Cellular Automata Parameters

• Bright green cells are closer, violet cells are further away, along the line of sight into the screen.

• Cell states: Binary -- "1" (alive, colored, and opaque). "O" (empty, black and transparent).

• Cell geometry: 3-D Cubic Close-Packed (Buckminster Fuller's "Vector Equilibrium"). The center cell is surrounded by 12 identical neighbors, which are located at the vertices of a cuboctahedron.

• This automaton has 50 unique patterns of live cells possible around the central atom. Each pattern corresponds to a rule specifying the state of the central cell in the next generation. Thus the number of possible rule-sets: is 2^50 = 1.1258999 x 10^15 = 1,125,899,900,000,000.

• Cell array typical size: 100 x 100 x 100 cells (1 million cells). Edges are wrapped in all 3 dimensions, corresponding to a finite but unbounded 4-dimensional hyper-torus universe.

• The initial "seed" population is often a random distributions of thousands of "1" values (alive) sprinkled throughout a universe originally filled with "0" values (dead/empty), with an adjustable overall occurrence of "1" (typically about 11%). Alternatively, predermined seeds can be pre-loaded, consisting of a few to hundreds of live cells.

• Most rule-sets are uninteresting, either dying or overpopulating quickly, or producing structureless chaos, or giving static ("still-life") or simple repeating ("blinker") patterns. A very small minority of rule-sets seem to provide examples of Wolfram's "Class IV" behavior, producing complex localized structures, sometimes long-lived. Moving "spaceships" have been spotted in many rule-sets. The unusual (to human experience) images produced by CA are often unpredicatble and surprising, and sometimes beautiful.

• I wrote my code in the PHP 8.1 langauge (since I already knew it), but plan to translate it to Python soon. The code runs within the Safari browser on my MacBook Pro (MacOS Monterey 12.2.1), using Atari for the server. The graphics for each video takes about 8 minutes to compute.

index.htm   updated 2022.04.11