effect on overall patterns of flow, one cannot realistically attribute the large-scale randomness that one sees in a turbulent fluid to randomness that exists at the level of individual particles.

Instead, what seems to be happening is that intrinsic randomness generation occurs directly at the level of large-scale fluid motion. And as an example of a simple approach to modelling this, one can consider having a collection of discrete eddies that occur at discrete positions in the fluid, and interact through simple cellular automaton rules.

The picture below shows an example of what can happen. And although many details are different from what one sees in real fluids, the overall mixture of regularity and randomness is strikingly similar.

One consequence of the idea that there is intrinsic randomness generation in fluids and that it occurs at the level of large-scale fluid motion is that with sufficiently careful preparation it should be possible to produce patterns of flow that seem quite random but that are nevertheless effectively repeatable—so that they look essentially the same on every successive run of an experiment.

And even if one looks at existing experiments on fluid flow, there turn out to be quite a few instances—particularly for example involving interactions between small numbers of vortices—where there are known patterns of fluid flow that look intricate, but are nevertheless essentially repeatable. And while none of these yet look complicated enough that they might reasonably be called random, I suspect that in time similar but vastly more complex examples will be found.

Among the patterns of fluid flow on page 377 each has its own particular details and characteristics. But while some of the simpler ones have been captured quite completely by methods based on traditional mathematical equations, the more complex ones have not. And in fact from the perspective of this book this is not surprising.

But now from the experience and intuition developed from the discoveries in this book, I expect that there will in fact be remarkably simple programs that can be found that will successfully manage to reproduce the main features of even the most intricate and apparently random forms of fluid flow.

A cellular automaton (rule 225) whose behavior is reminiscent of turbulent fluid flow.

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