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 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...
|
