Conway's Game of Life

Rules

• Any live cell with fewer than two live neighbors dies.
• Any live cell with two or three live neighbors survives to the next generation.
• Any live cell with more than three live neighbors dies of overpopulation.
• Any dead cell with exactly three live neighbors becomes a live cell.

Patterns

• Still lifes — patterns that remain unchanged.
• Methuselahs — patterns that evolve for a long time before reaching a stable state.
• Oscillators — patterns that repeat their state every n generations.
• Spaceships — patterns that move across the grid over time.
• Guns — patterns that periodically generate new patterns.
• Trains — patterns that move and leave trails behind them.
• Eaters — patterns that destroy moving patterns upon collision.
• Reflectors — patterns that change the direction of moving patterns after collision.

History

The renowned mathematician John von Neumann, in the 1940s, created a mathematical model of a machine capable of reproducing itself. However, the resulting model had complex rules. In von Neumann’s automaton, a cell could have one of 29 possible states. John Conway set himself the goal of inventing a much simpler Turing-complete cellular automaton. A team of enthusiasts, including Conway, managed through extensive experimentation with rules to arrive at what we now call the Game of Life. In 1970, John Conway outlined the rules and main details of the Game of Life in a letter to Martin Gardner. Gardner then presented the information about the Game of Life in his column in Scientific American.

Interesting Facts

• Despite its simplicity, the Game of Life can generate very complex yet beautiful patterns. Many of these patterns have their own names.
• The Game of Life is capable of constructing any Turing machine. Logical elements can also be implemented within it.