The Cook Book
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.