Simulations between triangular and hexagonal number-conserving cellular automata

Abstract. A number-conserving cellular automaton is a cellular au-tomaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical conservation laws of mass or energy. In this paper, we first propose a necessary condition for triangular and hexagonal cellular automata to be number-conserving. The local transi-tion function is expressed by the sum of arity two functions which can be regarded as ’flows ’ of numbers. The sufficiency is obtained through general results on number-conserving cellular automata. Then, using the previous flow functions, we can construct effective number-conserving simulations between hexagonal cellular automata and triangular cellular automata. Key words: Cellular automata; Number-conservation.