The Cook Book
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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