Strange Attractors
Three famous systems — Lorenz, Rössler, and Aizawa — each just three simple differential equations whose solutions never repeat yet never escape, tracing an infinitely detailed shape in space.
Overview
Drag the sliders and the butterfly reshapes. Below the Lorenz critical value the trajectory settles; above it, the path becomes forever unpredictable while staying bounded — chaos, not noise.
Methodology
Each frame advances the system with a fourth-order Runge–Kutta step and plots the trajectory as a living point cloud. Deterministic rules, unpredictable path — the hallmark of deterministic chaos.
Applications
The limits of weather prediction, chaotic secure communication, nonlinear control, fluid turbulence, and the mathematics behind sensitive dependence on initial conditions.