Two arms, infinite chaos

A double pendulum is just two linked swinging arms — yet its path is impossible to predict for long. Nudge the start by a hair and the motion changes completely.

Initial state

Arm 1 start angle

Arm 2 start angle

Arm 1 start speed

Arm 2 start speed

The pendulum

Arm 1 length

Arm 2 length

Bob 1 mass

Bob 2 mass

Gravity

Simulation (accuracy)

Time step — smaller = more accurate

Solved with RK4 integration. Watch the energy-drift number drop as you shrink the step.

Playback speed

# What am I looking at?

# The takeaway

Chaos is real, not random. Every move obeys exact physics — there's no dice-rolling — yet it's still unpredictable because tiny errors grow explosively.
"Accurate enough" is a choice. A smaller time step keeps energy steady longer, but no step is small enough to predict the far future. That's the signature of a chaotic system.