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A rose-producing cyclic cellular automaton

In addition to the generalisations to the standard cyclic cellular automaton we saw yesterday, it is natural to investigate what happens if you increase a cell’s value not by one, but by two, three, or more every time it should be updated (not altering the condition). It turns out, at least for N = 24 states and the standard threshold (1), that you obtain rounded square spirals if you increase by two instead of by one:

The final state of the cyclic cellular automaton with increment two.

If you increase the increment to three, you make roses:

An intermediate step of the cyclic cellular automaton with increment three, showing roses.

Eventually the roses cover the entire region:


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