Edge of Chaos
   HOME

TheInfoList



OR:

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. Even though the idea of the edge of chaos is an abstract one, it has many applications in such fields as ecology, business management, psychology, political science, and other domains of the social sciences. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.


History

The phrase ''edge of chaos'' was coined in the late
1980s File:1980s replacement montage02.PNG, 420px, From left, clockwise: The first Space Shuttle, ''Columbia'', lifts off in 1981; US president Ronald Reagan and Soviet leader Mikhail Gorbachev ease tensions between the two superpowers, leading to the ...
by
chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...
physicist Norman Packard. In the next decade, Packard and mathematician Doyne Farmer co-authored many papers on understanding how self-organization and order emerges at the edge of chaos. One of the original catalysts that led to the idea of the edge of chaos were the experiments with cellular automata done by
computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...
Christopher Langton __NOTOC__ Christopher Gale Langton (born 1948/49) is an American computer scientist and one of the founders of the field of artificial life. He coined the term in the late 1980s when he organized the first "Workshop on the Synthesis and Simulati ...
where a transition phenomenon was discovered. The phrase refers to an area in the range of a
variable Variable may refer to: * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed * Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...
, λ (lambda), which was varied while examining the behaviour of a cellular automaton (CA). As λ varied, the behaviour of the CA went through a phase transition of behaviours. Langton found a small area conducive to produce CAs capable of
universal computation A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
. At around the same time physicist
James P. Crutchfield James P. Crutchfield (born 1955) is an American mathematician and physicist. He received his B.A. summa cum laude in physics and mathematics from the University of California, Santa Cruz, in 1979 and his Ph.D. in physics there in 1983. He is curren ...
and others used the phrase ''onset of chaos'' to describe more or less the same concept. In the sciences in general, the phrase has come to refer to a metaphor that some
physical Physical may refer to: *Physical examination In a physical examination, medical examination, or clinical examination, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally co ...
,
biological Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary in ...
, economic and social
system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...
s operate in a region between order and either complete randomness or chaos, where the
complexity Complexity characterises the behaviour of a system or model whose components interaction, interact in multiple ways and follow local rules, leading to nonlinearity, randomness, collective dynamics, hierarchy, and emergence. The term is generall ...
is maximal. The generality and significance of the idea, however, has since been called into question by
Melanie Mitchell Melanie Mitchell is an American scientist. She is the Davis Professor of Complexity at the Santa Fe Institute. Her major work has been in the areas of analogical reasoning, complex systems, genetic algorithms and cellular automata, and her publi ...
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. Stuart Kauffman has studied
mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s of evolving systems in which the rate of evolution is maximized near the edge of chaos.


Adaptation

Adaptation In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment. The most important instruments for the
adaptation In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is ''"Adaptation to the edge of chaos"''. Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CAS) 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. In CAS,
coevolution In biology, coevolution occurs when two or more species reciprocally affect each other's evolution through the process of natural selection. The term sometimes is used for two traits in the same species affecting each other's evolution, as well ...
generally occurs near the edge of chaos, and a balance should be maintained between flexibility and stability to avoid structural failure. As a response to coping with turbulent environments, CAS bring out flexibility, creativity,
agility Agility or nimbleness is an ability to change the body's list of human positions, position quickly and requires the integration of isolated movement skills using a combination of balance (ability), balance, coordination (physiology), coordination ...
,
anti-fragility Antifragility is a property of systems in which they increase in capability to thrive as a result of stressors, shocks, volatility, noise, mistakes, faults, attacks, or failures. The concept was developed by Nassim Nicholas Taleb in his book, ''An ...
and innovation near the edge of chaos, provided these systems are sufficiently decentralized and non-hierarchical. Because of the importance of
adaptation In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a
genetic algorithm In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...
. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models. The simplest model for chaotic dynamics is the
logistic map The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popular ...
. 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.


See also

* Self-organized criticality * Complexity theory and organizations *
Chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...


References

* * * * Melanie Mitchell, James P. Crutchfield and Peter T. Hraber.
Dynamics, Computation, and the "Edge of Chaos": A Re-Examination
' *''Origins of Order: Self-Organization and Selection in Evolution'' by Stuart Kauffman *


External links



– a criticism of the idea's prevalence. {{Chaos theory Chaos theory Self-organization