Mathematical Physics of Cellular Automata
Cellular Automata and Lattice Gases
2012-03-20 v1 Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1203.3939,
title = {Mathematical Physics of Cellular Automata},
author = {Vladimir Garcia-Morales},
journal= {arXiv preprint arXiv:1203.3939},
year = {2012}
}
Comments
92 pages (main text+supporting information), submitted for publication