Chaos in Motion
A double pendulum is the simplest system that generates true chaos. Start 50 pendulums with nearly identical angles and watch them diverge into completely different futures — the butterfly effect made visible.
Pendulums: 50
Time: 0.0s
Divergence: 0.000°
Status: Running
Pendulum Count
50
Angle Spread (°)
0.01
Simulation Speed
1.0×
Trail Length
200
⚙️ What's happening?
Each pendulum is a double pendulum — two rods connected end-to-end, free to swing independently. Unlike a simple pendulum, double pendulums exhibit deterministic chaos: they follow exact physical laws, yet tiny differences in starting position cause wildly different outcomes.
The 50 pendulums start with angles separated by as little as 0.0001°. At first they move together. Then they diverge. This is the Butterfly Effect — sensitivity to initial conditions, the hallmark of chaotic systems, first described by Edward Lorenz in 1972.
θ₁'' = [−g(2m₁+m₂)sin θ₁ − m₂g·sin(θ₁−2θ₂) − 2sin(θ₁−θ₂)m₂(ω₂²L₂+ω₁²L₁cos(θ₁−θ₂))] / [L₁(2m₁+m₂−m₂cos(2θ₁−2θ₂))]