Pendulum — the chaos of a double pendulum
A double pendulum is two rods chained together with a mass at the joint and at the tip. It's the textbook example of chaos: tiny differences in the starting angle produce wildly different paths within seconds. Pendulum is a double pendulum simulator that lets you drop them and watch the inked tip trace beautiful, never-repeating curves.
How to play
Grab a glowing bob and swing it by hand, or drag empty space to drop a fresh pendulum — that point becomes the anchor, the drag direction sets the initial angle. Release with momentum to fling it; bobs collide elastically, kicking each other into new chaotic paths. Swing kicks every live pendulum with a fresh random impulse, Clear wipes the trail.
Why it's satisfying
A double pendulum is one of the simplest physical systems where exact prediction is impossible. The trail it leaves is mathematically beautiful — Lyapunov exponents made visible. Hard to look away.
The idea behind it
A single pendulum is perfectly predictable. Hang a second one from its tip and that ends: the motion is chaotic, which means a starting difference of a thousandth of a degree grows exponentially until, after a few seconds, the two paths have nothing in common. Nothing random is happening; the equations are fixed and simple, it is just impossible to know the start precisely enough. That is why the trail never repeats, and why two pendulums dropped side by side drift apart so quickly.
Tips
- Drag only slightly off the vertical: at small angles a double pendulum stays almost regular and the trail draws calm loops. Larger angles push it into chaos.
- Drop two pendulums from nearly the same spot with nearly the same drag. They move together for a moment, then split: that is chaos, seen live.
- When the trails slow down, press Swing to kick every pendulum back into motion.
About
Pendulum is part of Alcy, free contemplative micro-games. For more physics: Orbit, Wave, Spirograph.