The Design of Reversible Cellular Automata

Reversible cellular automata are not terribly easy to design. If you pick an automata at random, the chances that it will be a reversible one are likely to be negligable.

There are several techniques which allow reversible automata to be constructed from irreversible ones:

Toffoli (1977) showed that every n dimensional automata can be effectively embedded in a n+1 dimensional reversible one.

There are also methods of constructing automata of the same dimension - though normally the properties of the original automata are lost.

These techniques are typically not very useful if you are trying to construct a reversible automata with a particular set of properties.

There are a couple of interesting techniques: