Chapter 7: Mechanisms in Programs and Nature

Section 5: The Intrinsic Generation of Randomness

Cellular automata [as randomness generators]

From the discussion here it should not be thought that in general there is necessarily anything better about generating randomness with cellular automata than with systems based on numbers. But the point is that the specific method used for making practical linear congruential generators does not yield particularly good randomness and has led to some incorrect intuition about the generation of randomness. If one goes beyond the specifics of linear congruential generators, then one can find many features of systems based on numbers that seem to be perfectly random, as discussed in Chapter 4. In addition, one should recognize that while the complete evolution of the cellular automaton may effectively generate perfect randomness, there may be deviations from randomness introduced when one constructs a practical random number generator with a limited number of cells. Nevertheless, no such deviations have so far been found except when one looks at sequences whose lengths are close to the repetition period. (See however page 603.)

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