The rule used—that I call rule 30—is of exactly the same kind as before, and can be described as follows. First, look at each cell and its right-hand neighbor. If both of these were white on the previous step, then take the new color of the cell to be whatever the previous color of its left-hand neighbor was. Otherwise, take the new color to be the opposite of that.
The picture shows what happens when one starts with just one black cell and then applies this rule over and over again. And what one sees is something quite startling—and probably the single most surprising scientific discovery I have ever made. Rather than getting a simple regular pattern as we might expect, the cellular automaton instead produces a pattern that seems extremely irregular and complex.
But where does this complexity come from? We certainly did not put it into the system in any direct way when we set it up. For we just used a simple cellular automaton rule, and just started from a simple initial condition containing a single black cell. —Stephen Wolfram, A New Kind of Science
