- Edge of chaos
The phrase "edge of chaos" was coined by
computer scientist Christopher Langtonin 1990. 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 transitionof behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfieldand 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 randomnessor chaos, where the complexityis maximal.The generality and significance of the idea, however, has since been called into question by Melanie Mitchelland 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 Kauffmanhas studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.
*Christopher G. Langton. "Computation at the edge of chaos". "Physica D", 42,
*J. P. Crutchfield and K. Young, "Computation at the Onset of Chaos", in "Entropy, Complexity, and the Physics of Information", W. Zurek, editor, SFI Studies in the Sciences of Complexity, VIII, Addison-Wesley, Reading, Massachusetts (1990) pp. 223-269.
*Melanie Mitchell, Peter T. Hraber, and James P. Crutchfield. " [http://web.cecs.pdx.edu/~mm/rev-edge.pdf Revisiting the edge of chaos: Evolving cellular automata to perform computations] ". "Complex Systems", 7:89--130, 1993.
* Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. " [http://web.cecs.pdx.edu/~mm/dyn-comp-edge.pdf Dynamics, Computation, and the "Edge of Chaos": A Re-Examination] "
*"Origins of Order: Self-Organization and Selection in Evolution" by Stuart Kauffman
* [http://cscs.umich.edu/~crshalizi/notebooks/edge-of-chaos.html "The Edge of Chaos"] - a criticism of the idea's prevalence.
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