Conway's Game of Life is a cellular automaton created by the British mathematician John Conway in 1970. It takes place on an infinite two-dimensional grid of cells, each of which is either alive or dead. Despite having no players and no decisions to make after the initial setup, it produces extraordinarily complex behavior from just four simple rules.

The Rules

Once you choose a starting pattern, the simulation advances in discrete generations. Each cell's fate is determined entirely by its eight neighbors (the cells immediately adjacent to it, including diagonals):

1. Underpopulation. A living cell with fewer than two living neighbors dies.
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.
4. Reproduction. A dead cell with exactly three living neighbors becomes alive.

These rules are applied simultaneously to every cell on the grid, and the result is the next generation. The process then repeats.

Patterns

The Game of Life has a rich taxonomy of patterns that have been discovered and catalogued over the decades:

• Still lifes are patterns that don't change from one generation to the next. The block (a 2x2 square) and the beehive are common examples.
• Oscillators cycle through a fixed set of states. The blinker alternates between a horizontal and vertical line of three cells. The pulsar, included in the simulation above, is a period-3 oscillator with beautiful symmetry.
• Spaceships are patterns that translate across the grid. The glider, discovered by Richard Guy in 1970, is the smallest and most famous. It moves diagonally one cell every four generations. The lightweight spaceship (LWSS) moves horizontally.
• Methuselahs are small patterns that take a long time to stabilize. The R-pentomino, a five-cell pattern, takes 1,103 generations to reach a stable state. The acorn, just seven cells, takes 5,206 generations.
• Guns are stationary patterns that emit spaceships. Bill Gosper's glider gun, discovered in 1970, was the first known finite pattern with unbounded growth.

Why It Matters

Conway designed the Game of Life to be the simplest possible system that is Turing complete, meaning it can compute anything that any computer can compute. This was proved in the early 1980s and has been demonstrated dramatically: people have built working logic gates, adders, and even full computers entirely within the Game of Life.

This makes it a powerful demonstration of how complexity arises from simplicity. There is no central controller, no global communication, and no randomness in the rules themselves. Every pattern that emerges, from the graceful glider to a self-replicating universal constructor, is a consequence of four deterministic rules applied to a grid of on/off cells.

The Game of Life helped establish the field of cellular automata and influenced decades of research in artificial life, complexity theory, and emergent behavior. Stephen Wolfram's extensive study of one-dimensional cellular automata, published in A New Kind of Science (2002), was partly inspired by Conway's work. The simulation also appears in mathematical recreation, computer science education, and generative art.

The Patterns Above

The simulation includes twelve starting configurations. "Random" seeds 10% of the grid randomly and produces chaotic early evolution that gradually settles into a mix of still lifes, oscillators, and occasional spaceships. The named patterns (Glider, Oscillators, Stills, Spaceship, Weekender) demonstrate specific categories of behavior. The three "Infinite" patterns and the R-pentomino and Acorn are methuselahs that grow for hundreds or thousands of generations before stabilizing. The Gun is Gosper's glider gun, which fires a new glider every 30 generations.

Originally published March 18, 2014