Conway's Game of Life
Conway's Game of Life is a classic example of how complexity can blossom from just a few straightforward rules. Picture an infinite grid of cells—each one can be "on" (alive) or "off" (dead). Each turn (or "generation"), every cell checks how many neighbors are alive. If it's overcrowded, it dies. If it's too lonely, it also dies. But with exactly three neighbors, a dead cell will spark into life.
This simple set of rules leads to endlessly fascinating behavior—from stable formations and repeating oscillators, to self-propagating "spaceships" that traverse the grid. It's a perfect demonstration of how complexity can arise from simplicity, and it's even Turing complete, meaning it can, in theory, simulate any computation.
Pattern Examples
These classic patterns showcase the Game's emergent behavior. The "Glider" demonstrates movement across the grid, the "Pulsar" creates a mesmerizing oscillation, and the "Small Exploder" shows how simple shapes can evolve into complex forms.
The Algorithm
At its heart, the Game of Life runs on just a few elegant functions that determine life and death in our cellular universe:
// The core algorithm that determines life and death
function computeNextGeneration(currentGrid) {
const newGrid = createEmptyGrid(rows, cols);
for (let r = 0; r < rows; r++) {
for (let c = 0; c < cols; c++) {
const neighbors = countNeighbors(currentGrid, r, c);
const cellState = currentGrid[r][c];
// Apply Conway's rules of life
if (cellState === 1) {
// Live cell survives if it has 2 or 3 neighbors
newGrid[r][c] = (neighbors === 2 || neighbors === 3) ? 1 : 0;
} else {
// Dead cell springs to life if it has exactly 3 neighbors
newGrid[r][c] = (neighbors === 3) ? 1 : 0;
}
}
}
return newGrid;
}// Count live neighbors for each cell
function countNeighbors(g, row, col) {
let count = 0;
for (let i = 0; i < 8; i++) {
const nr = row + NEIGHBOR_OFFSETS[i * 2];
const nc = col + NEIGHBOR_OFFSETS[i * 2 + 1];
if (nr >= 0 && nr < rows && nc >= 0 && nc < cols) {
count += g[nr][nc];
}
}
return count;
}