Waves of two different frequencies crossing a "sunflower" lattice
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- čas přidán 7. 07. 2024
- Some recent simulations on this channel, such as • Waves of two different... , showed waves of two different frequencies, produced by two different sources, crossing a regular lattice of scatterers. Here the regular lattice has been replaced by a "sunflower" pattern of discs. This pattern is obtained by staring with a disc at the center of the display, and then gradually adding shifted discs, each time turning by a "golden" angle of (phi - 1) times 360°, where phi = 1.618... is the golden ratio or golden mean. The distance to the original circle 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 • A sunflower pinball or • Wave protection compar... .
The frequency of the lower source is three times the frequency of the upper one. The resulting wavelengths are such that the open intervals in the grating are between both wavelengths. As a result, waves of the lower source pass the grating more easily, as can be best seen on the energy plot.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:19
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: 35 minutes 28 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Raw Deal" by Gunnar Olsen
See also images.math.cnrs.fr/Des-ondes... 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...
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction #grating - Věda a technologie
I love the wave energy part showing rays sprayed from the lattice!
it's neat how you can see the waves following the natural spirals in the lattice, starting around 1:45.
The diffusion pattern of light has been maximized by the propagation of seeds in a circular pattern of 137.5° radially, creating an absorption pattern of light to the seed pod that promotes more growth.
Fantastic! Thanks for posting ! ❤
Cool!!
We 👏👏love 👏👏our 👏👏fibonacci
Could you try to simulate the irredecent scales on butterfly wings? They simplify easily to 2d I think
Are those also related to Fibonacci numbers?
@@NilsBerglund I don't think so. Light just resonates in there in such a way that yellow light gets canceled out
Is this kind of arrangement used for anything in the real world or is it just because it looks neat?
Something close is used by sunflowers because it's the most efficient radial packing of points I think.
@@lih3391 yeah no I know. Every Fibonacci nut will tell you all about sunflowers five times a day. I meant in the context of wave propagation.
I'm not aware of an application other than in phyllotaxis (the geometry of plants), but it is not impossible something like this is used for sound damping or similar applications.
@@NilsBerglund okay thanks! It definitely does look cool :)
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