This page integrates five classic chaotic systems — Lorenz, Aizawa, Halvorsen, Thomas, Dadras — with a 4th-order Runge-Kutta solver and plots up to 300,000 visited points as an additive-blended 3D point cloud in WebGL. Each system is a set of three coupled nonlinear ODEs: tiny changes in the starting point fan out into wildly different trajectories, yet the long-run path stays confined to a bounded, self-similar fractal shape — the strange attractor itself.
Deterministic chaos: fully predictable equations (no randomness anywhere) that still produce trajectories which never repeat and are practically impossible to forecast far ahead, because nearby paths diverge exponentially.
Pick a preset (Lorenz, Aizawa, Halvorsen, Thomas, Dadras), then drag the Morph A / Morph B sliders to rescale key parameters like σ, ρ or b and watch the shape deform live. The Points slider trades render density for speed, Autorotate spins the camera, and Reset re-integrates from the initial condition.
The Lorenz attractor came from a 1963 weather-modelling accident: Edward Lorenz re-entered a rounded mid-run number and got a completely different forecast, coining what we now call the butterfly effect.
It's the bounded, fractal-shaped region of space that a chaotic dynamical system's trajectory settles onto and wanders through forever without ever exactly repeating or leaving the region.
For a deterministic system, one state determines exactly one future path — if two trajectory segments crossed at the same point, they would have to follow identically from then on, so in continuous chaotic flows distinct trajectories never truly cross.
They scale a real coefficient in that attractor's equations — for Lorenz these are the σ (Prandtl-like) and ρ (Rayleigh-like) constants; changing them can shift the system between chaotic, periodic, or divergent regimes.
Each point requires one RK4 integration step (four equation evaluations) plus a GPU vertex upload, so render and compute cost scale roughly linearly with the point count, up to 300,000.
Yes for Lorenz, which models simplified atmospheric convection; the others (Aizawa, Halvorsen, Thomas, Dadras) are mathematically constructed chaotic systems studied for their geometric and dynamical properties rather than a specific physical process.