Chaos Pendulum - Double Pendulum Simulator
Chaos Pendulum is a real-time double pendulum physics simulator that visualizes chaos theory through stunning neon trail art. A double pendulum two pendulums connected end-to-end demonstrates extreme sensitivity to initial conditions, meaning tiny changes in starting angles produce wildly different, non-repeating patterns. Set your initial angles, arm lengths, and gravity, then watch as the system traces hypnotic geometric paths across the canvas. Each trail is unique and unrepeatable, embodying the butterfly effect where small changes cascade into dramatically different outcomes. Perfect for students learning chaos theory, artists seeking physics-inspired generative art, or anyone mesmerized by the beauty hidden in mathematics. Runs entirely client-side with no signup required.
Simulation Stats
How to Use This Simulator
- Step 1 - Adjust initial angles (0-360°) for both pendulum arms using the sliders. Small angle changes (even 1°) produce vastly different results due to chaotic sensitivity.
- Step 2 - Set arm lengths (50-200px) and gravity (0.5-2x). Longer arms create broader sweeps, while higher gravity increases speed and energy.
- Step 3 - Configure trail length (100-5000 points) to control how much history is visible. Longer trails reveal intricate patterns but may slow performance.
- Step 4 - Click Start to launch the simulation. The pendulum traces a rainbow gradient trail that shifts hue over time. Use Save Art to download your unique creation as a PNG image.
Why This Double Pendulum?
The double pendulum is a classic chaotic system governed by coupled differential equations with no closed-form solution. This simulator uses the Runge-Kutta numerical integration method to calculate angular accelerations based on gravity, mass, and arm length parameters. Unlike single pendulums with predictable periodic motion, double pendulums exhibit non-periodic behavior where trajectories never exactly repeat, no matter how long you run them.
The butterfly effect a hallmark of chaos theory means changing the initial angle by 0.1° produces an entirely different pattern after just a few seconds. The neon trail visualization uses HSL color cycling synchronized with elapsed time, creating dynamic art that reveals the pendulum's path through phase space. This behavior appears in weather systems, planetary orbits, and even stock markets anywhere small uncertainties grow exponentially over time.
Pro tip: Try angles near 90° and 180° for slower, elegant spirals, or extreme angles (near 0° or 360°) for violent, unpredictable motion. Set trail length to maximum (5000) and let it run for 30+ seconds to create intricate mandala-like patterns. The Save Art feature captures your unique chaos signature no two runs will ever produce the same image, making each export a one-of-a-kind physics-generated artwork.