Here are clusters grown after 512 steps, starting with a single seed in the upper-left corner. The color cycles every 86 steps. Shown are five different rules, depending on how many neighbors you need in the cluster in order for your site to be added. In other words, we are trying to color the cells of the cubic lattice with three different colors, so that cells are colored differently from each of their six neighbors. However, here there are still neighboring pairs of the same color, and these pairs form loops analogous to smoke rings or cosmic strings.
Horizontal dominoes are red or green, depending on parity, and vertical ones are blue or yellow.
Aztec diamond, 256x256 and 512x512 Stop sign, 256x256 and 512x512 Quantum random walks Quantum random walks consist of a diffusive process which is unitary rather than stochastic. Here are some random walks on a two-dimensional lattice. Note the beautiful interference effects in the interior. Copyright 2000 by Cris Moore. All rights reserved.