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.Comment: 4 figure