🦋 Lorenz Attractor

The butterfly effect in action — a deterministic system that never repeats.

Drag the Rotate sliders to view the attractor from different angles. Try changing σ, ρ, and β to see different behaviors.

How it works

The Lorenz system is a set of three ordinary differential equations originally developed by Edward Lorenz in 1963 as a simplified model of atmospheric convection. The classic parameters (σ=10, ρ=28, β=8/3) produce the famous "butterfly" shape — two lobes the trajectory spirals around, switching unpredictably between them.

Despite being completely deterministic (no randomness), the system is chaotic: tiny differences in initial conditions lead to wildly different trajectories. This is the origin of the phrase "butterfly effect."