Time Reversible Cellular Automata

I’ve just finished reading Greg Egan’s Permutation City. As ever, he is way out there, describing (amongst other things) a massive cellular automata universe, the rules of which are such that it can act as interesting ‘toy model’ of our world. The simple rules of the individual cells providing the sub-atomic structure that on bigger scales gives rise to atoms, molecules, gravity, and ultimately evolution. Entertaining and imaginative.

It caused me to wonder if the rules of cellular automata can be made time reversable while remaining interesting. It turns out that this is a very interesting question. If you click on the title of this item you can find out that

  • The forward and reverse rules have to be different otherwise the output is ‘trivial’.
  • Some CA’s demonstrate properties that resemble the Second Law of Thermodynamics (Increasing disorder.)
  • Though so far none of these also have the first law. (Conservation of ‘Energy’)
  • Steven Wolfram’s rule 37R is not trivial and it doesn’t evolve to random equilibrium.
  • Steven Wolfram thinks perhaps our universe might be one of these type
  • so perhaps the 2nd law isn’t true for this universe

Plenty more to find out in Stephen Wolfram’s New Kind of Science, a 1,000 page tome I’ve been meaning to read for ages.


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