A question from 1970
John Conway (1937 to 2020) was a mathematician at Cambridge who loved puzzles about simple rules that produce surprising results. In 1970 he went after a big one: can a few tiny rules create something that behaves like life, with growth, death and change?
He was building on John von Neumann, who had designed a self-copying machine on a grid in the 1940s and 1950s. Von Neumann's version gave every cell 29 possible states and needed pages of rules. Conway wanted the simplest version that was still interesting.
Start with a grid of cells
Picture graph paper that goes on forever. Each square is a cell, and each cell is either alive or dead. That is the whole world.
Every cell has eight neighbors, the squares that touch it along the sides and at the corners. Everything in the game comes down to counting them.
Decide what a good game needs
Conway set himself three goals. No starting pattern should be easy to prove it grows forever, so the game stays unpredictable. Some patterns should still seem to grow without limit.
And simple patterns should change for a long time before they end in one of three ways: dying out, freezing in place, or repeating forever.
Test rules by hand
Conway and his colleagues tried many rule sets by hand, using black and white stones on a Go board. Above, the same random start runs under three of them.
When cells survive too easily, the board clogs up and freezes. When almost nothing survives, it empties out quickly. Conway's rules sit in the middle and keep the board busy.
The four rules that worked
The balance Conway settled on is written B3/S23. A cell is Born when it has 3 live neighbors, and Survives when it has 2 or 3. The board on this page uses exactly those numbers.
Pick a rule above to replay it. The ringed cell is the one being decided.
Update every cell at the same time
To get the next generation, count the neighbors of every cell, apply the rules, and then switch all cells to their new state together. No cell ever sees a half-updated board.
This is the smallest example, called a blinker. The numbers are live-neighbor counts, and amber rings mark the cells that change. The middle cell has 2 neighbors and survives, the two ends have 1 and die, and the cells above and below have exactly 3 and are born. The row turns into a column, and then back again.
What grew out of it
Martin Gardner described the game in his Scientific American column in October 1970, and readers began running it on computers around the world. People started cataloguing what lived on the grid: still lifes that never change, oscillators like the blinker, and spaceships like the glider that walk across the board.
That same year Bill Gosper found the glider gun above, a pattern that fires a new glider every 30 generations. It showed that a pattern can grow forever, and it won a prize Conway had offered.
Later work showed that Life can carry out any calculation a computer can, even though its rules fit in a few lines. It is called a zero-player game: you choose the starting pattern and the rules decide everything else.
Now it’s your turn
The real board is next. You cannot break anything: Random and Clear start you over whenever you like.
- Draw a patternClick or drag on the board, then press Play and watch the rules take over.
- Start from a classicThe glider, the R-pentomino, the pulsar and the glider gun are one tap away.
- Look at it in 3DOlder cells grow into taller towers, and you can orbit the board.
- Hear itPiano mode turns every generation into a bar of music, and Score shows the notes as they are played.