Conway's Game of Life

First devised by mathematician John Conway in 1970, Conway’s Game of Life is a classic simulation of cellular evolution.

The Game of Life—an example of a cellular automaton—takes place on an infinite two-dimensional grid. Every cell can be alive or dead. Each turn, known as a generation, the state of a cell updates based on the states of its eight neighboring cells, which include those directly adjacent horizontally, vertically, or diagonally.

The starting layout forms the first generation. The next generation results from applying the rules to all cells at once, meaning births and deaths occur simultaneously. Subsequent generations are produced by repeatedly applying the same rules. For each generation, the fate of a cell is decided by these simple principles:

A living cell survives if it has exactly 2 or 3 living neighbors.

A dead cell becomes alive only if it has exactly 3 living neighbors.

Many rule variations exist depending on the numbers used to decide cell survival or death. Conway tested numerous versions before selecting this particular set. Some alternatives cause populations to die off rapidly, while others grow endlessly, filling large portions of the grid. The chosen rules lie near the boundary between these extremes. Just as in other chaotic systems, the most intricate and fascinating patterns emerge at this border, where expansion and decay are perfectly counterbalanced.

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