Imagine a universe governed not by complex laws of physics, but by three incredibly simple rules that a child could understand. This universe is a grid of squares, like a chessboard extending infinitely in every direction. Each square can either be "alive" or "dead".

This is Conway's Game of Life, created by mathematician John Horton Conway in 1970. It is a "zero-player game" because its evolution is determined entirely by its initial state. You set up a pattern of living cells, press play, and watch as the system unfolds.

The Rules of Life

In the Game of Life, every cell interacts with its eight neighbours (horizontal, vertical, and diagonal). At each step in time, the following transitions occur:

• Underpopulation: Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
• Survival: Any live cell with two or three live neighbours lives on to the next generation.
• Overpopulation: Any live cell with more than three live neighbours dies, as if by overpopulation.
• Reproduction: Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

These four rules determine the entire future of the grid. From these simple interactions, a staggering variety of behaviours can emerge.

Still Lifes, Oscillators, and Spaceships

As people began experimenting with the Game of Life, they discovered that certain patterns appeared repeatedly. These patterns can be categorized into a few main types:

• Still Lifes: Patterns that do not change from one generation to the next. They are completely stable. Examples include the Block, the Beehive, and the Loaf.
• Oscillators: Patterns that cycle through a repeating sequence of shapes. After a certain number of generations (the period), they return to their original form. A famous example is the Blinker, a line of three cells that flashes back and forth horizontally and vertically.
• Spaceships: These are patterns that translate themselves across the grid. The most famous spaceship is the Glider, a small five-cell pattern that creeps diagonally across the board, moving one cell every four generations.

Emergence: More Than the Sum of Its Parts

The Game of Life is one of the most powerful demonstrations of a concept called emergence. Emergence happens when simple rules or interactions produce complex, unexpected behaviours in a larger system. No single cell "knows" it is part of a Glider moving across the screen. The movement of the Glider is purely a result of the local interactions of the cells.

Incredibly, the Game of Life is "Turing Complete". This means that, in principle, it can simulate any computer algorithm. By carefully arranging groups of Gliders to act as streams of data, and using other patterns as logical gates (like AND or NOT gates), people have built functional calculators, digital clocks, and even a simulation of the Game of Life itself within the Game of Life!

Experience It Yourself

You can explore this universe in our interactive Game of Life experiment. Try drawing random shapes on the grid, or look up famous patterns like the Gosper Glider Gun to see how complexity arises from simplicity.