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Describe agents, rules, and data in a small language that reads like the model you are thinking about.
Learn the languageBuild living math models in the browser
MathPets is a friendly language and studio for math-powered agent simulations, experiments, and emergent behavior.
world: x: -60..60 y: -44..44 topology: box params: density: number = slider(62, 0..100) monitors: burned-trees: number = count patches where burned burning-trees: number = count patches where burning living-trees: number = count patches where tree patches: state: empty | tree | burning | burned = empty setup: patches: state := if (random-float(100) < density) then tree else empty where (tree and px = min-x): state := burning step staged: patches: where burning: state := burned where (tree and any neighbors4 where burning): state := burning stop when (count patches where burning = 0) step 0burning 0trees 0burned 0
Free self-paced course
Learn agent-based modeling by changing live worlds
Six units of short narrated lessons, runnable experiments, readable source, and end-of-unit checkpoints. No programming background or account required.
- Emergence, feedback, thresholds, and networks
- 27 lessons · 6 checkpoints · about 2 hours
Course path self-paced
1
A world of patchesGrids, state, and neighbours
20m2
Rules that make patternsConway's Life, read straight off the code
16m3
Pets that moveFlocking: three rules, no leader
20m4
Food chains and life cyclesWolves, sheep, energy, die and hatch
20m5
NetworksLinks, contagion, and graph structure
20m6
Network dynamicsLinks, flow, and collaboration
16mRun
Step through behavior, tune parameters, inspect state, and watch patterns emerge without leaving the page.
Explore simulationsRemix
Fork built-in models, reshape appearances, and save your own browser-local experiments.
See how remixing worksWatch behavior emerge
Every board below is a live simulation — scroll and the rules change under it.
Flocking
Birds align, separate, and cohere using only their nearest neighbors.
No bird is in charge. Watch ribbons and vees assemble out of three local steering rules — then dissolve and reform somewhere else.
Open modelAnts
Foragers lay pheromone trails that evaporate, diffuse, and recruit.
The first ant wanders at random. Watch highways condense between nest and food as trails reinforce — and fade once a source is exhausted.
Open modelTuring patterns
Two chemicals react and diffuse into spots, stripes, and labyrinths.
Activator and inhibitor race across the grid. The standing pattern that emerges is the same math behind seashell pigment and zebra stripes.
Open modelWolves & sheep
Predators, prey, and grass chase each other through boom and bust.
Populations oscillate without any schedule: too many wolves starve, sheep recover, grass regrows. Sometimes the whole system collapses instead.
Open modelOpen source
The MathPets language, compiler, and runtime are the open core behind the studio.
Explore the language