Number-conserving cellular automaton rules

Nino Boccara; Henryk Fuks

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arXiv · adap-org/9905004

Number-conserving cellular automaton rules

Nino Boccara·Henryk Fuks

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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.

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Nino Boccara, Henryk Fuks. 2000-05-17. Number-conserving cellular automaton rules. https://arxiv.org/abs/adap-org/9905004

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