Conway's Game of Life is a zero-player cellular automaton devised by mathematician John Conway in 1970. It takes place on a 2D grid of cells, each either alive or dead.
Rules (B3/S23)
At each generation, every cell's fate is determined by its eight neighbors:
Birth: A dead cell with exactly 3 live neighbors becomes alive.
Survival: A live cell with 2 or 3 live neighbors stays alive.
Death: All other live cells die (loneliness or overcrowding).
These simple rules give rise to astonishing complexity: gliders, oscillators, and even Turing-complete logic circuits.
This Notebook
We seed a 80×80 toroidal grid with an R-pentomino (a chaotic methuselah pattern) and a glider, then run 100 generations. The first cell renders the final state; the second shows a filmstrip of the evolution.
[1]Simulation & Final State
1 panel
Saved output from the author's last run. Press Run to execute live in your browser.
(output too large to embed; run the cell to regenerate it)
[2]Evolution Filmstrip
1 panel
Saved output from the author's last run. Press Run to execute live in your browser.
(output too large to embed; run the cell to regenerate it)
Emergent Behavior
Despite its three simple rules, the Game of Life produces rich emergent phenomena:
Gliders travel diagonally across the grid indefinitely.
Oscillators (blinkers, pulsars) cycle between fixed states.
Methuselahs like the R-pentomino take hundreds of generations to stabilize, producing a burst of activity from a tiny seed.
Glider guns produce an infinite stream of gliders.
Try Modifying
Seed the grid with a Gosper glider gun or a random fill.
Increase the grid size or number of generations.
Experiment with different boundary conditions (fixed edges vs. toroidal wrapping).
Try alternative rule sets: HighLife (B36/S23) adds a self-replicating pattern.