Number Conservation via Particle Flow in One-dimensional Cellular Automata

A number-conserving cellular automaton is a simplified model for system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional automata with kind particle. The output both methods "flow function", describes the movement In first method, puts increasingly stronger restrictions on particle flow until single function specified. There are no dead ends, every choice restriction steps ends flow. second method uses fact that functions be ordered and then form lattice. consists recipe slowest enforces given minimal speed in neighbourhood. All other maxima sets these flows. Other questions, like about nature non-deterministic rules, treated briefly at end.