chaos

Lorenz Attractor

Explore the butterfly effect with this iconic chaotic system. Watch a 3D trajectory trace the Lorenz attractor — two wing-like lobes that never repeat, showing sensitive dependence on initial conditions.

Lorenz

A-Level

The Lorenz system is a simplified model of atmospheric convection. It exhibits deterministic chaos: the trajectory never repeats yet is bounded. Tiny changes in initial conditions lead to wildly different outcomes — the butterfly effect.

σ10

ρ28

β2.7

Speed1.0

📐 Formulas

\dot{x}=\sigma(y-x),\;\dot{y}=x(\rho-z)-y,\;\dot{z}=xy-\beta zThree coupled ODEs

📋 Syllabus

OCR5.3.2