Emergence: Simple Rules, Complex Worlds

Interactive simulations of systems where complex, surprising behavior arises from simple local rules.

A flock of starlings wheels through the sky in perfect coordination, yet no bird is in charge. A traffic jam ripples backward through cars, though every driver just wants to move forward. Stripes form on a zebrafish from two chemicals that can only diffuse and react.

These explorations let you tune the rules and watch complexity emerge. Each simulation runs live in your browser. Adjust parameters, poke the system, and see what happens.

The Vocabulary

Five recurring ideas color-coded across the series. Watch for them, every simulation is a different arrangement of the same handful of pieces.

agent
An individual following simple local rules.
boids, cells, particles, nodes, grains, walkers
rule
The local interaction law that couples agents together.
neighborhood averaging, reaction kinetics, repulsion, copying
pattern
What emerges when many agents follow the same rules at once.
flocks, spirals, clusters, fractals, coherent oscillations
critical
The threshold where behavior snaps from one regime to another.
density tipping points, phase boundaries, percolation thresholds
feedback
Positive loops that amplify small differences into large ones.
growth cascades, runaway bubbles, pheromone reinforcement