I would like to do something like CellularAutomaton[10, {1, 0, 0, 0, 0}, 2^5], but instead of running for 2^5 steps, it should stop as soon as a configuration has been seen twice, and report the number of such steps taken. Is it possible to do this?
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2 Answers
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You can use the one-step functional version with NestWhileList:
NestWhileList[CellularAutomaton[30, #] &, {1, 0, 0, 0, 0}, UnsameQ, All]
{{1, 0, 0, 0, 0}, {1, 1, 0, 0, 1}, {0, 0, 1, 1, 1}, {1, 1, 1, 0, 0}, {1, 0, 0, 1, 1}, {0, 1, 1, 1, 0}, {1, 1, 0, 0, 1}}
For the number of steps taken until a configuration repeats:
Length @ %
7
Note: In general, CellularAutomaton[rule, init, n] can also be obtained by nesting the one-step functional version using NestList[CellularAutomaton[rule, #]&, init, n]:
CellularAutomaton[30, {0, 0, 1, 0, 0}, 2^5] ==
NestList[CellularAutomaton[30, #] &, {0, 0, 1, 0, 0}, 2^5]
True
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1$\begingroup$ One could use
UnsameQinstead ofDuplicateFreeQ @ {##} &in the third argument. $\endgroup$ Oct 17, 2018 at 1:20 -
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Clear[f]
f[state_] := f[f[state] = CellularAutomaton[30, state]]
{f[{1, 0, 0, 0, 0}], Length@DownValues[f]}
{{0, 0, 1, 1, 1}, 7}
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$\begingroup$ Interesting solution! This looks a bit like Floyd's algorithm. $\endgroup$ Oct 19, 2018 at 14:40