A "golden spiral" wave protection
Channel: Nils Berglund
Date: 14/08/2021

The obstacle arrangement in this simulation is based on a "real" golden spiral, as explained in the Numberphile video https://youtu.be/sj8Sg8qnjOg : each circle is obtained by rotating around the center of the arrangement by an angle equal to phi - 1 = 1/phi = 0.618.. times a full turn, and increasing the distance to the center by an amount chosen such that the density of circles remains constant. In addition, only circles falling within a vertical strip of fixed size have been kept. Apart from that, the arrangement is similar to what is found in certain flowers and other plants. The simulation has two parts. Part 1 shows the evolution of the wave height, while part 2 shows the evolution of the waves' energy. 
Wave height: 0:00
Wave energy: 2:20

Music: "Lazy Boy Blues" by 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!