Analytic Proof of the Attractors of a Class of Cellular Automaton

Details Analytic Proof of the Attractors of a Class of Cellular Automaton Analytic Proof of the Attractors of a Class of Cellular Automaton

2002-09-02

arxiv.org/abs/nlin/0209005v2

Phys. Lett. A, 322, 217 (2004)

Nonlinear Sciences

Cellular Automata and Lattice Gases

9 pages, no figure, to appear in Physics Letters A

Scientific paper

10.1016/j.physleta.2003.12.067

In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed attractors are homogenous, steady and periodic states for arbitrary initial configuration. Our method also provide exact enumeration of these attractors and it is shown explicitly in a particular model.

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