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## Fluid Flow

A great many striking phenomena in nature involve the flow of fluids like air and water—as illustrated on the facing page. Typical of what happens is what one sees when water flows around a solid object. At sufficiently slow speeds, the water in effect just slides smoothly around, yielding a very simple laminar pattern of flow. But at higher speeds, there starts to be a region of slow-moving water behind the object, and a pair of eddies are formed as the water swirls into this region.

As the speed increases, these eddies become progressively more elongated. And then suddenly, when a critical speed is reached, the eddies in effect start breaking off, and getting carried downstream. But every time one eddy breaks off, another starts to form, so that in the end a whole street of eddies are seen in the wake behind the object.

At first, these eddies are arranged in a very regular way. But as the speed of the flow is increased, glitches begin to appear, at first far behind the object, but eventually throughout the wake. Even at the highest speeds, some overall regularity nevertheless remains. But superimposed on this is all sorts of elaborate and seemingly quite random behavior.

But this is just one example of the very widespread phenomenon of fluid turbulence. For as the pictures on the facing page indicate—and as common experience suggests—almost any time a fluid is made to flow rapidly, it tends to form complex patterns that seem in many ways random.

So why fundamentally does this happen?

Traditional science, with its basis in mathematical equations, has never really been able to provide any convincing underlying explanation. But from my discovery that complex and seemingly random behavior is in a sense easy to get even with very simple programs, the phenomenon of fluid turbulence immediately begins to seem much less surprising.

But can simple programs really reproduce the particular kinds of behavior we see in fluids? At a microscopic level, physical fluids consist of large numbers of molecules moving around and colliding with each other. So as a simple idealization, one can consider having a large number of particles move around on a fixed discrete grid, and undergo collisions governed by simple cellular-automaton-like rules.

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