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Does this 2D cellular automaton have a known name and history?

  • n colors (numbered 1 to n), assigned randomly at the start.
  • For each generation, every cell that has at least one neighbour cell with a color that is one higher changes its color to that "next higher" color. Additionally, the "lowest" color is considered "next higher" to the highest one.
  • Emergent behaviour shows up best around n=16, disappears for much higher or much lower n

I have it implemented on my website so you can see it in action.

I saw this ages ago and always remembered it as a great example of emergent behaviour, but can't remember what it was called, and couldn't find it on Wikipedia or Wolfram Mathworld.

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Sounds familiar but I can't quite place it off the top of my head. Places to look would be the chapters on cellular automata in Gale's "Tracking the automatic ant", and of course Gardner's books and perhaps Hofstadter's collections from Sci Am. –  Alon Amit Apr 5 '10 at 22:39
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1 Answer

up vote 6 down vote accepted

Cyclic cellular automaton

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So obvious when you know it... Thanks! –  Michael Borgwardt Apr 5 '10 at 23:06
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