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Recipe for the week of April 10 - 16

A DLA crystal: answer to last week's puzzle, NOT

Several visitors to the kitchen last week suggested that the mystery algorithm for the title graphic at http://www.cs.vu.nl/~jprins/tp.html might be a form of diffusion limited aggregation (DLA). This famous model for dendritic growth goes back to a 1981 paper of Witten and Sander. One starts with a single 'sticky' particle at the origin, say, surrounded by a lattice gas of diffusing particles. Each time a gas particle lands on a site that neighbors a sticky site it stops and joins the sticky cluster. There are many ways to model a lattice gas as a CA. One simple rule with random dynamics has the particles undergo simple random walks with exclusion. See the CAM8 Applications page in the Kitchen Sink for an alternative deterministic CA implementation. A slightly more tractable mathematical variant of the Witten-Sander rule has the gas particles 'line up at infinity' and diffuse one by one until they stick.

I thought I'd offer a CAM-generated DLA crystal this week. Our graphic shows the result of a lattice gas simulation after all surrounding particles within the array have joined the crystal. The boundary has been painted white to highlight its dendritic structure.

There are certainly some qualitative similarities between this image and last week's Turbo Page puzzle, as pointed out by our visitors. But there is also a fundamental structural difference that argues against external aggregation as the puzzle's solution. Can you find it? Next week we'll serve up a basic quasi-fractal soup with ingredients much closer to those of tp.gif...

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