Waves hitting a Sierpinski carpet

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After having done a number of simulations solving the heat equation in fractal domains, we are ready to do the same for the wave equation. This animation shows solutions of the wave equation outside 4 different approximations of a Sierpinski carpet. It illustrates why fractal materials can have an insulating effect, by trapping and reflecting sound waves.
See • Wave hitting a Sierpin... for a version showing the energy density instead of the height of the waves.
Level 1: 0:00
Level 2: 1:32
Level 3: 3:05
Level 4: 4:36
(courtesy of My Craft)
Music: "The Emperor's Army", by Jeremy Blake@RedMeansRecording
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...
Reflections on the boundaries of the rectangle are minimized by adding Neumann-type boundary conditions on the time-derivative of the wave.
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!

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26 май 2024

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Комментарии : 1 тыс.

@adrien5568 2 года назад

And now you understand why mangroves are important for coastlines.

@NilsBerglund 2 года назад

Very true!

@beaconblaster33 2 года назад

for humans

@Danicker 2 года назад

Wow I never realised that!

@YukuriuddoHerusaizu 2 года назад

Awesome!

@bbgun061 2 года назад

I was thinking about some kind of breakwater for a harbor, but I hadn't made the connection to mangroves! Thanks!

@woollama 2 года назад

This is the pinnacle of 3 AM content

@emanwonkon2205 2 месяца назад

Im here a 6 am..

@turbofanct6679 2 месяца назад

Literally 3:24 am here

@unknownuserwhoisitlol8776 2 месяца назад

3:26 am here lol

@liam.28 2 месяца назад

3:‎29 here

@leonardorolingstella8554 2 месяца назад

I’m bored outta my mind at 8:30 pm right nkw

@oblonghas 2 месяца назад

The more people in the club, the more volume you need to get the sound to cross the dance floor, but in 3 dimensions

@AluminumHaste 2 месяца назад

That's why speakers are often mounted on ceiling

@ChrisStoneinator 2 месяца назад

That’s primarily due to absorption effects, which I don’t think are modelled here. This simulation just shows how the reflections lead to the wave energy becoming more diffuse more quickly, as opposed to reaching the shore in one go. The same sooooort of applies in a club, but 3D acoustics are very different so surface acoustics.

@DantevanGemert 2 года назад

Now I'm curious whether it's really the fractal shape or just the large amount of small squares that's good at stopping waves

@qu765 2 года назад

i would guess mainly the small squares, a grid might let some through, but a hex grid probably not.

@NilsBerglund 2 года назад

Probably, yes (see ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mgC3gw2kbBE.html for a simpler geometry). The fractal geometry might enhance particular high-frequency resonances, though.

@DantevanGemert 2 года назад

@@NilsBerglund ah I hadn't yet come across that one. Interesting, thanks for replying!

@bengravell5086 2 года назад

@@NilsBerglund Very cool! I think it would be a more "fair" comparison if the area of the black squares was kept constant; in this video each level adds more area.

@wmlye1 2 года назад

I'm also curious what happens as the ratio of the wavelength to the square spacing varies. Is it possible to build something akin to a Bragg reflector or a Bragg filter using a Serpinski fractal?

@jpopelish 2 года назад

I think it would have been a more useful comparison, if the black area had been constant, in these comparison runs.

@NilsBerglund 2 года назад

Thanks for the idea!

@PatrickPease 2 года назад

that's what i was expecting

@joshuavillwo 2 года назад

Yeah, the sizes need to be adjusted so the total area is the same between runs.

@aarontooth 3 месяца назад

@@PatrickPeasePatrick peaseeeee

@achromaticism 2 года назад

i’m awful at physics so all I’ve learned from this is that /naughty waves get put in the F R A C T A L S Q U A R E to atone for their crimes/

@KAngel32 2 года назад

Same here

@brada5142 2 года назад

I mean, you're not wrong

@Zenith_Guard 2 года назад

At least it isnt the _/P E A R W I G G L E R/_

@8bitorgy 2 года назад

Rectal square

@OghamTheBold 2 года назад

I got a Physics prize at school (and they had to hire an advanced Math teacher) in 2020 I worked for Aston Martin JCB Porsche Suzuki - they fired me with pneumonia I was in ICU

@yddishmcsquidish3904 2 года назад

This is the main reason for the need to protect mangroves in sensitive areas. Good demonstration!

@ryanbell3704 2 года назад

watch in 2x speed for the optimal experience

@Random_Nobody_Official 2 года назад

Yeah, i did that.

@fryncyaryorvjink2140 2 года назад

Yeah, I'd go higher if possible

@crabobserver 2 года назад

Thanks

@MiScusi69 2 года назад

I did that too

@Fiufsciak 2 года назад

Thanks for reminding this exists

@nomekop777 2 года назад

Alternate title: increasingly effective ways to stop a tsunami

@cassandra_classic 2 года назад

@@mingkanglin9017 yes that’s… Exactly what he said.

@scowell 2 года назад

A tsunami is a low-frequency event... this is a very high-frequency impulse event, absorbed by the carpet. If you raise the water level the carpet is inundated.

@tackontitan 2 года назад

Nothing stops a tsunami except time

@freerobux49 3 месяца назад

@@tackontitan and a giant wall.

