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Double Pendulum Simulator — Real RK4 Physics, Chaos & the Butterfly Effect
Simulate a double pendulum — two pendulums joined end to end — using real RK4 (fourth-order Runge-Kutta) numerical integration of the actual equations of motion, not a simplified visual approximation. Run two nearly identical starting angles side by side and watch them diverge completely within seconds: a direct, visible demonstration of deterministic chaos and the butterfly effect.
How to use Chaotic Double Pendulum Sandbox
- Set the starting angles and pendulum lengths.
- Run the simulation and watch the motion unfold.
- Add a second pendulum with a tiny angle difference.
- Watch the two trajectories diverge — chaos in action.
Frequently asked questions
- Why is a double pendulum considered chaotic?
- Its motion is fully deterministic — governed by exact equations with no randomness — yet arbitrarily small differences in starting conditions grow exponentially over time, making long-term behaviour practically unpredictable despite being mathematically determined.
- What is RK4 integration and why does it matter here?
- Fourth-order Runge-Kutta is a numerical method for solving the differential equations of motion accurately over time; a cruder integration method would visibly drift from the true physics, which matters a lot in a system this sensitive to error.
- Is this the same "butterfly effect" from chaos theory?
- Yes — the same core idea Edward Lorenz described with weather systems, demonstrated here in a system simple enough to watch happen in real time on two pendulums with almost identical starting angles.
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