Every simulation here is an example of a few much bigger ideas. Read one, then go and watch it happen.
When a change feeds back into its own cause, small pushes get amplified or damped. A driver braking makes the driver behind brake. Predators eating prey reduces the food for more predators. Most of the surprising behaviour in these simulations comes from feedback.
See it in Predators & PreyNo bus is programmed to make a jam. Each follows one rule about the bus ahead. The jam appears from their interaction, and it can move in a different direction from every single bus.
See it in Traffic RingA system can sit in balance and still be fragile. A pencil standing on its tip is balanced. So is a meadow of predators and prey, until you change the food. Whether a nudge fades or grows is the difference between the two.
See it in Predators & PreySome quantities cannot be created or destroyed, only traded. A planet trades speed for height as it swings out and back in, and the total stays the same. Spotting what is conserved is one of the quickest ways to understand a system.
See it inEach simulation page also explains its model, suggests experiments and compares scenarios. The short versions:
Traffic Ring
Each driver in this model only watches the bus directly ahead. Too close, and they brake. Plenty of room, and they speed up toward their target speed. That is the whole rule set. Nobody is slow on purpose and nobody is breaking anything.
Phantom Jam
Every driver here follows one rule: keep a safe gap to the car in front. When that gap shrinks, brake. When it opens, speed up. Nobody is slow on purpose and nothing blocks the road.
Green Light
When the light changes, only the first driver can see an empty road. The second looks at the first car, waits for it to move, reacts, and pulls away. The third does the same with the second. Each small delay is only a second or so, but a queue of twelve cars adds twelve of them. Much of a short green is spent passing the news down the line.
Predators & Prey
Hares graze in loose herds: they stay near each other, follow the group heading and keep a little space, and a fright spreads from one hare to the next. A hare that spots a fox bolts for the middle of the herd, sidestepping as it runs, until it tires. Foxes search where hares are thick, creep up on ones that have not noticed them, then sprint, aiming ahead of the hare and coming in from the side when a partner is already chasing. They pick off the young, the weak and the stragglers, give up when they run out of breath, and rest after a meal. Both species need a mate nearby, carry young for a while, and the young follow their mother. The grass grows back slowly and is eaten patch by patch. There is no population equation here: the numbers on the chart are simply a count of what is alive.