The Cook Book
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 WittenSander
rule has the gas particles 'line up at infinity' and diffuse one by one
until they stick.
 I thought I'd offer a CAMgenerated 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 quasifractal soup with ingredients much closer to
those of tp.gif...
