成分，这些成分在通常意义下为不稳定。一旦受到某种刺激，按照混沌控制思想及其尚不知原因的原理，很快地、自适应地选择目标并达到目标，这样就导致了各种复杂现象的产生.由于这些成分构成奇怪吸引子中的一个稠集，因而对于目标响应是非常敏感的，这就导致某种不可预测性存在。--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+

一个能出现复杂现象的系统往往具有很大的自由度数目，由于非线性的存在，导致在高维相空间中存在一个有很多大于零的Lyapunov特征指数的奇怪吸引子。在这样的奇怪吸引子中存在数目巨大的有序成分和各种各样反映为物理空间有结构、时间上为混沌的成分，这些成分在通常意义下为不稳定。一旦受到某种刺激，按照混沌控制思想及其尚不知原因的原理，很快地、自适应地选择目标并达到目标，这样就导致了各种复杂现象的产生.由于这些成分构成奇怪吸引子中的一个稠集，因而对于目标响应是非常敏感的，这就导致某种不可预测性存在。--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+

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.

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.

数学家'''Doyne Farmer'''提出了混沌一词，将其用于描述计算机科学家'''克里斯托弗·兰顿Christopher Langton'''发现的过渡现象。该短语最初指的是变量λ范围内的区域，该区域随着检查'''元胞自动机（CA）'''的行为发生变化。随着λ变化，CA的行为经历了行为的相变。兰顿发现了一个有利于生产具有通用计算能力CAs的小区域。大约在同一时间，物理学家'''詹姆士·克劳奇菲尔德James P. Crutchfield'''和其他人开始使用混沌来描述或多或少相同的概念。

混沌边缘一词由数学家'''Doyne Farmer'''提出，用于描述计算机科学家'''克里斯托弗·兰顿Christopher Langton'''发现的过渡现象。混沌边缘最初指的是变量λ范围内的区域，在该区域内观察'''元胞自动机（CA）'''的行为发生变化。随着λ变化，元胞自动机的行为发生了相变。兰顿发现了一个有利于生产具有通用计算能力的元胞自动机的小区域。大约在同一时间，物理学家'''詹姆士·克劳奇菲尔德James P. Crutchfield'''和其他人开始使用混沌边缘（onset of chaos）来描述这一大致相同的概念。

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.

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，该短语是指一个比喻，即某些物理、生物、经济、社会系统在有序、完全随机、混乱之间的区域内运行，其中复杂性是最大化的。但是'''梅勒妮 · 米切尔Melanie Mitchell'''等人对此概念的普遍性及意义提出了质疑。工商界也借用了该短语，不过时常使用的并不恰当，常在远超出该词原有含义范围的情况下使用。

一般在科学领域，混沌边缘一词用于形容某些物理、生物、经济、社会系统在或有序或完全随机或混沌的状态间运行，其中复杂性是最大化的。但是'''梅勒妮 · 米切尔Melanie Mitchell'''等人对此概念的普遍性及意义提出了质疑。工商界也借用了这个词，不过时常使用的并不恰当，常在远超出该词原有含义范围的情况下使用。

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.

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.

 

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.

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.