Efficient enumeration of three-state two-dimensional number-conserving cellular automata

We present a simple approach for finding all number-conserving two-dimensional cellular automata with the von Neumann neighborhood. We demonstrate the efficiency of this approach by enumerating and describing four special cases: totalistic, outer-totalistic, binary and three-state cellular automata. The last result was not published before. We then proceed to find all reversible two-dimensional number-conserving cellular automata with three states with the von Neumann neighborhood and show there are only trivial ones.