Conway's Game of Life

Conway's Game of Life demonstrates how complex macroscopic behavior emerges from deterministic, localized, two-dimensional cellular automata. The transition state of each cell is strictly governed by the sum of its eight immediate neighbors. Despite these basic mathematical rules, the system exhibits Turing completeness, capable of universal computation. It serves as a rigorous proof that extreme algorithmic complexity requires neither intent nor central processing.

Conway's Life is a zero-player game: you set the starting cells, press play, and never touch it again. Everything after that follows from just two rules — a dead cell with exactly 3 live neighbours comes alive, and a live cell survives only with 2 or 3 neighbours. From that, shapes sort themselves into three fates: some freeze forever, some blink in a loop, and some (like the glider) crawl steadily across the grid.

In 1970 Conway conjectured that no starting pattern could grow forever, and offered $50 through Martin Gardner's Scientific American column to anyone who could settle it. Within weeks Bill Gosper's group at MIT built the glider gun — a pattern that spits out a new glider every 30 generations, so its population climbs without limit. Gosper won the money and disproved the conjecture; the gun is one of the patterns you can load above.