RECURSIVE DEFINITION OF GLOBAL CELLULAR-AUTOMATA MAPPINGS

Authors
FELDBERG R KNUDSEN C RASMUSSEN S
Citation
R. Feldberg et al., RECURSIVE DEFINITION OF GLOBAL CELLULAR-AUTOMATA MAPPINGS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(2), 1994, pp. 1699-1711
Citations number
27
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
49
Issue
2
Year of publication
1994
Pages
1699 - 1711
Database
ISI
SICI code
1063-651X(1994)49:2<1699:RDOGCM>2.0.ZU;2-L
Abstract
A method for a recursive definition of global cellular-automata mappin gs 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-aut omaton mapping as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is der ived from an approximation to the exact recursive definition. The recu rsive definitions are applied to calculate the fractal dimension of th e set of reachable states and of the set of fixed points of cellular a utomata on an infinite lattice.