Journal ArticleDOI
Statistical mechanics of cellular automata
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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.Abstract:
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 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 \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 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.read more
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References
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Journal ArticleDOI
The vector string descriptor as a tool in the analysis of cellular automata systems
Jon T. Butler,Simeon C. Ntafos +1 more
TL;DR: In this paper, the vector string descriptor is introduced as a tool for the analysis of cellular spaces similar to those studied by S. Ulam, which is quite straightforward to show the existence of global properties which would otherwise be very difficult to prove.
Journal ArticleDOI
Periodic Forests whose Largest Clearings are of Size 3
TL;DR: In this paper, the basic theory of periodic forests is outlined and the number of forests whose largest clearings are of size 3 is examined; their corresponding tessellations are sketched.
Journal ArticleDOI
Periodic forests whose largest clearings are of size n ≥ 4
TL;DR: The number of distinct periodic forests whose largest clearings are of size n is known to be 1 (n = 1), 1(n = 2), 1, 1, 2, 12, and 4 as discussed by the authors.