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the behavior of a system. But as we discussed, there is in most practical situations a limit on the lengths of sequences whose randomness can realistically be attributed to such a mechanism. With intrinsic randomness generation, however, there is no such limit: in the cellular automaton above, for example, all one need do to get a longer random sequence is to run the cellular automaton for more steps.

But it is also possible to get long random sequences by continual interaction with a random external environment, as in the first mechanism for randomness discussed in this chapter.

The issue with this mechanism, however, is that it can take a long time to get a given amount of good-quality randomness from it. And the point is that in most cases, intrinsic randomness generation can produce similar randomness in a much shorter time.

Indeed, in general, intrinsic randomness generation tends to be much more efficient than getting randomness from the environment. The basic reason is that intrinsic randomness generation in a sense puts all the components in a system to work in producing new randomness, while getting randomness from the environment does not.

Thus, for example, in the rule 30 cellular automaton discussed above, every cell in effect actively contributes to the randomness we see. But in a system that just amplifies randomness from the environment, none of the components inside the system itself ever contribute any new randomness at all. Indeed, ironically enough, the more components that are involved in the process of amplification, the slower it will typically be to get each new piece of random output. For as we discussed two sections ago, each component in a sense adds what one can consider to be more inertia to the amplification process.

But with a larger number of components it becomes progressively easier for randomness to be generated through intrinsic randomness generation. And indeed unless the underlying rules for the system somehow explicitly prevent it, it turns out in the end that intrinsic randomness generation will almost inevitably occur—often producing so much randomness that it completely swamps any randomness that might be produced from either of the other two mechanisms.

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