The recently founded Santa Fe Institute is the gathering point for a new approach, which is usually presented as the study of "complex adaptive systems" (CAS). Whereas the authors in the "natural science" tradition are mostly European, while the cybernetics and systems researchers come from different continents, the CAS movement is predominantly American. Though it shares its subject, the general properties of complex systems across traditional disciplinary boundaries, with cybernetics and systems theory , the CAS approach is distinguished by the extensive use of computer simulations as a research tool, and an emphasis on systems, such as ecologies or markets, which are less integrated or "organized" than the ones, such as organisms, companies and machines, studied by the older tradition.
Two popular science books, one by the science writer Mitchell Waldrop and one by the Nobel laureate and co-founder of the Santa Fe Institute Murray Gell-Mann, offer good reviews of the main ideas underlying the CAS approach. Another Santa Fe collaborator, the systems analyst John Casti, has written several popular science books, discussing different issues in the modelling of complex systems, while integrating insights from the CAS approach with the two older traditions.
John Holland is the founder of the domain of genetic algorithms. These are parallel, computational representations of the processes of variation, recombination and selection on the basis of fitness that underly most processes of evolution and adaptation (Holland, 1992). They have been successfully applied to general problem solving, control and optimization tasks, inductive learning (classifier systems, Holland et al., 1986), and the modelling of ecological systems (the ECHO model, Holland, 1996). The biologist Stuart Kauffman has tried to understand how networks of mutually activating or inhibiting genes can give rise to the differentiation of organs and tissues during embryological development. This led him to investigate the properties of Boolean networks of different sizes and degrees of connectedness. Through a reasoning reminiscent of Ashby, he proposes that the self-organization exhibited by such networks of genes or chemical reactions is an essential factor in evolution, complementary to Darwinian selection by the environment.
Holland's and Kauffman's work, together with Dawkins' simulations of evolution and Varela's models of autopoietic systems, provide essential inspiration for the new discipline of artificial life, This approach, initiated by Chris Langton (1989, 1992), tries to develop technological systems (computer programs and autonomous robots) that exhibit lifelike properties, such as reproduction, sexuality, swarming, and co-evolution. Tom Ray's Tierra program proposes perhaps the best example of a complex, evolving ecosystem, with different species of "predators", "parasites" and "prey", that exists only in a computer.
Backed by Kauffman's work on co-evolution, Wolfram's cellular automata studies, and Bak's investigations of self-organized criticality, Langton (1990) has proposed the general thesis that complex systems emerge and maintain on the edge of chaos, the narrow domain between frozen constancy and chaotic turbulence. The "edge of chaos" idea is another step towards an elusive general definition of complexity. Another widely cited attempt at a definition in computational terms was proposed by Charles Bennett.
Another investigation which has strongly influenced the artificial life community is Robert Axelrod's game theoretic simulation of the evolution of cooperation. By letting different strategies compete in a repeated Prisoner's Dilemma game, Axelrod (1984) showed that mutually cooperating, "tit-for-tat"-like strategies tend to dominate purely selfish ones in the long run. This transition from biological evolution to social exchanges naturally leads into the modelling of economic processes (Anderson, Arrow & Pines, 1988). W. Brian Arthur has systematically investigated self-reinforcing processes in the economy, where the traditional law of decreasing returns is replaced by a law of increasing returns, leading to the path-dependence and lock-in of contingent developments. More recently (1994), he has simulated the seemingly chaotic behavior of stock exchange-like systems by programming agents that are continuously trying to guess the future behavior of the system to which they belong, and use these predictions as basis for their actions. The conclusion is that the different predictive strategies cancel each other out, so that the long term behavior of the system becomes intrinsically unpredictable. This result leads back to von Foerster's second-order cybernetics, according to which models of social systems change the very systems they intend to model.
Bibliography: see the "classic publications on complex, evolving systems".
See also: Web servers on complexity and self-organization