The Cook Book
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 threedimensional dynamic visualization. The proof is in
this week's pudding: a threedimensional 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 nearestneighbor 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 3d glasses.
 For fun, here is a little of the Forth code that CAM8 understands.
Recalling that a site in the threedimensional 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.
 : annealrule
 #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
