Chaos & the Double Pendulum pt. 2

The sensitivity to initial conditions is easier to see if you focus on the trail drawn by the lower ball. The simulation below is identical to the one from part one except that it only draws the trail of the lower ball. Try adjusting the mass and notice how drastically the resulting trajectory of the pendulum changes.

You may even notice that for low masses (it works best at 1kg), the pendulum traces out a shape that mathematicians refer to as a cardioid. The name cardioid comes from its heart-like appearance. That’s right, a heart. And nothing else. Get your mind out of the gutter.