CELLULAR-AUTOMATON RULES CONSERVING THE NUMBER OF ACTIVE-SITES

This paper shows how to determine ail of the unidimensional two-state cellular automaton rules of a given number of inputs which conserve th e 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 evol ution operators of systems of identical interacting particles whose to tal number is conserved. Some of these rules, which allow motion in bo th directions, mimic ensembles of one-dimensional pseudorandom walkers . Numerical evidence indicates that the corresponding stochastic proce sses might be non-Gaussian.