Three-dimensional Rotation-symmetric Number-conserving Cellular Automata
Barbara Wolnik, Nikodem Mrozek, Adam Dzedzej and Bernard De Baets
We study three-dimensional rotation-symmetric cellular automata with the von Neumann neighborhood that conserve the sum of states. We show that any non-trivial such automaton requires at least seven states, which agrees with intuition based on the known results for the one and two-dimensional cases. We also give a full characterization of these cellular automata with a seven-element state set and the result is quite surprising.