Cellular automaton rules conserving the number of active sites

1997/12/31 by Nino Boccara, Henryk Fukś, Henryk Fuks · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #DNA and Biological Computing #Mathematical Dynamics and Fractals #adap-org #nlin.AO

paper · pdf · doi:10.1088/0305-4470/31/28/014

published as J. Phys. A: Math. Gen. 31, 6007-6018 (1998) · 14 pages, 5 figures

openalex publication_date 1998/07/17 · arxiv created 1998/08/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper shows how to determine all of the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudorandom walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.

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• Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system
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