Nils Berglund | Waves branching through Poisson disc obstacles @NilsBerglund | Uploaded July 2024 | Updated October 2024, 4 minutes ago.
This is a simulation of waves originating from a point source crossing a set of obstacles forming a Poisson disc process, also known as blue noise. This is obtained by placing the obstacles randomly, but with an imposed minimal distance. Note the nice standing wave patterns in the wave height part, and the filamentation in the energy representation, similar to a branched flow, illustrated for instance in the video youtu.be/kOR6OiRlL8Y
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:27
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 37 minutes 6 seconds
Compression: crf 23
Color scheme: Part 1 - Parula, originally from Matlab
mathworks.com/help/matlab/ref/colormap.html
Part 2 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "Desert Catharsis" by Asher Fulero@AsherFulero
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ 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 hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction
This is a simulation of waves originating from a point source crossing a set of obstacles forming a Poisson disc process, also known as blue noise. This is obtained by placing the obstacles randomly, but with an imposed minimal distance. Note the nice standing wave patterns in the wave height part, and the filamentation in the energy representation, similar to a branched flow, illustrated for instance in the video youtu.be/kOR6OiRlL8Y
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:27
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 37 minutes 6 seconds
Compression: crf 23
Color scheme: Part 1 - Parula, originally from Matlab
mathworks.com/help/matlab/ref/colormap.html
Part 2 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "Desert Catharsis" by Asher Fulero@AsherFulero
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ 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 hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction
