Droplet in a stadium-shaped billiard (higher res version)
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- čas přidán 8. 04. 2021
- Wave front created by a drop of water in a stadium-shaped billiard. The dynamics in a Bunimovich stadium is chaotic, so I changed the color after each bounce to make things a bit less messy.
Music: "A Tall Ship" by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/...
Artist: audionautix.com/
For more information, see
images.math.cnrs.fr/Notre-uni...
www.idpoisson.fr/berglund/res... - Věda a technologie
when the water drop starts to look like biblically accurate angels:
w H e E z e -
Everybody gangsta till the center becomes the passageway to the neverland
*S H I T*
Uh oh
*RU RO RAGGY*
lol let's jump right in
Or hell
Wow, this one looks much more chaotic than the circle
They finally found a way to see what it looks like when you rub your eyes
This looks like a fun shape for a pool table.
That’s a good idea, different shaped pool tables! I went to a bowling place once and they had an air hockey table that was a complete square for four players, and a triangular table for three players.
@@cringekid07 That sounds awesome; I've never seen any tables like that.
Having them change color on bounce was a stroke of genius.
Yes, it was a hue-mongus achievement! 😎🌈
Unfortunately in the real world, a single droplet is not capable of such immense energy XD
Yes, big xd.
What about a single droplet traveling at 10,000km/s?
@@someonehungarian9002 that would just create a big splash but would not ripple for that long
@@mylo5641 what about liquid lava would that have enaugh force to keep the waves lasting?
@@someonehungarian9002 liquid lava is very viscous and would have trouble even keeping a single ripple
At first: ahhh so calm
Midway: uhh yeah I think I'm being hypnotized?
End: ALL I SEE IS COLORS
Holy jeeper jeeper jeeper jeepers, this is freaking chaotic and I guess I love it
2⁸th like
Jeepers creepers bro
This is a good representation of what my brain feels like in the moments just before I black out from a seizure; only the soundtrack isn't nearly as pleasant...
Love your animations Nils, keep it up!
Thanks, will do!
this went from 0 to a 100 real quick
You should make a video using "Giorgio by moroden" as background music
True, some Daft Punk tracks would go well with these
looks super cool, thanks for uploading
Thanks for the visit
i like how the middle is chaos then suddenly it becomes empty
I love it when I drop water into my pool and then it becomes the primordial soup
Bruh this one drop created what dr strange could only dream of
Amazing content!
Glad you enjoyed it
Billiard? More like "Brilliant"...ly colored! Thanks for making these.
This should be in a museum
from 0:50 onwards, it starts to look asymmetrical, probably due to youtube compression
i think it's just being poorly calculated from that point onwards, because there's too much going on for the computer to handle
@@demonindenim yea maybe
It got chaotic very quickly
Started as a droplet and ended up looking like an alian egg 😂
Wow, these are really interesting! Please keep up the good work.
Thanks, will do!
Chaotic but perfect
I believe every time the wave changes colour the music adds on
I looked away for 5 seconds and I come back and its complete chaos
This requires some next level eye cells.
this looks like a fever dream
It looks so asymmetrical despite the fact its probably perfectly so.
I knew I subscribed for something good. (:
This is nicely ergodic!
Pretty neat
This is my favorite one
imagine you take a piss in a pond and the waves start to look like this
This is the visual embodiment of
"Crap went from 0 to 100 real quick"
Damn this one went crazy
Real title: *drop in a stadium shaped pond creates chaos*
And this proves that we are still babies attracted to flashing colors
Character hiding on the ceiling:
Sweat droplet:
I knew it’s something chaotic.
No one:
Biblical accurate angel videos
Well that escalated quickly
Ah yes, the music helps the resolution.
I feel like I'm unlocking the secrets to the universe
you should make a few of these where the shape the drop is inside of is hidden, only to be revealed by the ripple.
At the beginning, this felt like watching a cat's cradle.
Oh, wow
You can see from the video how this was drawn to the screen.
There's a number of particles bouncing around, and a line is drawn between the 1st and 2nd, 2nd and 3rd etc.
Towards the end they get so spread out that you can easily see these straight lines, and even trace the path of individual objects (for example: at 0:57, blue line, bottom-right).
This is a different method to his later videos, in which Nils draws the velocity vectors of each of the bodies. I wonder what prompted the change?
Just a neat observation.
Just had this idea:
I don't know how many objects there are in this simulation, so in this case my source is "dude, trust me", but it *looks* to be much more than the later simulations.
This: czcams.com/video/Hi2ShwiPtWU/video.html uses only 500, for example (to reduce processor workload, presumably).
