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The origin of the xenomorph: wave in a rotating ellipse
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- Опубліковано 15 сер 2024
- This is a variant of the video • Classics revisited: ci... with a slowly rotating ellipse. The angular speed of the ellipse has been kept rather small, to avoid having too much numerical dispersion. As in the static case, the focal points play a special role, but the rotating boundary creates some extra spinning of the waves.
The colors indicate the energy, according to the bar on the right. The rotating boundary conditions are implemented in the simplest possible way by setting the wave to zero outside the rotating ellipse. They thus do not take into account any energy that the boundary might transfer to the wave.
Note: I'll be traveling for a few days, so may not reply to comments right away.
Don't let the bedbugs bite...
Render time: 24 minutes 30 seconds
Color scheme: Magma by Nathaniel J. Smith and Stefan van der Walt
github.com/BID...
Music: Inner Sanctum by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommon...
Source: incompetech.com...
Artist: incompetech.com/
See also images.math.cn... 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....
C code: github.com/nil...
www.idpoisson....
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!
I'm a little surprised this didn't become chaotic.
What is mundane for the spider is chaos for the fly.
If the medium is perfect as well as the relative geometries, "chaos" would cost more energy than is in the system.
It didn't?
It did become chaotic
@@sundog3247 whys that?
Oh how fascinating, I love the “whorls” that form around the foci!
I like how the waves always maintain the symmetries of the container. Like here with the 180° rotational symmetry.
Well, the starting conditions were symmetrical and there was nothing to change it, so I would expect symmetry.
@@chixenlegjo ok, glad you're feeling that way. I think it's cool
Interesting insight
I tried to imagine how fast the ellipse would rotate if you sped the video up to make the waves go at sonic speed.
Came to the conclusion, that our everyday objects are quite stationary from the perspective of sound waves.
There is a causal relationship. At normal pressure, it takes a whole bunch of energy to keep something moving at any significant fraction of the speed of sound.
Even little tiny things rotating near the speed of sound are painfully loud.
"Don't let the bedbugs bite..." Haha, I very much liked this reference!
Fantastic! The ellipse never disappoints!
How did you decide on a rate of rotation? Did you try different speeds until you found one that looked the coolest, only try the one shown in this video, or something else?
i agree
I tried 2 or 3 different speeds. The rotation is slower here than in other rotating domains, because I wanted avoid the patterns to blur too quickly. I then chose the speed that produced the best-looking result.
Interesting that most of the energy ends up being concentrated in the long sides of the ellipse, and furthermore that most of the energy passes through or close to the ellipse's center.
This sounds like disc_11 on steroids.
I like how the oval turns slowly throughout the video
Fascinating. Let's put this on Ripley
I have no idea what I am looking at, even after reading the description, but I am still enjoying it. Very interesting stuff.. I think.
I love the vortices around the ellipse foci :3
I love the symmetries produced by the devolving wavelengths
You reach a new level with every video. It’s magnificent.
Wow, thank you!
I don't know why I love these so much, I just do.
I'm here for the music!
This is so trippy.
I feel like I never really knew what the term “hauntingly beautiful” meant until I heard this.
This is the feeling of existential dread in sound. That feeling of being mortal, of being limited by the ticking clock, made manifest in audio.
Beautiful! How about using fourier transform to translate wave patterns to audio? The music is fantastic tho.
I haven't tried it for this shape, but see www.idpoisson.fr/berglund/isospectral.html for some different ones.
I love these animations! Reminds me of my 4th-year in maths: solitons, dynamical systems, and computational ergodic theory 🥲
You cannot comprehend the true form of Giygas’s attack!
Hypnotizing
Mesmerizing stuff
Mitosis echoes
spoooky
The universe is a torus and so is everything inside of it. As above so below.
I like the music in this one.
Cool. This got on my recommendation page.
Sounds like an LSD trip. Awesome math!
Watch it at 2x speed.
Stuff getting deeper
Excellent ... like the sound too ... hahaha ... cheers ...
Give it one billion years and it will become alive ;))
This music is freaking me out
How hard would it be to make the bounds rotation reactive to energy dissipated on it?
Maybe making the energy dissipated a torque and starting the wave off center
In principle, I believe one could compute the torque from the velocity of the waves near the boundary. Some modelling is required, but this has certainly be done by people modeling the effect of moving fluids on various objects (planes, boats, bridge pillars...)
Looks like those pics of cosmic background radiation.
Is the rotation speed related to the propagation time from focal point to focal point? (Is the time to rotate the ellipse180º a simple multiple of the time for the wave to propagate from one focal point to the other? All paths would be the same length in a stationary ellipse.) The closer the relationship, the more I would expect to see some resolution after a number of "propagation-time-units".
