Wave protection comparison 7: "Golden spiral" versus Poisson disc sampling
Channel: Nils Berglund
Date: 25/08/2021

This seventh comparison between different types of wave protections features two quite effective arrangements we have seen so far: the "golden spiral" (or "sunflower") grid, and a Poisson disc sampling arrangement. Both designs have close to 160 obstacles. The "golden spiral" grid is obtained by rotating around a central point, by an angle given by (phi-1)*360°, where phi = 1.618... is the golden ratio, and increasing the radius in such a way that the density of obstacles remains constant. The Poisson disc sampling algorithm used here is explained on the page https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3 
The colors indicate the energy of the wave: blue means low energy, red means high energy. The numbers in the four corners and at the top and bottom show the total energy in areas at the left and at the right of the obstacles, as well as in the area occupied by obstacles, compared to the energy of the incoming wave. The total energy is sometimes slightly larger than 1 due to round-off errors. 
There are periodic boundary conditions on the top and bottom sides of the displayed domain, and absorbing boundary conditions on the sides, which however don't work perfectly, explaining why you see some waves reflected from the boundary. 

Music: "Atmospheria" by Francis Preve@francispreve

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!