Cellular automaton rules conserving the number of active sites
adap-org
2009-10-30 v2 Adaptation and Self-Organizing Systems
Abstract
This paper shows how to determine all 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 pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.
Cite
@article{arxiv.adap-org/9712003,
title = {Cellular automaton rules conserving the number of active sites},
author = {Nino Boccara and Henryk Fuks},
journal= {arXiv preprint arXiv:adap-org/9712003},
year = {2009}
}
Comments
14 pages, 5 figures