In 1970 the mathematician John Conway invented a “game” with no players and no goal — just a grid of cells that are either alive or dead, and four rules applied to everyone at once, forever.

life.c — gen 0 · pop 0
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Click and drag on the screen to draw cells. play runs the simulation; step advances one generation; random reseeds a soup; clear empties the grid.

The rules

At each tick, every cell looks at its eight neighbours and obeys:

  1. A live cell with 2 or 3 live neighbours survives.
  2. A dead cell with exactly 3 live neighbours is born.
  3. Everyone else dies (loneliness or overcrowding), or stays dead.

That’s the whole specification. Formally, if nn is a cell’s number of live neighbours and ss its current state, the next state is

s′={1if s=1 and n∈{2,3}1if s=0 and n=30otherwises' = \begin{cases} 1 & \text{if } s = 1 \text{ and } n \in \{2, 3\} \\ 1 & \text{if } s = 0 \text{ and } n = 3 \\ 0 & \text{otherwise} \end{cases}

Why I like it

There are no birds in the Game of Life, and yet — gliders crawl across the grid, guns spit out streams of them, and whole self-replicating machines have been built inside it. None of that is in the rules. It emerges from them.

That gap — between a trivially simple local rule and the wild global behaviour it produces — is exactly what fascinates me about swarm robotics. A robot, like a cell, only ever sees its neighbours. The interesting question is never “what does one agent do?” but “what does a thousand of them become?”

Press random, hit play, and watch a while. Somewhere in that flicker is the same idea I chase in my research.