Imagine a world divided into a tight grid of cells, like a Go board. Each cell is in one of two states: "alive" or "dead." There's no god in this world, and no cell thinks for itself — there's only a single fixed rule. Count how many of the 8 neighboring cells (including diagonals) are alive, and that decides whether the cell lives or dies in the next moment. This is the "Game of Life," created by mathematician John Conway in 1970.
There are exactly four rules. ① A living cell with fewer than 2 living neighbors dies of loneliness (underpopulation). ② A living cell with 2 or 3 neighbors survives unchanged into the next generation. ③ A living cell with 4 or more neighbors dies from overcrowding (overpopulation). ④ A dead cell with exactly 3 living neighbors comes to life (birth). Apply these rules to every cell on the grid at the same time, and one generation passes. That's it — no probability, no randomness at all.
What's fascinating is that unexpected motion emerges from this deterministic rule. A "blinker" — three cells in a row — flips back and forth between a horizontal and vertical line, and a five-cell pattern called a "glider" keeps its shape while crawling diagonally across the grid on its own (moving one cell every 4 generations, to be precise). No one ever told it to "move" — the overall motion emerges purely from local rules. By contrast, a "block" made of four cells in a square always has exactly 3 neighbors for each of its cells, so it never changes no matter how many generations pass.
This simple rule turns out to be so powerful that the Game of Life has been proven to be "Turing complete." That means, in theory, these rules alone can carry out any computation — even logic circuits and calculators. Enthusiasts have actually combined logic gates within the Game of Life to build working calculators. This principle of "complex behavior emerging from simple rules" became the root of artificial life research and of simulations (cellular automata) that mimic natural phenomena like wildfire spread or city growth.
In the mini grid at the top of the activity page, you can turn neighboring cells on and off yourself and check, following the rules, whether the center cell lives or dies in the next generation. In the larger grid below, choose patterns like the blinker, toad, glider, or block and press play to watch them move, or click empty cells to draw your own pattern.