Four rules. A live cell with 2 or 3 neighbors survives. A dead cell with exactly 3 neighbors comes alive. Everything else dies. That is the entire program. Conway designed them by trial and error: he wanted a system complex enough for universal computation but simple enough to hand-simulate on a Go board.
In 1970 Bill Gosper discovered the glider gun, a pattern that periodically emits gliders. That was the key result. Gliders act as signals, guns act as emitters, and collisions act as logic gates. Together they proved the Game of Life is Turing-complete: anything computable can, in principle, be built from these four rules.
The automaton exhibits three classes of persistent structure. Still lifes (blocks, beehives) are stable. Oscillators (blinkers, pulsars) cycle through a fixed period. Spaceships (gliders, lightweight spaceships) translate across the grid. Everything else either decays into one of these forms or grows without bound.
Draw cells or load a pattern and press play. Watch how random initial conditions settle into a mix of still lifes and oscillators, punctuated by the occasional glider escaping to infinity.
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