Conservation Laws in Rectangular CA
Tim Boykett, Jarkko Kari and Siamak Taati
A 1D Reversible Cellular Automata (RCA) with forward and backward radius-1 2 neighborhoods is called Rectangular. It was previously conjectured that the conservation laws in 1D Rectangular RCA can be described as linear combinations of independent constant-speed flows to the right or to the left. This is indeed the case; so is a similar statement about a more general class of Rectangular RCA in any dimension.