But my purpose here is to explore what kinds of systems can be reversible. And of the 256 elementary cellular automata with two colors and nearest-neighbor rules, only the six shown below turn out to be reversible. And as the pictures demonstrate, all of these exhibit fairly trivial behavior, in which only rather simple transformations are ever made to the initial configuration of cells.
So is it possible to get more complex behavior while maintaining reversibility? There are a total of 7,625,597,484,987 cellular automata with three colors and nearest-neighbor rules, and searching through these one finds just 1800 that are reversible. Of these 1800, many again exhibit simple behavior, much like the pictures above. But some exhibit more complex behavior, as in the pictures below.