A two-layer representation of four-state reversible number-conserving 2D cellular automata

We present a novel representation of 1D reversible and number-conserving cellular automata with four states. Carrying this view over to two dimensions, we are able to construct 65 four-state reversible and number-conserving 2D cellular automata with the von Neumann neighborhood. A clever use of the split-and-perturb decomposition of number-conserving CAs allows to prove by elimination that this list is complete.