A cellular automaton is a grid of cells, each looking at its neighbours at every step and deciding what to become by one fixed rule. Out of this grow Sierpiński triangles, spiral waves, mazes and “creatures” crawling about.
How it works
“Elementary 1D” is a row of cells, 0 or 1. A cell's new value depends on itself and its two neighbours: eight cases, whose eight answers form the bits of the rule number, 0 to 255. Each generation is drawn a row below the last: a space-time diagram.
In the “cyclic” automaton N colours stand in a circle, and a cell moves on to the next colour when enough neighbours already have it. Each colour preys on the one before, and random noise self-organises into spiral waves, as in the Belousov–Zhabotinsky reaction.
In Life, B/S lists how many live neighbours out of eight bring a dead cell to life (B) and keep a live one alive (S). Generations rules add dying states: a cell fades over several steps and cannot be reborn meanwhile.
A bit of history
In the late 1940s John von Neumann, with Stanisław Ulam, built a self-reproducing automaton on a cell grid; it needed 29 states. In October 1970 Martin Gardner described John Conway's Life in Scientific American, and that same year Bill Gosper found a “gun” firing gliders forever; gliders were later wired into a universal computer. From 1983 Stephen Wolfram surveyed all 256 elementary rules, work that culminated in A New Kind of Science (2002). Rule 30 is so chaotic that Mathematica used it to generate random numbers, and its pattern clads Cambridge North station. Matthew Cook proved rule 110 universal: it can compute anything computable. David Griffeath studied the cyclic automaton in the late 1980s; Brian Silverman invented Brian's Brain.
What to tweak
- With “Automaton” “elementary 1D”, “1D rule” 90 and “Start” “centre” grow a Sierpiński triangle from one cell; 30 gives chaos, 110 moving structures on a periodic background.
- For cyclic spirals try “States” 14, “Neighbourhood range” 1, “Threshold” 1 and a von Neumann “Neighbourhood”.
- “Life rule” set to “Maze” grows corridors out of noise; “Coral” is best grown from the centre.
- “Colouring” “history” leaves melting trails behind dying cells; “Cell shape” “circles” plus a “Gap” makes an LED board.
- Animated, the 1D automaton scrolls up like a chart recorder, and Brian's Brain under the “Kaleidoscope” effect becomes a living ornament.
Reaction–diffusion
Physarum
Venation