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Edge of chaos

For the computer game, see Independence War 2: Edge of Chaos.

The phrase edge of chaos was coined by computer scientist Christopher Langton in 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 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.

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 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.


  • Christopher G. Langton. "Computation at the edge of chaos". Physica D, 42, 1990.
  • 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. 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. Dynamics, Computation, and the "Edge of Chaos": A Re-Examination
  • Origins of Order: Self-Organization and Selection in Evolution by Stuart Kauffman
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Edge_of_chaos". A list of authors is available in Wikipedia.
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