Conway's Game of Life
This is an interactive demonstration of Conway's Game of Life, a cellular automaton devised by mathematician John Conway in 1970. Despite its simple rules, the Game of Life exhibits remarkably complex and often unpredictable behavior, making it a classic example of emergent complexity from simple rules.
The Rules
The Game of Life is played on an infinite two-dimensional grid of cells (we use a finite grid with wraparound). Each cell can be in one of two states: alive (colored) or dead (empty).
The state of each cell evolves according to these four rules:
- Underpopulation: Any live cell with fewer than 2 live neighbors dies
- Survival: Any live cell with 2 or 3 live neighbors survives
- Overpopulation: Any live cell with more than 3 live neighbors dies
- Reproduction: Any dead cell with exactly 3 live neighbors becomes alive
These rules are applied simultaneously to all cells, creating the next "generation."
How to Use
- Click and drag on the grid to draw live cells
- Use Play/Pause to start or stop the simulation
- Use Step to advance one generation at a time
- Use Clear to reset the grid
- Use Randomize to fill the grid with random cells
- Click pattern buttons to add classic patterns at random positions
Pattern Types
Still Lifes
Patterns that don't change from one generation to the next:
- Block (2x2 square)
- Beehive
- Loaf
Oscillators
Patterns that return to their initial state after a fixed number of generations:
- Blinker (period 2): The simplest oscillator - three cells in a row
- Toad (period 2): Two overlapping rows of three cells
- Beacon (period 2): Two diagonal blocks that blink
- Pulsar (period 3): A beautiful symmetric oscillator
- Pentadecathlon (period 15): A long-period oscillator
Spaceships
Patterns that translate across the grid:
- Glider: The smallest spaceship, moves diagonally
- LWSS (Lightweight Spaceship): Moves horizontally
Methuselahs
Small patterns that take a long time to stabilize:
- R-pentomino: 5 cells that evolve for 1103 generations before stabilizing
- Acorn: 7 cells that take 5206 generations to stabilize
- Diehard: 7 cells that completely vanish after exactly 130 generations
Guns
Patterns that periodically emit spaceships:
- Gosper Glider Gun: The first gun discovered, produces a new glider every 30 generations
Why It Matters
The Game of Life demonstrates several important concepts in complexity science and cognitive science:
- Emergence: Complex global patterns arise from simple local rules
- Self-organization: Order emerges without central control
- Computation: The Game of Life is Turing complete - it can compute anything a computer can
- Unpredictability: Despite deterministic rules, long-term behavior is often unpredictable
References
- Gardner, M. (1970). "Mathematical Games: The fantastic combinations of John Conway's new solitaire game 'life'". Scientific American, 223(4), 120-123.
- Berlekamp, E., Conway, J., & Guy, R. (2001). Winning Ways for Your Mathematical Plays (2nd ed.). A K Peters.
- LifeWiki - Comprehensive encyclopedia of Game of Life patterns