Nils Berglund | Waves escaping a ring of obstacles: Sunflower grid @NilsBerglund | Uploaded July 2024 | Updated October 2024, 3 minutes ago.
This is a simulation of waves originating from a point source crossing a set of circular obstacles placed in an annular region based on the golden mean. This pattern is obtained by gradually adding discs, each time turning with respect to the center of the screen by a "golden" angle of (phi - 1) times 360°, where phi = 1.618... is the golden ratio or golden mean. The distance to the center is gradually increased, in such a way that the density of circles remains constant. This arrangement has appeared before on this channel, see for instance youtu.be/fQaVL3mE6VY or youtu.be/c8sKkM8ZDTs .
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:11
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. 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.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
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: 29 minutes 22 seconds
Compression: crf 23
Color scheme: Part 1 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Moorland" by Underbelly@yousuckatproducing
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 circular obstacles placed in an annular region based on the golden mean. This pattern is obtained by gradually adding discs, each time turning with respect to the center of the screen by a "golden" angle of (phi - 1) times 360°, where phi = 1.618... is the golden ratio or golden mean. The distance to the center is gradually increased, in such a way that the density of circles remains constant. This arrangement has appeared before on this channel, see for instance youtu.be/fQaVL3mE6VY or youtu.be/c8sKkM8ZDTs .
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:11
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. 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.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
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: 29 minutes 22 seconds
Compression: crf 23
Color scheme: Part 1 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Moorland" by Underbelly@yousuckatproducing
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
