And as a result, the system one is looking at will be subjected to at least some level of random perturbations from the environment.

But what the pictures on the previous page demonstrate is that when such perturbations are small enough, they will have essentially no effect. And what this means is that when intrinsic randomness generation is the dominant mechanism it is indeed realistic to expect at least some level of repeatability in the random behavior one sees in real experiments.

So has such repeatability actually been seen in practice?

Unfortunately there is so far very little good information on this point, since without the idea of intrinsic randomness generation there was never any reason to look for such repeatability when behavior that seemed random was observed in an experiment.

But scattered around the scientific literature—in various corners of physics, chemistry, biology and elsewhere—I have managed to find at least some cases where multiple runs of the same carefully controlled experiment are reported, and in which there are clear hints of repeatability even in behavior that looks quite random.

If one goes beyond pure numerical data of the kind traditionally collected in scientific experiments, and instead looks for example at the visual appearance of systems, then sometimes the phenomenon of repeatability becomes more obvious. Indeed, for example, as I will discuss in Chapter 8, different members of the same biological species often have many detailed visual similarities—even in features that on their own seem complex and apparently quite random.

And when there are, for example, two symmetrical sides to a particular system, it is often possible to compare the visual patterns produced on each side, and see what similarities exist. And as various examples in Chapter 8 demonstrate, across a whole range of physical, biological and other systems there can indeed be remarkable similarities.

So in all of these cases the randomness one sees cannot reasonably be attributed to randomness that is introduced from the environment—either continually or through initial conditions. And instead, there is no choice but to conclude that the randomness must in fact come from the mechanism of intrinsic randomness generation that I have discovered in simple programs, and discussed in this section.

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