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The “replicator” cellular automaton

An interesting life-like cellular automaton is B1357/S1357. Nicknamed “Replicator”, this automaton will produce an infinite number of copies of any small initial figure. Below, this rule is applied to a rasterised version of the capital Latin letter “A”:

The “Replicator” cellular automaton applied to the letter A.

The simulation is run for 96 iterations. At each multiple of 16, the state consists of a number of perfect copies of the initial letter. (At the remaining multiples of 8, the state consists of a mixture of perfect and distorted copies.) To confirm that this is indeed a general phenomenon (and not something that requires the precise shape of the letter “A”), let us redo the experiment using a (rasterisation of a) benzene ring as the initial figure:

The “Replicator” cellular automaton applied to a benzene ring.

(Of course, the “chemical formulae” formed, consisting of adjoined benzene rings, are not valid.)

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