Conway's Game of Life
A zero-player game taking place on an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours. From three simple rules governing birth, death, and survival, immense complexity and self-organising structures emerge.
The Rules
The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of square cells. Each cell interacts with its eight adjacent neighbours (horizontal, vertical, diagonal). At each step in time, the following transitions occur:
- Any live cell with fewer than two live neighbours dies (underpopulation).
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies (overpopulation).
- Any dead cell with exactly three live neighbours becomes a live cell (reproduction).
The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed, births and deaths occur simultaneously.
Emergence
Conway's Game of Life is a quintessential example of emergence and self-organisation. It is Turing complete, meaning it can simulate a universal constructor or any other Turing machine. Complex structures like "gliders" that travel across the grid, "oscillators" that cycle through a set of shapes, and "guns" that emit other patterns all arise organically from these rudimentary rules.