Other reversible systems

Reversible examples can be found of essentially all the types of systems discussed in this book. Reversible mobile automata can for instance be constructed using

Table[(IntegerDigits[i, 2, 3]  If[First[#]  0, {#, -1}, {Reverse[#], 1}]&)[IntegerDigits[perm〚i〛, 2, 3]], {i, 8}]

where perm is an element of Permutations[Range[8]]. An example that exhibits complex behavior is:

Systems based on numbers are typically reversible whenever the mathematical operations they involve are invertible. Thus, for example, the system on page 121 based on successive multiplication by 3/2 is reversible by using division by 3/2. Page 905 gives another example of a reversible system based on numbers.

Multiway systems are reversible whenever both a  b and b  a are present as rules, so that the system corresponds mathematically to a semigroup. (See page 938.)