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Recipe for the week of May 22 - 28

Majority Vote in Space!

Last week I mentioned that the CAM8 mixmaster is the first interactive visualization device with sufficient power and flexibility for effective three-dimensional dynamic visualization. The proof is in this week's pudding: a three-dimensional annealing simulation from CAM8's architects, Norm Margolus and Tom Toffoli at MIT. Cooking takes about 30 seconds.

Here we see rendered a 512 by 512 by 64 (deep) array, in which simulated matter congeals into convexifying and then shriking blobs using a nearest-neighbor randomized majority vote, a kind of thermalized annealing rule. At each step, the state of a cell will tend to agree with the majority of its neighbors. Just as in two dimensions, larger and larger domains form over time. A light and shadow palette effectively conveys some aspects of the spatial geometry. Norm and Tom even have a variant of their code that generates a stereoscopic image suitable for viewing with 3-d glasses.

For fun, here is a little of the Forth code that CAM8 understands. Recalling that a site in the three-dimensional integers has 6 nearest neighbors (not 8 as some of us math folks would prefer), you should be able to figure out the details of the stochastic transition mechanism.

: anneal-rule

#particles {{ 0 0 rand.25 rand.50 rand.50 rand.75 1 1 }}

dup -> north
dup -> south
dup -> east
dup -> west
dup -> up
dup -> down
-> center

rand0 rand1 xor -> rand0
rand1 -> rand1

Take me higher...
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