Cellular Automata: Can Simple Rules Create Life?
Four rules. Infinite complexity. Welcome to Conway's Game of Life.
Four rules. Infinite complexity. Welcome to Conway's Game of Life.
Imagine a flat world made of tiny square cells. Each cell is either alive or dead. Click the grid below to toggle cells on and off. Right now, nothing happens on its own. The grid just sits there, waiting for rules.
Click or drag on the grid to draw living cells
This is the foundation of every cellular automaton: a grid of cells, each with a simple state. What makes it interesting is what happens when we add rules for how cells change from one generation to the next.
In 1970, mathematician John Conway defined four rules that determine whether a cell lives, dies, or is born. Each cell checks its 8 neighbors every generation. Click "Apply Rule" on each card to see the rule in action.
A living cell with fewer than 2 neighbors dies. It's too lonely to survive.
A living cell with 2 or 3 neighbors survives to the next generation.
A living cell with more than 3 neighbors dies from overcrowding.
A dead cell with exactly 3 living neighbors comes to life.
Just four rules. Every cell checks its neighbors, applies the rules, and updates simultaneously. From this simplicity, astonishing complexity emerges.
Now let's see the rules in action on a full grid. Hit "Random" to seed the grid, then press "Play" and watch as patterns emerge, collide, and stabilize.
Click on the grid to draw cells while paused or running
No single cell "knows" what pattern it's part of. Each one just follows four local rules. Yet from random starting conditions, order spontaneously appears: stable blocks, blinking shapes, and things that move. This is called emergent behavior.
Over decades, enthusiasts have cataloged thousands of patterns. They fall into three main families. Click any pattern to load it, then hit "Play" to watch it go.
Patterns that never change. Every cell has exactly 2 or 3 neighbors, so nothing dies or is born.
Patterns that cycle between two or more states, then repeat. They pulse like a heartbeat.
Patterns that move across the grid. They rebuild themselves one cell over each cycle.
These building blocks combine to form larger structures. Gliders carry information. Oscillators act as clocks. Still lifes serve as memory. Together, they can build anything.
In 1970, Bill Gosper discovered a pattern that produces a new glider every 30 generations, forever. This was the first proof that the Game of Life could generate unlimited growth.
Because glider guns can generate streams of gliders, and gliders can interact to form logic gates (AND, OR, NOT), the Game of Life can simulate any computer program. A grid of black and white cells is, in theory, as powerful as your laptop. Conway's simple game is Turing complete.
People have built working calculators, Turing machines, and even a Game of Life simulator running inside the Game of Life. The rabbit hole goes deep.
Now it's your turn. Draw anything you want on the grid below, load patterns, adjust the speed, and see what evolves. There are no goals here, just exploration.
Draw cells, load a pattern, and hit Play. What world will you create?
Load the "R-Pentomino" (just 5 cells) and watch it run for over 1000 generations before stabilizing. Or try "Acorn" (7 cells) which takes 5206 generations to settle. Tiny seeds can create enormous histories.
You now understand how four simple rules on a grid of cells can produce gliders, oscillators, and infinite complexity. The same principles appear in nature, computing, and art.
Simple rules can create complex, unpredictable behavior when applied across many cells.
Underpopulation, survival, overpopulation, and reproduction govern life and death on the grid.
Still lifes, oscillators, and spaceships are the fundamental patterns that emerge.
The Game of Life can simulate any computation. A grid of cells is a universal computer.
Cellular automata model real phenomena: crystal growth, pigment patterns, and population dynamics.
Put your new knowledge into practice!