Chapter 6: Starting from Randomness

Section 1: The Emergence of Order

History [of emergence of order]

The fact that despite initial randomness processes like friction can make systems settle down into definite configurations has been the basis for all sorts of engineering throughout history. The rise of statistical mechanics in the late 1800s emphasized the idea of entropy increase and the fundamental tendency for systems to become progressively more disordered as they evolve to thermodynamic equilibrium. Theories were nevertheless developed for a few cases of spontaneous pattern formation—notably in convection, cirrus clouds and ocean waves. When the study of feedback and stability became popular in the 1940s, there were many results about how specific simple fixed or repetitive behaviors in time could emerge despite random input. In the 1950s it was suggested that reaction-diffusion processes might be responsible for spontaneous pattern formation in biology (see page 1012)—and starting in the 1970s such processes were discussed as prime examples of the phenomenon of self-organization. But in their usual form, they yield essentially only rather simple repetitive patterns. Ever since around 1900 it tended to be assumed that any fundamental theory of systems with many components must be based on statistical mechanics. But almost all work in the field of statistical mechanics concentrated on systems in or very near thermal equilibrium—in which in a sense there is almost complete disorder. In the 1970s there began to be more discussion of phenomena far from equilibrium, although typically it got no further than to consider how external forces could lead to reaction-diffusion-like phenomena. My own work on cellular automata in 1981 emerged in part from thinking about self-gravitating systems (see page 880) where it seemed conceivable that there might be very basic rules quite different from those usually studied in statistical mechanics. And when I first generated pictures of the behavior of arbitrary cellular automaton rules, what struck me most was the order that emerged even from random initial conditions. But while it was immediately clear that most cellular automata do not have the kind of reversible underlying rules assumed in traditional statistical mechanics, it still seemed initially very surprising that their overall behavior could be so elaborate—and so far from the complete orderlessness one might expect on the basis of traditional ideas of entropy maximization.

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From Stephen Wolfram: A New Kind of Science [citation]