But what the pictures on the facing page demonstrate is that even in a completely closed system, where no information at all is allowed to escape, a system like rule 37R still does not follow the uniform trend towards increasing randomness that is suggested by the Second Law.

And indeed what happens is similar to what we have seen many times in this book: the evolution of the cellular automaton generates enough randomness that the effects of the underlying grid tend to be washed out, with the result that the overall behavior produced ends up showing essentially no distinction between different directions in space.

And in fact, as I mentioned at the end of the previous section , what I expect instead is that there will always tend to be all sorts of complicated and seemingly random behavior at small scales—though at larger scales this will typically get washed out to yield the kind of consistent average properties that we ordinarily associate with space.

Probably the situation is somewhat analogous to what we saw with fluid behavior in cellular automata in Chapter 8 —that at least if there are underlying rules whose behavior is complicated enough to generate significant effective randomness, then almost whenever the rules lead to conservation of total particle number and momentum something close to the ordinary Navier–Stokes equation behavior emerges.

If we can find no simple features whatsoever—as in the case of perfect randomness—then we tend to lose interest.

Beyond randomness, the last example in the previous chapter was rule 110: a cellular automaton whose behavior becomes partitioned into a complex mixture of regular and irregular parts.

Class 4 Behavior and Universality If one looks at the typical behavior of rule 110 with random initial conditions, then the most obvious feature of what one sees is that there are a large number of localized structures that move around and interact with each other in complicated ways.

Many possible perturbations to repetitive initial conditions again yield seemingly random behavior.

But as soon as there are more than two pairs things become much more complicated, and as the pictures on the facing page demonstrate, even with very short blocks remarkably long and seemingly quite random sequences can be required in order to satisfy the constraints.

At first biology seems to do better by repeatedly making random modifications to genetic programs, and then applying natural selection.