A resonator made of four parabolas
Channel: Nils Berglund
Date: 11/09/2021

Dynamics of a wave in a cavity made of 4 parabolic reflectors that share the same focal point. The initial state is a circular wave originating in the focus. Parabolas have the property of turning such a wave into a planar/linear wave, and vice versa. We thus get a wave that keeps transforming from circular to planar and back to circular. The wavelength of the initial state is larger than in the simulation https://youtu.be/n19XjuK_Dgs which seems to reduce numerical dispersion. 
This simulation has two parts: 
Wave energy: 0:00
Wave amplitude: 3:52
The colors in the first half show the wave's energy, with blue indicating low energy and red indicating high energy. The colors in the second half show the wave height: blue means height zero, green-yellow-red hues indicate positive height, while purple-red-orange hues indicate negative height.

Render time: 24 minutes

Music: "Six Seasons" by the Unicorn Heads@UnicornHeads

See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on  a few previous simulations of wave equations. 

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf 
C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html 
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!