Simple rules, complex behaviour.

Step 1 of 8

The rules

The Turing machine showed that a whole computation can come from a few simple rules. In 1970 John Conway went a step further: a board of cells, and one rule all the cells obey at once. This is the Game of Life, an example of a cellular automaton.

Every cell is alive or dead. Each generation, every cell counts how many of its eight neighbours are alive, diagonals included:

• A dead cell with exactly 3 live neighbours is born.
• A live cell with 2 or 3 live neighbours survives.
• Every other cell dies, or stays dead.

Look inside is open at Neighbours: each cell shows its number of live neighbours, in a colour that says what happens to it next generation.

Step 2 of 8

One generation

On the board is the R-pentomino, only five cells. All cells update together, by the counts of the current generation: a cell born now is not counted until the next generation.

Step 3 of 8

Counting births

Births happen in empty cells, so you have to count the neighbours of the cells around the shape too, not just of the live ones.

Step 4 of 8

Shapes that move

Later on the R-pentomino bursts into a thousand generations of chaos, filling the board and throwing shapes out. To understand what goes on, look at small shapes one at a time. Start is Pattern zoo: in the back row shapes that do not change, in the middle shapes that blink, and at the front two that do something else.

Step 5 of 8

Still or blinking

Look inside at Patterns, forty generations after the start. Each group of cells is coloured by what it does: a still life does not change, an oscillator comes back to itself after a few generations, and a spaceship comes back to itself somewhere else.

Step 6 of 8

Changing the rule

The Game of Life’s rule was not picked at random. Conway looked for a rule under which shapes neither die out too fast nor fill the board, so that something interesting goes on for a long time. Here the board starts from a Random soup.

Step 7 of 8

A rule that freezes

Born with and Survives with are free now. There are sixteen combinations; try some and watch the soup.

Step 8 of 8

A computer made of cells

Start is Glider gun, a shape that comes back to itself every thirty generations and fires a new glider each time. Nobody designed it into the rule; it was found inside it.