Statistical mechanics of cellular automata

Journal Article · Fri Jul 01 00:00:00 EDT 1983 · Rev. Mod. Phys.; (United States)

DOI:https://doi.org/10.1103/RevModPhys.55.601· OSTI ID:5907680

Wolfram, S

Cellular automata are used as simple mathematical models to investigate self-organization 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 p definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions approx. =1.59 or approx. =1.69. With ''random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization 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.

• Research Organization: The Institute for Advanced Study, Princeton, New Jersey 08540
• DOE Contract Number: AC03-81ER40050
• OSTI ID: 5907680
• Journal Information: Rev. Mod. Phys.; (United States), Journal Name: Rev. Mod. Phys.; (United States) Vol. 55:3; ISSN RMPHA
• Country of Publication: United States
• Language: English

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SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
ENTROPY
MATHEMATICAL MODELS
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TIME DEPENDENCE