Number-conserving cellular automaton rules

Authors:
Nino Boccara;Henryk Fukś
Affiliations:
Department of Physics, University of Illinois, Chicago and DRECAM/SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France;Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1, Canada
Venue:
Fundamenta Informaticae - Special issue on cellular automata
Year:
2002

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Abstract

A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their flow diagrams are determined. Various examples are presented and applications to car traffic are indicated. Two nontrivial three-state three-input self-conjugate rules have been found. They can be used to model the dynamics of random walkers.