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Conway's Game of Life - Online Cellular Automaton Simulator

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Conway's Game of Life

Online Cellular Automaton Simulator — Create, explore, and watch life evolve

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Gen: 0 Alive: 0

Preset Patterns — Click to load

Glider
LWSS
Pulsar
Glider Gun
Blinker
Toad
Beacon
Pentadecathlon
Acorn

Frequently Asked Questions

What is Conway's Game of Life?
Conway's Game of Life is a cellular automaton devised by British mathematician John Horton Conway in 1970. It's a zero-player game where the evolution of a grid of cells is determined entirely by its initial state. Each cell can be either alive or dead, and the state evolves through discrete time steps based on four simple rules. Despite its simplicity, the Game of Life can produce incredibly complex and beautiful patterns, including structures that can simulate logic gates, making it Turing-complete.
What are the rules of the Game of Life?
There are exactly four rules that govern the Game of Life:
  1. Underpopulation: Any live cell with fewer than 2 live neighbours dies.
  2. Survival: Any live cell with 2 or 3 live neighbours lives on to the next generation.
  3. Overpopulation: Any live cell with more than 3 live neighbours dies.
  4. Reproduction: Any dead cell with exactly 3 live neighbours becomes a live cell.
These rules are applied simultaneously to all cells in each generation.
What is a Glider in the Game of Life?
A Glider is the smallest and most famous spaceship pattern in the Game of Life. It consists of just 5 live cells and moves diagonally across the grid at a speed of c/4 (one cell every four generations). The glider was discovered in 1970 by Richard Guy and is fundamental to many larger constructions, including the Gosper Glider Gun. It's often used as a signal or messenger in complex Life patterns.
What is the Gosper Glider Gun?
The Gosper Glider Gun, discovered by Bill Gosper in 1970, was the first pattern proven to exhibit infinite growth. It continuously produces a new glider every 30 generations. This discovery was groundbreaking because it demonstrated that the Game of Life could support unbounded computation. The pattern uses about 36×9 cells and is considered one of the most iconic constructions in cellular automaton history.
Is the Game of Life Turing-complete?
Yes. The Game of Life is Turing-complete, meaning it can simulate any computer algorithm given enough space and time. This was proven by constructing patterns that act as logic gates (AND, OR, NOT), memory cells, and signal pathways. In fact, a working universal Turing machine has been built entirely within the Game of Life, demonstrating that this simple cellular automaton is capable of universal computation.
What are oscillators and still lifes?
Still lifes are patterns that do not change from one generation to the next — they remain static indefinitely (e.g., the Block, Beehive, Boat). Oscillators are patterns that cycle through a set of states and return to their original configuration after a fixed period. Examples include the Blinker (period 2), Toad (period 2), Pulsar (period 3), and Pentadecathlon (period 15). These patterns are essential building blocks for more complex Life constructions.
How can I create my own patterns?
Use the Draw mode (blue dot) to click or drag on the grid to place live cells. Switch to Erase mode (red dot) to remove cells. You can start from a blank grid, load a preset pattern as a starting point, or use the Random button to generate a random seed. Press Play to watch your pattern evolve, or use Step to advance one generation at a time. Keyboard shortcuts: Space (play/pause), S (step), R (random), C (clear).

Key Concepts

Cellular Automaton

A discrete model studied in mathematics and computer science, consisting of a regular grid of cells, each in one of a finite number of states. The grid evolves through time steps according to a set of rules based on neighboring cell states.

Emergent Behavior

Complex patterns and behaviors that arise from simple rules, without any central controller. The Game of Life is a prime example — intricate structures like gliders and logic gates emerge from just four basic rules applied locally.

Von Neumann's Automaton

John von Neumann originally conceived of cellular automata in the 1940s as a theoretical model for self-replicating machines. Conway simplified these ideas dramatically, creating the elegant Game of Life we know today.

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