Conway's Game of Life

Conway's Game of Life is a classic cellular automaton devised by mathematician John Conway in 1970.

This "game," a famous example of a cellular automaton, unfolds on an infinite two-dimensional grid of cells. Each cell exists in one of two states: alive or dead. With every turn, known as a generation, a cell's state updates based on the states of its eight immediate neighbors. These neighbors are the cells directly adjacent horizontally, vertically, or diagonally.

The starting configuration is called the first generation. The second generation emerges by applying the rules to every cell on the grid simultaneously—meaning births and deaths occur at the same time. This process then repeats iteratively to produce subsequent generations. In each step, a cell's fate is decided by a simple set of rules:

If a cell is alive, it remains alive only if it has exactly 2 or 3 living neighbors.

If a cell is dead, it becomes alive only if it has exactly 3 living neighbors.

Naturally, countless rule variations exist, based on different numerical thresholds for survival and birth. Conway experimented with many alternatives before selecting these specific parameters. Some rules cause populations to vanish rapidly, while others lead to unlimited expansion across the simulated universe. The chosen rules sit very close to the boundary between these two extremes. As with other chaotic systems, the most intricate and fascinating patterns often arise precisely at this delicate balance, where the forces of unchecked growth and extinction are held in equilibrium.