Technique · Simulations
Cellular automata
Life, Brian's Brain, cyclic spirals and excitable-medium waves: a grid of cells updated by a rule that looks only at neighbours.
Cellular automata is a simulation that evolves step by step. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Cellular automata were first studied by John von Neumann and Stanislaw Ulam in the 1940s, as a way to ask whether a machine could build a copy of itself; the grid and its simple rules were Ulam's idea.
- Stephen Wolfram sorted the behaviour of cellular automata into four classes: those that settle at once, those that repeat, those that look random, and the rare ones that make lasting, moving structures, the class that Life belongs to.
- John Conway devised the Game of Life in 1970 and Martin Gardner described it in Scientific American that October; Conway called it a game with no players, because you choose a start and then only watch.
- Life's patterns have names: still lifes such as the block and the beehive never change, oscillators such as the blinker flip between shapes, and spaceships such as the glider crawl across the grid, one cell diagonally every four steps.
- Conway tuned the rules by hand, with counters on a Go board, looking for a game in which it was hard to tell what a pattern would do and in particular whether it would grow without limit.
- Because Life is universal, its gliders, guns and other patterns can be arranged to build a computer: in 2000 Paul Rendell built a Turing machine inside it.
- Bill Gosper found the first glider gun in 1970, a pattern that fires a glider every thirty steps for ever, and so showed that Life patterns can grow without limit.
The mathematics
- Each cell has eight neighbours, so there are 512 possible local situations (its own state and the eight around it), and the rule gives a fixed answer to each; everything seen here follows from that table.
- All cells change at the same instant, a synchronous update, so the whole grid is a function applied again and again, and the same start always gives the same history, apart from the random sparks.
- The ghosts are not part of the rule at all: a second number on each cell fades after the cell dies, and only the picture uses it.
In art
- Life and its relatives have been used for pixel-art animations, screensavers and music; the free program Golly collects thousands of patterns people have found.
- Spiral waves like these have been photographed in chemical dishes, in slime mould colonies and in heart tissue, and the pictures all look like each other, which is why the simple model is so convincing.
More ways to use it
Related techniques
Reaction-diffusion · Sandpile · Grain growth · Slime mould · Flocking boids · Attractor cloud · Elementary automaton · Synchrony