Chapter 5: Two Dimensions and Beyond

Section 2: Cellular Automata

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The pictures below show the upper-right quadrant for more steps. Most of the lines visible are 8 cells across, and grow by 4 cells every 12 steps. They typically survive being hit by more complicated growth from the side. But occasionally runners 3 cells wide will start on the side of a line. And since these go 2 cells every 3 steps they always catch up with lines, producing complicated growth, often terminating the lines.

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