Recursive definition of global cellular-automata mappings

Journal Article · Mon Jan 31 23:00:00 EST 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.1699· OSTI ID:5323314

Feldberg, R; Knudsen, C; Rasmussen, S ^[1]

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1. Physics Department and Center for Modeling, Nonlinear Dynamics Irreversible Thermodynamics, The Technical University of Denmark, DK-2800 Lyngby (Denmark) Analysis Division Office, Section for Simulation Applications, Center for Nonlinear Studies, and Theoretical Division, Complex Systems Group, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501 (United States)

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.

• OSTI ID: 5323314
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:2; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DISCRETE ORDINATE METHOD
DYNAMICS
EQUATIONS
FRACTALS
MAPPING
MECHANICS
NONLINEAR PROBLEMS
RECURSION RELATIONS