An important strand of work leading to the analysis of complex evolution is thermodynamics. Ilya Prigogine received the Nobel prize for his work, in collaboration with other members of the "Brussels School", showing that physical and chemical systems far from thermodynamical equilibrium tend to self-organize by exporting entropy and thus to form dissipative structures. Both his philosophical musings (Prigogine & Stengers, 1984) about the new world view implied by self-organization and irreversible change, and his scientific work (Nicolis & Prigogine, 1977, 1989; Prigogine, 1980) on bifurcations and order through fluctuations remain classics, cited in the most diverse contexts. Inspired by Prigogine's theories, Erich Jantsch has made an ambitious attempt to synthesize everything that was known at the time (1979) about self-organizing processes, from the Big Bang to the evolution of society, into an encompassing world view.
The physicist Hermann Haken (1978) has suggested the label of synergetics for the field that studies the collective patterns emerging from many interacting components, as they are found in chemical reactions, crystal formations or lasers. Another Nobel laureate, Manfred Eigen (1992), has focused on the origin of life, the domain where chemical self-organization and biological evolution meet. He has introduced the concepts of hypercycle, an autocatalytic cycle of chemical reactions containing other cycles, and of quasispecies, the fuzzy distribution of genotypes characterizing a population of quickly mutating organisms or molecules (1979).
The modelling of non-linear systems in physics has led to the concept of chaos, a deterministic process characterized by extreme sensitivity to its initial conditions (Crutchfield, Farmer, Packard & Shaw, 1986). Although chaotic dynamics is not strictly a form of evolution, it is an important aspect of the behavior of complex systems. The science journalist James Gleick has written a popular history of, and introduction to, the field. Cellular automata, mathematical models of distributed dynamical processes characterized by a discrete space and time, have been widely used to study phenomena such as chaos, attractors and the analogy between dynamics and computation through computer simulation. Stephen Wolfram has made a fundamental classification of their types of behavior. Catastrophe theory proposes a mathematical classification of the critical behavior of continuous mappings. It was developed by René Thom (1975) in order to model the (continuous) development of (discontinuous) forms in organisms, thus extending the much older work by the biologist D' Arcy Thompson (1917).
Another French mathematician, Benoit Mandelbrot (1983), has founded the field of fractal geometry, which models the recurrence of similar patterns at different scales which characterizes most natural systems. Such self-similar structures exhibit power laws, like the famous Zipf's law governing the frequency of words. By studying processes such as avalanches and earthquakes, Per Bak (1988, 1991) has shown that many complex systems will spontaneously evolve to the critical edge between order (stability) and chaos, where the size of disturbances obeys a power law, large disturbances being less frequent than small ones. This phenomenon, which he called self-organized criticality, may also provide an explanation for the punctuated equilibrium dynamics seen in biological evolution.
Bibliography: see the "classic publications on complex, evolving systems".
See also: Web servers on complexity and self-organization