A method to identify the invariant subsets of bi‐infinite configurations of cellular automata that propagate rigidly with a constant velocity ν is described. Causal traveling configurations, propagating at speeds not greater than the automaton range, |ν|≤r, are considered. The sets of traveling configurations are presented by finite automata and its topological entropy is calculated. When the invariant subset of traveling configurations has nonzero topological entropy, the dynamics is dominated by the interaction of domains, composed of traveling patterns of finite size. The sets of traveling patterns and domains are presented by finite automata. End‐resolving CA are shown to always have sets of traveling configurations that are spatially periodic with zero entropy, except possibly for traveling configurations at top speed. The elementary CA are examined exhaustively along these lines.
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September 1996
Research Article|
September 01 1996
Traveling patterns in cellular automata Available to Purchase
Jesús Urías;
Jesús Urías
Instituto de Investigación en Comunicación Optica, Universidad Autónoma de San Luis Potosí, 78000, San Luis Potosí, SLP, México
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G. Salazar‐Anaya;
G. Salazar‐Anaya
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada
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Edgardo Ugalde;
Edgardo Ugalde
CPT, Luminy, Case 907, F‐13288 Marseille, Cedex 9, France
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Agustín Enciso
Agustín Enciso
Escuela de Física, Universidad Autónoma de Zacatecas, 98000 Zacatecas, Zac., México
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Jesús Urías
Instituto de Investigación en Comunicación Optica, Universidad Autónoma de San Luis Potosí, 78000, San Luis Potosí, SLP, México
G. Salazar‐Anaya
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada
Edgardo Ugalde
CPT, Luminy, Case 907, F‐13288 Marseille, Cedex 9, France
Agustín Enciso
Escuela de Física, Universidad Autónoma de Zacatecas, 98000 Zacatecas, Zac., México
Chaos 6, 493–503 (1996)
Article history
Received:
December 05 1994
Accepted:
May 16 1996
Citation
Jesús Urías, G. Salazar‐Anaya, Edgardo Ugalde, Agustín Enciso; Traveling patterns in cellular automata. Chaos 1 September 1996; 6 (3): 493–503. https://doi.org/10.1063/1.166190
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