Chapter 9: Fundamental Physics

Section 2: The Notion of Reversibility

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[permi, 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.)

From Stephen Wolfram: A New Kind of Science [citation]