This is beautiful. Have you tried the 3d simulations similar to this? Eg the Platonic solids
3d would be far too costly in terms of computer time with the method I'm using here, with that resolution. There may be other ways of achieving that (e.g. using a GPU, Fourier decomposition).
What does a numerical simulation have anything to do with the xenomorph?
Just an association the visuals created in my brain ;)
Yes, I was expecting it to end with a picture emerging, but I don't see anything clear where it stopped.
Is this system integrable? In principle, you should be able to derive the stationary modes of an ellipse, and the rotation will add extra non-inertial terms into the Hamiltonian. This should allow, in principle, a solution without needing numerical integration. Very neat channel!
Thanks! For a non-rotating ellipse, the system is indeed integrable. I'm not quite sure what if this remains the case when it rotates, because the equation in an ellipse is not separable in polar coordinates, you have to use another set of coordinates.
Looks like cosmic background radiation that people have been stuck on since the beginning of the big bang theory except there is no room for explaining the popcorn effect that made it suddenly expand. LOL.
I don't quite get how this is the origin of the xenomorph? Is there a reference or joke I'm missing?
I think it's simply that there's something weirdly alien about the wave patterns that appear, and the colors were chosen to emphasize that weirdness.
Yeah, the shapes kind of reminded me of H.R. Giger's style :)
It’s like if you let this continue, the emerging complex structure would have life and intelligence. That and the ellipse is shaped like an egg. Gotta extrapolate a bit. Nils may not have the CPU power and resources to produce a 100 million year simulation for us on UA-cam. That is the scale that I would imagine these complex evolutions to exist in, especially if we are talking true “origins.”
Are all the ripples accurate depictions of interference patterns, or are they artifacts of a imperfect computation? I barely understand these simulations and have no idea how you make them. Do you have videos explaining this? Would you consider publishing an FAQ?
Ripples are already present in the initial state. They are probably amplified by discretization errors in the numerical simulation.
I'm thinking of making some tutorials when I find the time. Meanwhile, you may want to have a look at the overview article hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
yay
I'm curious what output might look like if one painted the values of waves at the point of reflection over this whole animation. Between the inscribed circle and circumscribed circle, I wonder if any interesting patterns might appear like hotspots of reflection or even continuous paths?
3:20 oh yeah, its all coming together 😏
you should make a chamber shaped like a human
The Egg
I'd love to see this arrangement, but with the ellipse rotating much more quickly, and whether or not any energy is able to propagate to the furthest points. I think it could be quite interesting if the rotation speed were set such that the velocity of the foci matched 'c' for the simulation.
You're probably right, but that would be quite challenging to simulate correctly, because the moving boundary causes a lot of numerical errors, which increase with the speed of rotation.
The way the waves diffract as they pass one another implies an interaction beyond addition? Is there any such thing in your code? A residue? A slight stickiness to the media? Or is this just an illusion of sorts?
The simulation (approximately) solves the linear wave equation, so there is no interaction intended. Whatever you see beyond interference must be either an optical illusion, or a numerical dispersion phenomenon. Also keep in mind that the colors show the energy, which is a sum of two quantities squared (proportional to variation of the wave in time and space).
Trippy
What is that background music?
Have you tried rotating it about other points, other than the center?
Not yet.
Hmmm, that's funny. Now I feel like watching some old-school Dr.Who eps. Wonder why? 🤔
backlit/underlit water pond with overhead parasol display. landscaping water feature design and installation company
It multiplied *_*
aaaaaeeeeaaaaeeeoooooouuueeeaaaiiiiiiyyyeeeaa
fuzzy
very good
Thanks
What simulation tool do you use?
I code these in C, with some OpenGL libraries. The code is open source, there is a link in the description to my GitHub page.
@@NilsBerglund cool. Thanks.
♥
Why don’t you make it interesting and make the ellipse react to the wave ;). Give it a small mass and let the waves have some momentum, that actually more interesting, it will speed up, slow down and so on in interesting ways.
Very nice. But the background music is not nice. It's scary.
Where is the xenomorph?
Lurking in the dark somewhere, ready to jump on you...
this must be how the universe was formed
You should make some NFT’s
Now do something non-linear!
I might indeed... :)
Thank God I got yet another blessed cheatcode in order to advance my brains neural network to the next level beyond the apex of human experience into the realm of the unique and unknown now known yet shrouded from view, blessed be thine resonator 🙏🙏
God I miss cocaine
So...alien?