N. Boccara et H. Fuks, CELLULAR-AUTOMATON RULES CONSERVING THE NUMBER OF ACTIVE-SITES, Journal of physics. A, mathematical and general, 31(28), 1998, pp. 6007-6018
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.