Statistical mechanics of cellular automata
Abstract
Cellular automata are used as simple mathematical models to investigate selforganization in statistical mechanics. A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate selfsimilar patterns with fractal dimensions ~= 1.59 or ~= 1.69. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several selforganization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.
 Publication:

Reviews of Modern Physics
 Pub Date:
 July 1983
 DOI:
 10.1103/RevModPhys.55.601
 Bibcode:
 1983RvMP...55..601W