Nils Berglund | A light source moving between the focal points of an ellipse @NilsBerglund | Uploaded May 2024 | Updated October 2024, 2 minutes ago.
This video is mostly me playing around with my software. I wanted to see what happens when a source of light moves from one focal point to the other one in an ellipse with reflecting boundaries.
In this simulation, a pulsating source of light first stays for a while on one focal point of the ellipse, then moves to the other point, and finally stays there for a while. Interference patterns reveal all sorts of curves. Some of them are probably confocal ellipses and hyperbolae, but there are other curves, that may have something to do with involutes and evolutes and what have you.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:40
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.
Render time: 27 minutes 2 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis, by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Timelapsed Tides" by Asher Fulero@AsherFulero
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 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 #ellipse #focus
This video is mostly me playing around with my software. I wanted to see what happens when a source of light moves from one focal point to the other one in an ellipse with reflecting boundaries.
In this simulation, a pulsating source of light first stays for a while on one focal point of the ellipse, then moves to the other point, and finally stays there for a while. Interference patterns reveal all sorts of curves. Some of them are probably confocal ellipses and hyperbolae, but there are other curves, that may have something to do with involutes and evolutes and what have you.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:40
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.
Render time: 27 minutes 2 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis, by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Timelapsed Tides" by Asher Fulero@AsherFulero
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 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 #ellipse #focus
