Six simulations in the browser
Simple rules, complex behaviour
A flock has no leader. A leopard has no blueprint for its spots. A sandpile does not know when it will collapse. All of it happens anyway, and always for the same reason: a handful of rules that amount to nothing on their own, applied simultaneously and very many times.
Each of these six pages states the whole rule — four sentences at most — and hands you the dials. What comes out of it is written down nowhere.
The pieces
6 in total
Flock
A thousand birds, three rules, no leader. The shape of the flock is written down nowhere.
Pattern
Two substances that consume one another and drift apart. Out of an even liquid come spots, stripes and worms.
Rule
A row of cells, eight possible neighbourhoods, one byte of rules. Enough for something indistinguishable from randomness.
Flow
Thousands of particles follow an invisible field of angles. Nobody decides the composition.
Growth
Replace every character with a longer string, and read the result as a plant.
Sandpile
Grain by grain, and every so often it collapses. The pile holds itself exactly at the edge.
Why this is worth your time
Emergence is the word for what happens when the whole does something that cannot be found in any of its parts. There is nothing mystical about it: the flock on these pages is fully determined by the four sentences printed beside it, and nothing is hidden inside them. And still there is no way to read off, from those four sentences, how the cloud will turn.
That is the uncomfortable part. We are used to thinking that understanding means being able to predict. With these systems that equation comes apart. You can know the rule completely, you can have written it yourself, and the only way to find out what it does is still to run it and watch.
Hence the dials. Every piece is built so that you can turn a single parameter and watch the behaviour tip over — usually somewhere you did not expect, and rarely by degrees.