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 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
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