A Construction Method of Moore Neighborhood Number-Conserving Cellular Automata

A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total of the numbers (states) of all cells of a global configuration is conserved throughout its computing process. It can be thought to be a kind of modelization of the physical conservation law of mass or energy. In this paper, we show a sufficient condition for a Moore neighborhood CA to be number-conserving. According to this condition, the local function of rotation-symmetric NCCA is expressed by a summation of quaternary functions. On this framework, we construct a 6-state logically universal NCCA.