Uploaded October 2021 | Updated September 2026, 2 weeks ago

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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@gpcbass reproduced the absolutely brilliant composition "Jesus bleibet meine Freude", originally made by J S Bach almost 300 years ago.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 youtube.com/watch?v=MVsiOKTaCdw and here youtube.com/watch?v=WC08VRTqKj0.

Further details:
1. One ball in a circle having radius R
2. Two balls separated by 0.01*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, youtube.com/watch?v=6z4qRhpBIyA