Recursive definition of global cellular-automata mappings

Rasmus Feldberg, Carsten Knudsen, Steen Rasmussen

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Abstract

A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set of fixed points of cellular automata on an infinite lattice.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume49
Issue number2
Pages (from-to)1699-1711
ISSN1063-651X
DOIs
Publication statusPublished - 1994

Bibliographical note

Copyright (1994) by the American Physical Society.

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