Edge of chaos
History

The phrase edge of chaos was coined in the late 1980s by chaos theory 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 Christopher Langton where a transition phenomenon was discovered. The phrase refers to an area in the range of a variable, 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. 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.

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.

Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.
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