Edge of chaos
Encyclopedia
The phrase edge of chaos was coined by mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 Doyne Farmer to describe the transition phenomenon discovered by computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....

 Christopher Langton
Christopher Langton
Christopher Langton 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 Simulation of Living Systems" at the Los Alamos National Laboratory in 1987.Langton made...

. The phrase originally refers to an area in the range of a variable
Variable (programming)
In computer programming, a variable is a symbolic name given to some known or unknown quantity or information, for the purpose of allowing the name to be used independently of the information it represents...

, λ (lambda), which was varied while examining the behavior of a cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...

 (CA). As λ varied, the behavior of the CA went through a phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

 of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

 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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, biological
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, economic
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 and social
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...

  system
System
System is a set of interacting or interdependent components forming an integrated whole....

s operate in a region between order and either complete randomness
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....

 or chaos
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

, where the complexity
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

 is maximal.
The generality and significance of the idea, however, has since been called into question by Melanie Mitchell
Melanie Mitchell
Melanie Mitchell is a professor of computer science at Portland State University. She has worked at the Santa Fe Institute and Los Alamos National Laboratory...

 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
Stuart Kauffman
Stuart Alan Kauffman is an American theoretical biologist and complex systems researcher concerning the origin of life on Earth...

 has studied mathematical model
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 not only in the natural sciences and engineering disciplines A mathematical model is a...

s of evolving
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...

systems in which the rate of evolution is maximized near the edge of chaos.

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