Mathematical Physics of Cellular Automata

Details Mathematical Physics of Cellular Automata Mathematical Physics of Cellular Automata

2012-03-18

arxiv.org/abs/1203.3939v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

92 pages (main text+supporting information), submitted for publication

Scientific paper

A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA rules into equivalence classes. Complexity in 1D systems is then shown to emerge from the weak symmetry breaking of the addition modulo an integer number p. The latter symmetry is possessed by certain rules that produce Pascal simplices in their time evolution. These results elucidate Wolfram's classification of CA dynamics.

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