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And indeed when random initial conditions are used, rule 90 does manage to produce random behavior of the kind expected in class 3.

But if there are deviations from perfect randomness in the initial conditions, then these will almost inevitably show up in the evolution of the system. And thus, for example, if the initial density of black cells is low, then correspondingly low densities will occur again at various later steps, as in the second picture below.

With rule 22, on the other hand, there is no such effect, and instead after just a few steps no visible trace remains of the low density of initial black cells.


Examples of evolution from random initial conditions with a low density of black cells. In rule 22 the low initial density has no long-term effect. But in rule 90 its effect continues forever. The reason for this difference is that in rule 22 the randomness we see is intrinsically generated by the evolution of the system, while in rule 90 it comes from randomness in the initial conditions.


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