1999/01/01 by Nino Boccara, Boccara, Nino, Henryk Fukś +3 · 4 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Cellular Automata and Applications #FOS: Physical sciences #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Traffic control and management #adap-org #nlin.AO
paper · pdf · doi:10.48550/arxiv.adap-org/9905004
4 figures
openalex publication_date 1999/05/06 · arxiv created 2000/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.