  Invertible cellular automata are useful as models of physical systems with
microscopically revesible dyanmics. There are several well-understood ways to
construct them: partitioning rules, second-order rules, and alternating-grid
rules. We present another way (a generalization of the alternating-grid
approach), based on the idea that a cell may either transmit information to its
neighbors or receive information from its neighbors, but not both at the same
time. We also examine an interesting simple example of this class of rules, one
with an additive conserved "energy".

Cellular Automata and Lattice Gases