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Recipe for the week of November 28 - December 4

Fossil Record in a Cyclic Cellular Automaton

Well this week I'm trying to beat a deadline on a million dollar grant proposal, so this will have to be brief! The soup is a 4-color Cyclic Cellular Automaton (CCA) with a range 2 Box neighborhood, and threshold 9 for updating to the next color in the cycle. The threshold is so high that flat wave fronts are barely able to advance, and so the dynamics are nearly convex-confined. Starting from a uniform configuration, this soup was created by a CAM6 processor, on an array of nearly one million cells, after 100,000 updates. Unfortunately our software for CAM6 did not permit dynamic visualization on large arrays, so we have no idea how the complex "fossils" etched in the image arise and evolve. Hopefully our new and much more flexible CAM8 machine (cf. the MIT page referenced in the Kitchen Sink) will shed more light on the process...

For more about the mathematics behind Cyclic Cellular Automata, and an extensive classification of their phenomenology, see R. Fisch, J. Gravner and D. Griffeath, "Threshold-Range Scaling of Excitable Cellular Automata." Statistics and Computing 1 (1991), 23-39. That article contains numerous color graphics, cutoff tabulations, and phase diagrams for both CCA and GH dynamics.

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