But like many of the processes we have seen in this book, the evolution of the universe no doubt intrinsically generates apparent randomness. And the result is that most aspects of the network that represents the current state of our universe will seem essentially random. … One might however imagine that as a first approximation one could take account of underlying apparent randomness just by saying that there are certain probabilities for particles to behave in particular ways.

And in more recent times sensitivity to initial conditions and quantum randomness have been proposed as more appropriate scientific explanations. But much as in our discussion of randomness in Chapter 6 nothing like this is actually needed. … And the crucial point is that this happens just through the intrinsic evolution of the system—without the need for any additional input from outside or from any sort of explicit source of randomness.

Cosmology and the Second Law In the standard big bang model it is assumed that all matter in the universe was initially in completely random thermal equilibrium. But such equilibrium implies uniformity, and from this it follows that the initial conditions for the gravitational forces in the universe must have been highly regular, resulting in simple overall expansion, rather than random expansion in some places and contraction in others. As I discuss on page 1026 I suspect that in fact the universe as a whole probably had what were ultimately very simple initial conditions, and it is just that the effective rules for the evolution of matter led to rapid randomization, whereas those for gravity did not.

Ocean surfaces At low wind speeds, regular ripples are seen; at higher wind speeds, a random pattern of creases occurs. It seems likely that randomness in the wind has little to do with the behavior of the ocean surface; instead it is the intrinsic dynamics of the water that is most important.

Rule 45 The center column of the pattern appears for practical purposes random, just as in rule 30. The left edge of the pattern moves 1 cell every 2 steps; the boundary between repetition and randomness moves on average 0.17 cells per step.

In the other cases, the fluctuations are more complicated, and seem in many respects random.

[No text on this page] An example of a sequential substitution system that yields apparently random behavior.

Some small-scale structure is visible, but on a larger scale the pattern seems for all practical purposes random.

But even after all these steps there are no signs of overall regularity—and indeed even continuing for a million steps many aspects of the pattern obtained seem perfectly random according to standard mathematical and statistical tests.

[No text on this page] A Turing machine that exhibits behavior which seems in many respects random.