Conway’s Game of Life
You found it.
Four trivial rules, applied to every cell at once, produce unbounded complexity. From them you can build oscillators, mobile ‘spaceships’, logic gates, glider guns that emit them, and a working universal Turing machine.
Click or drag to paint. The grid wraps at the edges.
Further down the rabbit hole
- Conway’s Game of Life — Wikipedia: rules, history, and why a 4-rule cellular automaton is Turing-complete.
- LifeWiki — encyclopedic catalogue of patterns. Still lifes, oscillators, spaceships, guns, puffers, eaters, reflectors — thousands of them.
- conwaylife.com forums — the research community is still active. New patterns get discovered every week.
- Golly — the high-performance simulator. Uses Hashlife to run universes that would crush the naive algorithm above by many orders of magnitude.
- Paul Rendell’s Universal Turing Machine — a working UTM built inside Life. Glider streams as signals, glider guns as clocks, eaters as gates, all wired into a tape-and-state machine. Load it in Golly and watch it compute. The constructive proof that Life is Turing-complete.
- 0E0P metacell — Adam Goucher’s self-replicating pattern (2018). A von Neumann universal constructor that copies itself from empty space, no background grid required. Decades after Life’s invention before someone actually built one.
- “Life in Life” — the Game of Life simulating itself, via the OTCA metapixel. Sit with this one.
- Hashlife in Python — John Williamson’s pure-Python implementation. The quadtree memoization that makes Golly fast, in code you can read in an evening. (For production use: python-lifelib, by the same author as the 0E0P metacell above.)
- xkcd 2293 — Randall Munroe’s tribute to John Conway, who died of COVID in April 2020.
Built by a glider, for a glider.