What a cellular automaton is
A cellular automaton is a board of squares, each in some state (here, alive or dead), that changes in steps called generations. At each step all squares update at once using the same rule, which only looks at the eight neighbors around each square.
The Game of Life is not won or lost: you choose the starting position and the rules do the rest. What is fascinating is that such simple rules produce very complex, unpredictable behavior, which is why it is studied in mathematics, computer science and even biology.
The rules in plain language
You count the live neighbors of each square (the eight around it, diagonals included) and apply these rules at the same time across the whole board:
- A live cell with fewer than two live neighbors dies of loneliness.
- A live cell with two or three live neighbors stays alive.
- A live cell with more than three live neighbors dies of overpopulation.
- A dead square with exactly three live neighbors comes to life.
The shorthand notation for these rules is B3/S23: B (birth) 3 means a cell is born with 3 neighbors, and S (survival) 23 means it survives with 2 or 3. The alternative rules in the tool use the same notation; for example, HighLife is B36/S23 and Seeds is B2/S.
One generation worked out by hand
Take the blinker: three live cells in a horizontal row. The middle one has 2 live neighbors, so it survives. The ones at the ends have only 1 neighbor, so they die. The squares directly above and below the center have 3 live neighbors (the three in the row), so they are born. Result: a vertical row of three cells.
In the next generation the process repeats and it becomes horizontal again. That is why the blinker is a period-2 oscillator. Try the same with the block, a 2 × 2 square: each cell has 3 neighbors, so all of them survive, and no empty square has 3 live neighbors. It never changes, which is why it is called a still life.
History: Conway, Gardner and the magazine
The British mathematician John Conway devised the game in 1970. Martin Gardner spread it in his mathematical games column in Scientific American, in the October 1970 issue, and it has since built a huge community of enthusiasts who search for and catalog patterns.
It was later proven that the game is Turing complete: with the right shapes, it can in principle compute anything a computer can. That is one reason it remains famous: unlimited complexity from minimal rules.
Pattern families and which to try
Patterns are classified by behavior. All of them are in the tool's "Pattern" menu under these names:
| Family | Pattern | What it does |
|---|---|---|
| Still life | Block, Beehive | Never changes: 4 cells for the block, 6 for the beehive |
| Oscillator | Blinker, Toad, Beacon | Period 2: starts over every 2 generations |
| Oscillator | Pulsar | Period 3, 48 cells in its starting phase |
| Oscillator | Pentadecathlon | Period 15 |
| Spaceship | Glider | 5 cells; moves 1 square diagonally every 4 generations |
| Spaceship | Lightweight spaceship | Crosses the board in a straight line, period 4 |
| Gun | Gosper glider gun | Fires a new glider every 30 generations |
| Early chaos | R-pentomino | 5 cells that take 1,103 generations to stabilize on an infinite plane |
The Gosper gun was found by Bill Gosper in 1970 and was the first proof that a population can grow without limit. Besides these, the tool includes Acorn and Die Hard, two tiny patterns that take a very long time to settle.
How to use the Game of Life tool
- Click or drag on the board to draw live cells (click a live square again to remove it), or pick a pattern from the "Pattern" menu.
- Press "Play." "One generation" moves ahead a single step so you can follow the evolution calmly, and "Pause" stops everything. With the board selected you can also use the keyboard: space starts or pauses, N advances one step, R fills at random and C clears.
- Adjust the "Speed," the "Board size" and the "Rule," and try "Random" (with its "Random density") to start with a board full of cells. "Clear" empties the board.
- Turn on "Color cells by age" to see which areas have been stable the longest. The generation and the live cells are shown at the top, and the tool lets you know when the board stabilizes, falls into a cycle or runs out of life.
Everything is computed on your device and nothing is sent to a server. The tool saves your settings (size, speed, rule) in your browser, but not the drawing.
Experiments to try
- Load the glider and count how many generations it takes to move one square diagonally: 4. With wrapped edges, it goes around the board and reappears on the other side.
- Put two gliders on a collision course and watch how it ends: depending on how they meet, they can destroy each other or leave a still life.
- Load the Gosper gun on a board of at least 48 × 48 and count how long it takes to fire each glider: 30 generations.
- Load the R-pentomino on a large board and compare with and without wrapped edges. On an infinite plane it takes 1,103 generations to stabilize, but on a finite board the result changes.
- Change the rule with the same drawing. With Seeds (B2/S) every cell dies each generation and only births remain, so the drawing spreads outward; with Maze (B3/S12345) corridor-like structures appear.
Limits of a finite board
The original game takes place on an infinite plane. The tool's board has a fixed size, so what reaches the edge behaves differently: with wrapped edges, it comes back in from the opposite side (the board becomes a kind of doughnut), and without wrapping, it dies out against a wall.
That is why large patterns need room (the Gosper gun needs at least 48 × 48) and some, like the R-pentomino, may end differently from what you would see on an unbounded plane. If a pattern does not fit, the tool asks you for a larger board.
Frequently asked questions
What are the rules of Conway's Game of Life?
A live cell with 2 or 3 live neighbors stays alive; with fewer than 2 it dies of loneliness and with more than 3 of overpopulation. A dead square with exactly 3 live neighbors comes to life. It is summarized as B3/S23.
What does B3/S23 mean?
B is birth and S is survival. B3 means a cell is born with 3 live neighbors, and S23 means a cell with 2 or 3 survives.
What is a glider?
It is a five-cell shape that moves diagonally, one square every 4 generations. It is the best-known pattern in the game.
Who invented the Game of Life?
The British mathematician John Conway, in 1970. Martin Gardner made it known that year in Scientific American.
Why does my drawing vanish or freeze?
That is the most common outcome: many small shapes die out or stabilize within a few generations. Try a different starting point, a larger board or "Random."