Conway's Game of Life
Four rules. A grid of cells. Emergent complexity.
What is this?
In 1970, the mathematician John Horton Conway designed a "game" with no players, no objectives, and no winner. You set up an initial pattern of live cells on a grid, press start, and watch what happens.
From rules simple enough to fit on a napkin, you get behaviour rich enough that mathematicians have spent half a century cataloguing its menagerie of patterns — gliders that crawl, oscillators that pulse, "guns" that fire infinite streams, and configurations elaborate enough to simulate a Turing machine.
The four rules
Every cell is either alive or dead. At each tick, every cell looks at its eight neighbours and updates simultaneously. The center cell in each diagram shows what happens next.
Patterns worth knowing
The Glider
Five cells that march diagonally forever, cycling through four shapes. The unofficial emblem of the hacker community.
The Gosper Glider Gun
The first pattern proven to grow without bound. Fires a brand-new glider every thirty generations — forever. Won Bill Gosper a $50 prize from Conway in 1970.
The Pulsar
A symmetric oscillator that cycles between three shapes with a period of three. Among the most common large oscillators that appear from random soup.
The Spaceship
A larger structure that glides horizontally. Demonstrates straight-line movement, not just diagonal.
The R-Pentomino
Only five cells. But it churns chaotically for 1,103 generations before stabilising. The classic example of how a trivial seed produces overwhelming complexity.
Why it matters
The Game of Life is the canonical demonstration of emergence: the way simple, local rules — nothing more than "look at your neighbours and count" — can produce behaviour that is, in any meaningful sense, unpredictable. You cannot stare at the rules and deduce the existence of gliders. Gliders just happen.
It's a proof of concept for the idea, central to so much of modern science, that complexity does not require a complex cause. A handful of rules and a grid are enough to produce an entire universe.
About the visualization
Cells are colour-coded by age: cyan when freshly born, drifting through blue and violet as they mature, settling into amber if they survive past thirty generations.
The grid wraps around at the edges — the top is connected to the bottom, the left to the right. Mathematicians call this a torus. The history scrubber lets you rewind up to 500 generations.