Butterfly effect in a circle

Balls falling under gravity in a circle is another example of a chaotic system, sometimes referred to as the butterfly effect. @gpcbass reproduced the absolutely brilliant composition “Jesus bleibet meine Freude“, originally made by J S Bach almost 300 years ago. A full version can be found here and here Further details: 1. One ball in a circle having radius R 2. Two balls separated by *R 3. 100 balls, each pair being separated by 1e-6*R. Done in Python and FFmpeg. SymPy was used to solve some equations. Visuals inspired by @Numberphile,