Thought Toys · Exhibit 07

Conway's Game of Life

A grid of cells, each just alive or dead. Every tick, four plain rules about crowding and company decide who lives. There is no player and nothing is aiming at anything — yet shapes start to crawl, blink, and breed. Draw a few cells, or drop a glider gun, and watch a machine build little spaceships out of nothing forever.

A grid of cells. Press play to advance generations.

Generation 0 Population 0 Now paused
Drop a pattern

Tip: click and drag on the grid to paint living cells, then press Play.

What you're seeing

Each square is a cell with one of two states — on or off, alive or dead. Time moves in ticks called generations. At every tick, each cell looks at its eight touching neighbours and obeys the same four rules: a living cell with two or three live neighbours stays alive; with fewer it dies of loneliness, with more it dies of crowding; and a dead cell with exactly three live neighbours is born. That's the entire universe. No one steers it.

From those rules a whole zoo falls out. Some clumps lock into still lifes that never change. Others become oscillators that blink between shapes — the pulsar button drops one with a three-beat pulse. And some shapes actually travel: the glider is five cells that reincarnate one step diagonally every four generations, so it appears to walk across the grid. Press Random soup and most of the chaos quickly burns down to a quiet ash of still lifes and blinkers — the board settling into its debris.

The showpiece is the glider gun. It's a configuration that returns to its own shape every thirty generations, but each cycle it spits out a brand-new glider that sails off across the board. A finite pattern, following only those four little rules, manufacturing endless moving structure — this is what people mean when they say simple rules can compute and create without limit. Try drawing your own cells and see what your hand sets loose.

The rule, exactly. Standard Life, written B3/S23. Count the live cells among a cell's 8 neighbours (the Moore neighbourhood). Birth: a dead cell with exactly 3 live neighbours becomes alive. Survival: a live cell with 2 or 3 live neighbours stays alive. Everything else is dead next tick. All cells update simultaneously from the same snapshot; the edges here are walls (off-grid counts as dead). (Checked offline before shipping: the blinker repeats with period 2, the block never moves, a glider returns to its exact shape shifted one cell diagonally every 4 generations, and the Gosper glider gun's population keeps climbing as it emits.)

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