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Journal article

Recursive definition of global cellular-automata mappings

By Feldberg, Rasmus1; Knudsen, Carsten1,2; Rasmussen, Steen3

From

Department of Physics, Technical University of Denmark1

Biophysics and Fluids, Department of Physics, Technical University of Denmark2

Santa Fe Institute3

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.

Language: English
Year: 1994
Pages: 1699-1711
ISSN: 10953787 , 1063651x , 24700053 and 24700045
Types: Journal article
DOI: 10.1103/PhysRevE.49.1699

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