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Cellular automaton producing a nested pattern from random initial conditions

Another example of a cellular automaton that produces a nested pattern even from random initial conditions. The particular rule shown involves next-nearest as well as nearest neighbors and has rule number 4067213884. As in rule 184, the nested behavior seen here is most obvious when the density of black and white cells in the initial conditions is equal.

From Stephen Wolfram: A New Kind of Science [citation]