Flowery pattern in mathematical billiard with circle boundary (using Matplotlib)

This is a mathematical billiard. It assumes no external forces. This is plotted and animated using Python Matplotlib. The reflection takes place only at the (solid) boundaries, and with respect to the tangent line at point of reflection.

The initial conditions is 500 non-interacting balls (or particles), then the particles move at different direction with equal velocity. Every time a particle is reflected, it's color changes (for artistic value).

The dynamics is not 100% accurate, but it is with small error. Because there are approximations in calculating, for example, the tangent slope at reflection point.

Inspired by Nils Berglund videos on Youtube.

Github:

Music:
- imagiro - wool gloves
- Glimlip x Yasper - I'm sorry
- mell-ø - Nova
- goosetaf x the fields tape x francis - carried away