  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.
