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Recipe for the week of October 31 - November 6

The Cyclic Particle System

A prescribed number of colors N are arranged cyclically in a "color wheel." Each color can only be replaced (eaten) by its successor (mod N). Cell x chooses a site y at random from its four nearest neighbors in the two-dimensional array (with wrap-around at the boundaries). If the color at y can eat the color at x it does; i.e., site x is painted with the color from y next time. From a completely random initial configuration this probabilistic interaction nucleates wave activity that self-organizes into a very stable steady state of spirals.

The current graphic depicts the equilibrium of a 12-color cyclic particle system, started from uniform randomness and run for many thousands of updates. The computations were performed using a CAM6 Cellular Automaton Machine from MIT. The original array contained more than 3 million cells. A videotape of this dynamic has been produced by the Pittsburgh Supercomputer Center. An expository article describing the discovery of the rule appeared in the December 1988 "Computers and Mathematics" column of the Notices of the American Mathematical Society.

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