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Recipe for the week of February 20 - 26

Dynamic Formation of a 3-strand Spiral

Already on the Kitchen Shelf are excitable CA dynamics that make tightly-knit spirals, and others that form pasta parades. The former occur when the excitation threshold is sufficiently low that wave ends can wrap easily, whereas macaroni and spaghetti result from an inability of wave fragments to bend into viable spiral cores. There is a delicate intermediate regime in which wave ends bend, but only with great difficulty. In this case a single wave strand is unable to make a tight spiral core, but interaction between several wave ends may give rise to a multi-stranded spiral. Since such an arrangment requires fortuitious interaction, these exotic stable periodic objects tend to form dynamically, often after hundreds or even thousands of cell updates.

Our soup this week is a Greenberg-Hastings Model with range 5 Box neighbor set, threshold 15, and 6 colors. Note the 3-stranded spiral that has formed by chance, now in the process of displacing weaker vortices such as the one at the lower left. Needless to say, this effect is much more intriguing in real-time animation. You will be able to watch a multi-stranded spiral form for yourself by downloading beta release #2 of WinCA, our Windows interactive modeling environment for cellular automata. The new beta will be advertised here in the Kitchen next week. A demo script spomovie.xpt that stabilizes after about 900 steps will be among two dozen experiments included with the release.

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