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Yet having said this, one can ask how one can tell in an actual experiment on some particular system in nature to what extent intrinsic randomness generation is really the mechanism responsible for whatever seemingly random behavior one observed.

The clearest sign is a somewhat unexpected phenomenon: that details of the random behavior can be repeatable from one run of the experiment to another. It is not surprising that general features of the behavior will be the same. But what is remarkable is that if intrinsic randomness generation is the mechanism at work, then the precise details of the behavior can also be repeatable.

In the mechanism where randomness comes from continual interaction with the environment, no repeatability can be expected. For every time the experiment is run, the state of the environment will be different, and so the behavior one sees will also be correspondingly different. And similarly, in the mechanism where randomness comes from the details of initial conditions, there will again be little, if any, repeatability. For the details of the initial conditions are typically affected by the environment of the system, and cannot realistically be kept the same from one run to another.

But the point is that with the mechanism of intrinsic randomness generation, there is no dependence on the environment. And as a result, so long as the setup of the system one is looking at remains the same, the behavior it produces will be exactly the same. Thus for example, however many times one runs a rule 30 cellular automaton, starting with a single black cell, the behavior one gets will always be exactly the same. And so for example the sequence of colors of the center cell, while seemingly random, will also be exactly the same.

But how easy is it to disturb this sequence? If one makes a fairly drastic perturbation, such as changing the colors of cells all the way from white to black, then the sequence will indeed often change, as illustrated in the pictures at the top of the next page.

But with less drastic perturbations, the sequence can be quite robust. As an example, one can consider allowing each cell to be not just black or white, but any shade of gray, as in the continuous cellular automata we discussed on page 155. And in such systems, one can

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