Number-conserving cellular automaton rules

Issue title: Cellular Automata

Article type: Research Article

Authors: Boccara, Nino^; | Fukś, Henryk

Affiliations: Department of Physics, University of Illinois, Chicago, USA | DRECAM/SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France | Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1, Canada

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.

Keywords: number-conserving systems, interacting particles, highway traffic, random walks

Journal: Fundamenta Informaticae, vol. 52, no. 1-3, pp. 1-13, 2002