Number-conserving cellular automata with a von Neumann neighborhood of range one
Barbara Wolnik, Adam Dzedzej, Jan Marcel Baetens, Bernard De Baets · Journal of Physics A Mathematical and Theoretical · 2017
Abstract We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions.