Conway's Game of Life, Wolfram's rules, and emergent complexity
Cellular automata are computational systems where a grid of cells evolves according to simple local rules. Despite their simplicity, they can produce incredibly complex, lifelike behavior - including patterns that are Turing complete (capable of universal computation).
The most famous example is Conway's Game of Life, invented by mathematician John Conway in 1970. With just two rules, it creates a universe of gliders, spaceships, and self-replicating machines.
Watch patterns evolve, or draw your own. Try the "Glider Gun" to see a machine that produces an endless stream of gliders:
Click and drag to draw cells. The Glider Gun produces a stream of gliders forever - one of the most famous patterns!
Each cell is either alive or dead. Every step, each cell counts its 8 neighbors and applies these rules:
A dead cell with exactly 3 live neighbors becomes alive.
A live cell with 2 or 3 neighbors stays alive.
A live cell with fewer than 2 neighbors dies (loneliness).
A live cell with more than 3 neighbors dies (overcrowding).
The simplest spaceship - it moves diagonally across the grid forever.
Discovered by Bill Gosper in 1970. It shoots out new gliders indefinitely.
A period-3 oscillator that pulses in a symmetric pattern.
The Game of Life is Turing complete - it can compute anything a computer can compute. People have built working computers, digital clocks, and even a Game of Life simulation running inside Game of Life!
This demonstrates a profound idea: immense complexity and even intelligence can emerge from incredibly simple rules. It suggests that the complexity of life itself might arise from simple physical laws iterated over billions of years.