Conway's Game of Life

What Is Conway’s Game of Life?

The Game of Life is a cellular automaton devised by mathematician John Conway in 1970. It’s not really a game in the traditional sense—there are no players, no winning, and no losing. Instead, you set up an initial configuration of cells on a grid, press play, and watch what happens. The results can be surprisingly complex, beautiful, and even philosophically provocative.

The simulation takes place on a two-dimensional grid of cells. Each cell is either alive (filled) or dead (empty). At each step—each “generation”—every cell looks at its eight neighbors and follows four simple rules:

1. Underpopulation: A living cell with fewer than two living neighbors dies, as if by isolation.
2. Survival: A living cell with two or three living neighbors survives to the next generation.
3. Overpopulation: A living cell with more than three living neighbors dies, as if by overcrowding.
4. Reproduction: A dead cell with exactly three living neighbors comes to life, as if by reproduction.

That’s it. Four rules. No randomness, no hidden variables. Every generation is entirely determined by the one before it. And yet, from these minimal ingredients, staggeringly rich behavior emerges.

Using the Simulator

Draw: Click or drag on the grid to toggle cells alive or dead. This is how you set up your initial pattern.

Play / Pause: Start or stop the simulation. While running, the grid updates automatically each generation.

Step forward: Advance exactly one generation. Useful for watching the rules play out in slow motion.

Step backward: Rewind one generation. The simulator remembers up to 500 previous states, so you can scrub back through the history to see how a pattern evolved.

Speed: Drag the slider to control how fast generations advance, from a leisurely crawl to a rapid blur.

Presets: Load classic patterns to explore. Each one demonstrates something different about Life’s dynamics.

A Field Guide to the Presets

Still Lifes & Oscillators

A Blinker is the simplest oscillator—three cells in a line that flip between horizontal and vertical every generation. The Toad is a period-2 oscillator that looks like two offset rows rocking back and forth. The Beacon is two diagonal blocks that blink in alternation. The Pulsar is a stunning period-3 oscillator with four-fold symmetry—it looks almost organic, like a beating heart.

Spaceships

The Glider is perhaps the most famous pattern in Life: five cells that walk diagonally across the grid forever, reassembling themselves every four generations. The Lightweight Spaceship (LWSS) travels horizontally and is the smallest known orthogonal spaceship. These moving patterns were key to proving Life’s computational universality—they can carry information across the grid.

Guns & Factories

The Gosper Glider Gun, discovered by Bill Gosper in 1970, was the first known pattern that grows without bound. It periodically emits gliders—an infinite stream of them marching off into the void. Its discovery won a $50 prize from Conway, who had conjectured that no finite pattern could grow forever.

Methuselahs

The R-pentomino is a small pattern of just five cells that takes 1,103 generations to stabilize, producing a mess of gliders, blocks, blinkers, and other debris along the way. It was one of the first patterns to reveal that Life could produce long-lived, unpredictable evolution from tiny seeds—a hallmark of chaotic systems.

Things to Try

• Load the Gosper Glider Gun and watch it produce a stream of gliders. Follow a single glider as it walks across the grid and wraps around (the grid is toroidal—edges connect to the opposite side).
• Hit Random and watch the chaos settle into a mix of still lifes, oscillators, and the occasional escaping glider. Most random starts stabilize within a few hundred generations.
• Draw a single line of cells (hold and drag). Short lines oscillate; longer ones explode into complex debris before calming down.
• Load the R-pentomino and let it run. Use the step backward button to rewind and study the critical moments where gliders are born.
• Try to build your own oscillator. Draw a symmetric shape and see if it repeats. Most random shapes either die out or settle into known still lifes—finding new oscillators is surprisingly hard.

The Bigger Picture

Conway’s Game of Life is more than a curiosity. It’s a window into how simple rules can generate unbounded complexity, how order can emerge from chaos, and how computation itself can arise from the most minimal ingredients. Every time you press play on this grid, you’re watching a universe boot up from nothing but a handful of rules and a pattern you drew with your mouse. What happens next is entirely determined—and entirely surprising.

John Conway passed away in April 2020, but his Life endures. It remains one of the most elegant demonstrations in all of mathematics: proof that you don’t need much to build something extraordinary.