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The pictures on the next page show an example where this happens. The detailed pattern of black and white cells in these pictures changes at every step. But the point is that the large domains of black and white that form have boundaries which move only rather slowly. And at an overall level these boundaries then behave in a way that looks quite smooth and continuous.

It is still true, however, that at a small scale the boundaries consist of discrete cells. But as the picture below shows, the detailed configuration of these cells changes rapidly in a seemingly random way. And just as in the other systems we have discussed, what then emerges on average from all these small-scale random changes is overall behavior that again seems in many ways smooth and continuous.

Captions on this page:

The behavior of an individual domain of black cells in the cellular automaton shown on the next page. The boundary of the domain exhibits seemingly random fluctuations. But at an overall level, the behavior that is produced seems in many respects quite smooth and continuous. The domain effectively behaves as if it has a surface tension, so that it first evolves to a roughly circular shape, then shrinks eventually to nothing. The main black rectangle is initially 39×29 cells in size.

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