S. Wolfram has in has book \"A New Kind of Science\" listed 256 simple rules of

Question

S. Wolfram has in has book "A New Kind of Science" listed 256 simple rules of cellular automata. Which of these rules could via iteration essentially contribute to render an input sequence more random in a certain sense?

Rule 170, for examples, simply produces a left shift and evidently is not of use in this, if I don't err. My limited computations with inputs that are more or less random seem to indicate that the majority of the 256 rules are even contraproductive in this context. How could one best proceed to clarify this issue or are there already relevant published results available?

Explanation / Answer

Rule 30 is probably the "most random" of all 256 rules. It has been used as random number generator, but there are some issues:

Some initial states will result in repetitive output, which is not what we want from a random number generator. However, given that the automaton is large enough, and that the initial state is itself somewhat random, this shouldn't a problem.

There are better ways to generate random numbers.

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