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Recipe for the week of November 14 - 20

Short-term Nucleation in the Rug Rule

Here is an interesting soup that I discovered while playing with WinCA, our Windows-based interactive modeling environment for cellular automata. To pick up the first beta version of WinCA look in the kitchen sink. Then you can try cooking for yourself.

For this week's recipe, a specified number of colors are arranged cyclically in a "color wheel." The highest color is inert, a sort of ground state. All other colors update by a small perturbation of modular smoothing. Namely, a color's index is replaced by 1 + the (rounded) average of the indices of its neighbors, modulo the total number of colors. The result is a kind of digital heat equation with nonlinearity. Complex diffusive wave patterns emerge. Patterns reminiscent of Oriental carpets evolve if the initial configuration is simple and symmetric, so this family of CA dynamics is widely known as the rug rule.. A WinCA experiment called rug.xpt produces such a carpet.

To make this week's soup, however, we start the 256-color rug rule from a uniformly random initial configuration using the WinCA palette rainbow.pal, which has a full spectrum of colors culminating with purples and reds for state values up to 216, and then has a black to white grayscale for values 217 through 255. The initial white sites form a random field of inert nucleation centers with density 1/255. Over time, gray blobs aggregate and consolidate around the centers. Cook for 100 updates, or until the blobs achieve optimal heaviosity. Be careful, though, not to let the soup boil over -- an unappetizing gray mush will result.

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