Journal ArticleDOI
Statistical Properties of the Additive Automaton Networks
TLDR
A set of theorem about the evolutionary properties of the automaton networks are presented, which includes the theorems that, for an additive automaton network, the tree structures are identical, and that the geometric entropy equals to its topological entropy.Abstract:
A set of theorems about the evolutionary properties of the automaton networks are presented in this article, which includes the theorems that, for an additive automaton network, the tree structures are identical, and that the geometric entropy equals to its topological entropy. The exact analytical formula for the entropy of the additive automaton networks is introduced, and applied to investigate the evolutionary properties of the elementary cellular automata of number 90 and number 150.read more
References
More filters
Journal ArticleDOI
Statistical mechanics of cellular automata
TL;DR: 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 p definite rules involving the values of its nearest neighbors.
Universality and complexity in cellular automata
TL;DR: In this article, it was shown that all one-dimensional cellular automata fall into four distinct universality classes: limit points, limit cycles, chaotic attractors, and limit cycles.
Journal ArticleDOI
Universality and complexity in cellular automata
TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
Journal ArticleDOI
Algebraic properties of cellular automata
TL;DR: Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata, and the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities.
Journal ArticleDOI
Exact results for deterministic cellular automata with additive rules
Pu-hua Guan,Yu He +1 more
TL;DR: It is shown that all state transition diagrams of the CA have identical trees rooted on cycles, and general formulae for cycle lengths and multiplicities are given.