Registered: Jan 2004
Posts: 350

If you look at the first 256 steps of output from the elementary 4 color modulistic cellular automaton for rule 52, you might expect that rule 52’s behavior is a classic case of simple nesting.

And that is true so far as it goes. But let the cellular automaton run past step 256 and you are in for a big surprise.

Attached is a graphic of the first 1800 steps. I have run the cellular automaton 1,100,000 steps without finding any cycle.

Lawrence J. Thaden has attached this image:

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L. J. Thaden

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Registered: Jun 2005
Posts: 39

I am sure that:

The number of states < or = 4^256.

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If something is zero, and zero is nothing, then something must be nothing.

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