A particle displacement representation for conservation laws in two-dimensional cellular automata

Abstract. The problem of describing the dynamics of a conserved energy in a cellular automaton in terms of local movements of “particles ” (quanta of that energy) has attracted some people’s attention. The one-dimensional case was already solved by Fuks ́ (2000) and Pivato (2002). For the two-dimensional cellular automata, we show that every (context-free) conservation law can be expressed in terms of such particle displacements