Statistical mechanics of cellular automata Export

@article{citeulike:1758405, 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 ≃ 1.59 or ≃ 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.}, author = {Wolfram, Stephen}, citeulike-article-id = {1758405}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/RevModPhys.55.601}, citeulike-linkout-1 = {http://link.aps.org/abstract/RMP/v55/i3/p601_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/RMP/v55/i3/p601_1}, doi = {10.1103/RevModPhys.55.601}, journal = {Reviews of Modern Physics}, keywords = {cellular\_automata, statistical\_mechanics}, month = {July}, number = {3}, pages = {601+}, posted-at = {2009-02-08 11:46:30}, priority = {2}, publisher = {American Physical Society}, title = {Statistical mechanics of cellular automata}, url = {http://dx.doi.org/10.1103/RevModPhys.55.601}, volume = {55}, year = {1983} }

TY - JOUR ID - citeulike:1758405 L3 - citeulike-article-id:1758405 N2 - 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 ≃ 1.59 or ≃ 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. IS - 3 JF - Reviews of Modern Physics TI - Statistical mechanics of cellular automata PB - American Physical Society VL - 55 SP - 601 KW - cellular_automata KW - statistical_mechanics AU - Wolfram, Stephen PY - 1983/07// UR - http://dx.doi.org/10.1103/RevModPhys.55.601 ER -