Conway's Game of Life – Draw & Simulate Custom Patterns

Conway's Game of Life is a cellular automaton devised by British mathematician John Horton Conway in 1970. It is a zero-player game, meaning its evolution is determined entirely by its initial state. The "game" takes place on an infinite two-dimensional grid of square cells, each of which is either alive or dead. Every cell interacts with its eight neighbors (horizontally, vertically, and diagonally adjacent), and the grid evolves through discrete time steps according to a simple set of rules.

At each generation, the following transitions occur simultaneously for every cell:

• Birth: A dead cell with exactly 3 live neighbors becomes alive (reproduction).
• Survival: A live cell with 2 or 3 live neighbors stays alive.
• Death by underpopulation: A live cell with fewer than 2 live neighbors dies.
• Death by overpopulation: A live cell with more than 3 live neighbors dies.

The Game of Life hosts a rich ecosystem of patterns. Here are some classics: Glider — a small pattern that moves diagonally across the grid (the icon of the Game of Life). Lightweight Spaceship (LWSS) — a pattern that moves horizontally. Pulsar — a period-3 oscillator with beautiful symmetry. Gosper Glider Gun — the first discovered pattern that produces an infinite stream of gliders, proving the Game of Life is capable of unbounded growth. Block — a simple still life (static pattern). Blinker — a period-2 oscillator (flips between horizontal and vertical). Toad — a period-2 oscillator. Beacon — a period-2 oscillator. Use our preset buttons above to place them instantly!

Yes! Conway's Game of Life is Turing complete. This means that, given a sufficiently large grid and the right initial configuration, it can simulate any Turing machine — and therefore compute anything that is computable. Patterns like glider guns, logic gates (AND, OR, NOT), and memory storage have been constructed entirely within the Game of Life, proving its computational universality. In theory, you could build a full computer inside the Game of Life!

Simply click or drag on the grid to paint living cells. Right-click (or long-press on mobile) to erase cells. Use the Random button to generate a random starting configuration, or pick a Preset Pattern from the buttons above. Once your pattern is ready, press Play to watch it evolve! You can adjust the simulation speed using the slider, step through one generation at a time with the Step button, or Clear the entire grid to start fresh.

This simulator uses fixed boundaries — cells at the edges of the grid have fewer neighbors (those outside the grid are treated as permanently dead). In the theoretical Game of Life, the grid is infinite. Fixed boundaries mean patterns near the edges may behave differently than they would on an infinite plane. For best results, place your patterns near the center of the grid where they have room to evolve naturally.

The Game of Life was invented by British mathematician John Horton Conway (1937–2020) and first published in October 1970 in Martin Gardner's "Mathematical Games" column in Scientific American. It became an instant sensation and remains one of the most famous mathematical recreations of all time. Conway originally developed it to explore how complex behaviors can emerge from simple rules — a foundational concept in complexity science and artificial life research.