Lorenz Attractor
In 1963 Edward Lorenz stripped weather down to three equations and found something strange: the solution never repeats yet never escapes, looping forever on a butterfly-shaped surface. This tool integrates those equations and draws the trajectory as a glowing ribbon you can rotate in 3D. Release a swarm of nearby starting points and watch them track together, then peel apart onto different wings — the butterfly effect made visual. Drag the Rayleigh number ρ and the other parameters to move between a quiet fixed point and full chaos, switch to other classic attractors, and orbit the camera with the mouse.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The Lorenz system is dx/dt = σ(y − x), dy/dt = x(ρ − z) − y, dz/dt = xy − βz; with the classic σ=10, β=8/3, ρ=28 it never settles and never repeats.
- Two trajectories starting a millionth apart stay together briefly, then diverge exponentially onto opposite wings — sensitive dependence on initial conditions, the defining mark of chaos.
- The motion is deterministic and bounded yet unpredictable: it is trapped forever on the attractor but you cannot say which wing it will be on far ahead, which is why long-range weather forecasts are impossible.
- Runs 100% in your browser — simulations are computed locally on your device.
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