The Game of Life

What is Conway's Game of Life?

The Game of Life is a cellular automaton devised in 1970 by the mathematician John Horton Conway. It is a zero-player game: you set up an initial configuration and then only watch, as the pattern evolves entirely on its own according to a few fixed rules.

The world is a grid of cells, each either alive or dead. Time moves in discrete steps called generations. At every step, each cell looks at its eight neighbours (horizontal, vertical, and diagonal) and updates simultaneously.

The rules

1. A live cell with fewer than two live neighbours dies, as if by underpopulation.
2. A live cell with two or three live neighbours lives on to the next generation.
3. A live cell with more than three live neighbours dies, as if by overpopulation.
4. A dead cell with exactly three live neighbours becomes alive, as if by reproduction.

That is the entire rulebook. From it come still lifes that never change, oscillators that repeat forever, and spaceships such as the glider that travel across the grid. A glider gun even manufactures a steady stream of new gliders.

Why it matters

Despite trivial rules, the Game of Life is very powerful. It is Turing complete: the Game of Life is capable of constructing any Turing machine. Logical elements can also be implemented within it, so AND, OR, and NOT gates, wires, memory, and in principle a complete computer can be assembled out of gliders and still lifes.

Extraordinary complexity does not require complicated rules. It can emerge from simple, well-understood parts interacting locally. Understand and construct the parts and the rules, and you can engineer the whole.