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Starting from Randomness

The Emergence of Order

In the past several chapters, we have seen many examples of behavior that simple programs can produce. But while we have discussed a whole range of different kinds of underlying rules, we have for the most part considered only the simplest possible initial conditions—so that for example we have usually started with just a single black cell.

My purpose in this chapter is to go to the opposite extreme, and to consider completely random initial conditions, in which, for example, every cell is chosen to be black or white at random.

One might think that starting from such randomness no order would ever emerge. But in fact what we will find in this chapter is that many systems spontaneously tend to organize themselves, so that even with completely random initial conditions they end up producing behavior that has many features that are not at all random.

The picture at the top of the next page shows as a simple first example a cellular automaton which starts from a typical random initial condition, then evolves down the page according to the very simple rule that a cell becomes black if either of its neighbors are black.

What the picture then shows is that every region of white that exists in the initial conditions progressively gets filled in with black, so that in the end all that remains is a uniform state with every cell black.

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