Home▸Physics & Mechanics▸Driven Pendulum: Bifurcation Diagram & the Butterfly Effect

Driven Pendulum: Bifurcation Diagram & the Butterfly Effect

Interactive 3D driven-damped-pendulum simulator: sweep the drive amplitude to build a live bifurcation diagram showing the period-doubling route to chaos, and watch two near-identical pendulums diverge exponentially once the motion turns chaotic.

Physics & Mechanics3DModerate60 FPS

A driven, damped pendulum is one of the simplest systems that can turn fully chaotic. Sweep the drive amplitude and watch the live bifurcation diagram grow — periodic swinging splits into period-2, then period-4, then a chaotic smear. Two pendulums released a fraction of a radian apart show what that transition means physically: past the chaotic threshold, the tiny gap between them blows up exponentially.

⚙ Under the hood

Sweep the drive amplitude of a damped, driven pendulum and watch a live bifurcation diagram build up as the motion period-doubles its way into chaos. Two pendulums released a fraction of a radian apart reveal the butterfly effect: their gap stays bounded in periodic regimes and explodes exponentially once the system turns chaotic.

chaosbifurcationdriven pendulumperiod-doublingbutterfly effectnonlinear dynamicsLyapunov exponent

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install