Millions of particles forming cardioid caustics in a circle billiard @animations_ag
Millions of particles forming cardioid caustics in a circle billiard  @animations_ag
Uploaded October 2024 | Updated September 2026, 2 weeks ago
This is a classical counterpart of the quantum circle billiard uploaded yesterday: youtube.com/watch?v=akh7KbPyOBI

Simulation was done in Mathematica, i.e., analytically computed reflections. The initial configuration of the particles is normally distributed with similar parameters as in the quantum version.

The quantum and classical solutions are very similar, and I tried blending both animations by fading back and forth between them in the same video, which unfortunately "screwed up the bitrate" badly when uploaded on YT - hence they are separated in two videos.

The beautiful song is made by Dennie a.k.a. @gpcbass (keys and bass) and Rogge (guitar). The song can be listened to/viewed in its entirety here: youtube.com/watch?v=GMYXI39MYOU. This song is a remake of J. S. Bach's Preludium BWV935.
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Alexander Gustafsson |

Millions of particles forming cardioid caustics in a circle billiard

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