Thus, individual objects become distinguishable after only a couple bounces - and so would the lines between them. The velocity vectors are a much less unsightly alternative.
@@piotrdomagalski5096 The 8 year old video used 500 particles, partly because computers were slower back then, but also to show that dispersion is much slower in the circle than in the stadium billiard. I got the idea to display the wave front by connecting particles after a colleague showed me the article hal.archives-ouvertes.fr/hal-02541470/document in which the evolution of the front's length in a circular billiard is shown to grow linearly with time on average. This simulation uses 20 000 particles.
I then did some simulations of fronts in an elliptical domain, where it turned out that the expansion near the focal points is so strong that I had to keep adding particles to obtain a nice-looking curve, up to 200 000 of them. Something similar could be done for the stadium, of course.
I later did a couple other videos with again fewer particles represented by velocity vectors, because they allow to highlight other properties, such as the amount of dispersion.
Imagine dropping a stone in a pool and suddenly the pool stars boiling and the fabric of spacetime starts melting
Well. This escalated quickly. But it is beautifull.
wouldnt surprise me if a few of these frames were album covers
This isn't chaos, it's just complexity. Which makes one think all chaos is complexity but just too complex for our puny minds.
music: piano
the video: *complete chaos*
Sweet Cheezy Crust...
This looks like what 5 year old me thought mind control looked like.
This looks like my mind everytime I'm going to sleep.
Everything until it gets completely covered works as a reticle
It doesn’t look symmetrical, but it just somehow is
I just wanted to see some math-related videos but ended up having a psychedelic experience.
Yo nice music my brother is dancing on the floor. Idk its some kind of new style of dancing, because i neverseen it before.
That multiplied fast
CZcams compression went crazy
Yep, i miss the eliptic pond one now lol
The droplet is on drugs
🤯
This looks like the windows movie player background animation
Feels like it'll start lagging any moment now
0:49 POV: youre standing up after only 5 minutes of sitting
Chaos
May the Algorithm bless you
POV: You’re fighting Asriel Dreemurr but they left
you kids and your new fangled ripples
back in my day we *continues on for seven and a half hors about why ripples in ponds should just be circles*
How about a square/rectangular pool triggered from one of the corners?
it should be perfectly symmetric right? because the end looks unsymmetric. a rounding error i assume.
Yes, indeed, round-off errors become important after a while in chaotic systems.
Bill Niegh the Dry Ants Guy
When you take too much cough syrup
Synchronising alien dna.....
so thats why they say infinity can make a black hole
Try plotting it differently to sow something besides just the wave fronts.
It do be multiplying though
when you look one time away and the whole screen becomes blue
It stayed symmetrical for quite a while, but near the end some of the areas weren’t’ so, and were a bit more chaotic, not in accordance with the symmetry. Is this an unintentional artifact of the simulation?
It has to do with the order in which I draw the segments of the curve. Near the end, the curve has become very long, and you can see the straight line segments it is made of. The lines drawn last overlap some of the lines drawn earlier.
My brain when I rub my eyes too hard
Double the chaos with PlaybackSpeed x2
Triple the chaos if you play at x speed and then press f13
@@logandekmarques8412 sorry im on my phone
@@logandekmarques8412 I could download hacker keyboard tho
But nah
@@yourbadtrip4207 I just realized my joke was only viable a couple of years ago because of this lol
REEEEEEEEEEEE LET IT PLAY ALL THE WAY 'TIL IT'S "SETTLED" YA FRICKER!
My last brain cell when I need it:
How does it become asymmetrical at the end tho 😮
Because the front is made of line segments, that are drawn in a specific order, and they start overlapping at the end.
How can such a smooth boundary create so many discontinuities? Any intuitive explanation?
The mechanism is called defocussing. See czcams.com/video/yNFJba320dY/video.html for an explanation.
what software u use to simulate？
A C code with OpenGL libraries, and ffmpeg to create the movie.
Here is a version of the code: www.idpoisson.fr/berglund/vid_drop_ellipse.c
God bless youtube's algorithm
What if the boundary is the mandelbrot set boundary?
It would be hard to define the law of reflection on the boundary. You could look at waves in the Mandelbrot set, though it will not be that easy to simulate.
0:01 my dream
0:20 my mind
0:40 my night mare
0:50 my night mare when I watched a horror movie
How does this one not have an epilepsy warning?
What if you did a square
The end isn’t symmetrical. That’s interesting
imagine watching this high on acid
Ehat where the break my Mind lyrics again?
Its looks spinning
So this is touhou everyone is talking about
Hhhhhhhhhhhhhhh