Give every cell on a grid three rules about its neighbours, or every bird in a sky three rules about the birds nearby. Nothing tells the whole what to do, yet travelling shapes, factories and flocks appear on their own.
Click or drag on the grid to draw cells. Try the glider gun: a pattern of 36 cells that builds a new glider every 30 generations, forever.
Game of Life. Each square is alive or dead. Every generation, all cells update at once: a dead cell with exactly three live neighbours is born, a live cell with two or three survives, and every other cell dies or stays empty. Bright cells are newborn; they dim as they age.
Flocking. Each bird sees only neighbours within a short distance. It steers away from any that are too close, turns toward their average heading, and drifts toward their average position. Birds are coloured by the direction they fly, so a flock shows up as one colour.
Nothing in the rules mentions gliders, guns or flocks. Those are patterns in the behaviour of the whole, and you can only find them by running the rules and watching. Even with the rules in hand, there is in general no shortcut to predicting the future: Life is powerful enough to run any computer program, so asking whether a pattern ever dies out is as hard as the unsolvable halting problem.
John Conway's game first appeared in Martin Gardner's column in Scientific American in October 1970. Bill Gosper found the glider gun weeks later and won Conway's $50 prize.
When a crowd, a swarm or a traffic stream is too complex to describe from the top down, it is often easier to write down what each member does and let the computer run it.
Batman Returns (1992) used a boids-style model to fill scenes with swarming bats and marching penguins. Later tools such as Massive, built for the Lord of the Rings battles, give each digital extra simple rules and let the crowd act out the scene.
In the demo: nobody animates the flock; each bird follows three rules.In 2014 a Harvard team had 1,024 coin-sized "Kilobots" arrange themselves into a star and a letter K. Each robot only talked to its neighbours and followed the same few rules. Swarm rules like these are being tested for search and rescue and for teams of drones.
In the demo: local rules only, yet the whole group moves as one.The Nagel and Schreckenberg traffic model of 1992 is a cellular automaton: cars on a grid of road cells, with a rule to speed up, keep a gap, and sometimes brake at random. It produces jams with no cause. In a 2008 Japanese experiment, 22 cars on a circular track did the same.
In the demo: Life's cells, swapped for cars on a road.Cellular automata in which each patch of land can catch fire from burning neighbours are used to study how wildfires spread. Similar grids model how cities grow, how tumours invade tissue and how patterns form in shells and animal coats.
In the demo: each cell's next state depends only on its neighbours.Pedestrian simulations give each walker a goal and a sense of personal space, then watch where pressure builds. Engineers use them to size exits and walkways for stadiums, stations and large pilgrimages before anyone walks through them.
In the demo: separation is personal space; turn it down and crowds pack tight.Gliders can carry signals, and streams of them can be crossed to make logic gates. People have built working Turing machines inside Life, and even a Life pattern that simulates Life. Stephen Wolfram's one-dimensional Rule 30 automaton has been used as a random number generator.
In the demo: the glider gun is a clock that emits one signal every 30 ticks.