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The “Persian rugs” cellular automaton

The life-like cellular automaton B234/S is known as “Persian rugs” or “Serviettes” because of the beautiful patterns it creates when the initial seed is a small, symmetric figure. Below, this automaton is run for 99 generations on a 200×200 grid with a central 2×2 square as the initial state. A family of lovely carpets of increasing size is obtained.

An animation showing 99 square patterns of increasing size.

Among these patterns, some personal favourites are the following:

Generation 70:

A picture of generation 70.

Generation 73:

A picture of generation 73.

Generation 80:

A picture of generation 80.

Generation 97:

A picture of generation 97.

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