@Baburun-Sama 3 месяца назад

Another Alternate title: Defending the Menger Sponge Fractal from a Lot of Swarms

@mattiarecchi4024 2 года назад

This configuration is an excellent acustic barrier

@il_vero_saspacifico6141 2 года назад

Boh non è considerato che il suono si propaga anche nei muri, tecnicamente in questo modello finisco un semplice muro continuo è un isolamento perfetto

@mattiarecchi4024 2 года назад

@@il_vero_saspacifico6141 ho pensato che una parete semplicemente ha un certo coefficiente di assorbimento che va ad attenuare il suono. Una struttura come questa ha dalla sua parte che produce una miriade di sorgenti a fase casuali che mediamente fanno interferenze distruttiva

@vigilancebrandon3888 2 года назад

Or maybe a method for preventing shoreline erosion?

@danielebonaldo6864 2 года назад

@@mattiarecchi4024 è la base dei metamateriali, sia acustici che ottici, i quali sfruttano geometrie periodiche di materiali "normali" per ottenere proprietà estreme (come altissimi assorbimenti in acustica o indici di rifrazione negativi in ottica)

@mattiarecchi4024 2 года назад

@@danielebonaldo6864 very very figo

@Erin-ks4jp 2 года назад

Hang on, does this mean that a material with a sierpinski carpet cross section would make a very good *directional* acoustic insulator? Because that's what this is looking like. It would conduct well in the direction that in this is in and out of the plane, but insulate very well in the other two directions.

@NilsBerglund 2 года назад

I'm not a specialist, but it seems that some researchers are interested in that kind of application, see for instance hal.archives-ouvertes.fr/hal-01555279

@tenix6698 2 года назад

I think that in the real word the individual squares would giggle and lass the waves further

@firefly618 2 года назад

you can make a wall by stacking pipes horizontally: they would allow sound in the direction of the pipes, but they would block it in the traversal direction.

@DeRien8 2 года назад

@@firefly618 but would that conduct sound laterally that had reached the wall from a perpendicular approach? Feel like unless the outside pipes would need to be resonant to pick up the incident sound in the first place.

@jakubw.2779 2 года назад

I thought about radar waves. But then i saw level 4 and majority of waves being reflected and i thought it wouldn't really work. Not in this shape at least

@Drawoon 2 года назад

when you reach infinite levels, is it practically just a square again?

@NilsBerglund 2 года назад

I think so, yes, because the waves do not have infinitely small wavelengths (or rather, there is no energy at arbitrarily small scales).

@ekosh6266 2 года назад

No it's not a square, our mind is not able to picture it but some math can reveal the amount of area it covers, and it's way less than what a square would

@Drawoon 2 года назад

@@ekosh6266 Let's do the math then. The first iteration splits the square in 9 pieces and removes the middle one. The second iteration splits those each in 9 pieces and removes the middle ones. The third iteration splits those each in 9 pieces and removes the middle ones. I hope it's clear each iteration multiplies the remaining uncovered area by 8/9. after infinite iterations, the leftover area is 8/9^infinity which would be 0, so the shape covers the whole square. Did I get that right?

@ekosh6266 2 года назад

@@Drawoon Okey yes, you got that right, but unfortunately, a set having area zero does not mean it's empty. Or the opposite, even if adding infinite squares add up to the total area we are aiming, it doesn't mean it ends up being the whole square. Easy proof: give some coordinates, the bottom left corner of the container square is (0,0) and top right is (3,3), then our fractal will never contain the point (2,2) (for example, it will never contain many other points, infinitely uncountable points are left out) . Hard proof: search for the Cantor's set and diagonal proof.

@Drawoon 2 года назад

@@ekosh6266 sure I guess, but when it comes to the waves from the video it'd act just like a big square even if it technically isn't

@hexagon8899 2 года назад

i like how level 3 lets basically no noise get passed

@matthewhubka6350 2 года назад

I thought the same thing but then I realized that the black let’s nothing pass through it at all, so it isn’t really a good simulation of if this would be good soundproofing. Also, constructing this shape would be a nightmare. Normally, the black parts are holes, but in this case the black parts are where the wall is

@xxportalxx. 2 года назад

@@matthewhubka6350 some square extrusion with mounts at the ends would be a fairly good analog you could build pretty easy. You could also 3dp that easily as well on smaller scales. I doubt this would be as effective as normal sound proofing panels tho

@diacoal2433 2 года назад

I think it simulates water waves, not sound waves.

@mynamesbigmynamesbigmyname4757 2 года назад

@@diacoal2433 waves are waves

@diacoal2433 2 года назад

@@mynamesbigmynamesbigmyname4757 But sound waves move through objects whereas water ones don't

@eyewind7379 2 года назад

This music makes me feel like I'm playing a flash game

@pisscvre69 Месяц назад

goes unreasonably hard and i love it

@wflinner 2 года назад

The music feels like it’s from a coolmath-games flash game

@lumotroph 2 года назад

The green-energy-level echoes of the third level really remind me of Conway’s game of life!

@eduardo98m 2 года назад

Some fluid simulation methods are based on the same principles as Conway's game of life (Cellular automata)

@ldavilla8971 2 года назад

Dude, this shit has to do with quantum tunneling, the carpet is the barrier

@josephvictory9536 2 года назад

Interesting. Except its dynamic now with a sliding float due to changing energy from the wave (instead of binary). Kinda neat observation. Thx for saying

@ldavilla8971 2 года назад

@@josephvictory9536 who are you replying?

@donerskine7935 3 месяца назад

Exactly, that is what struck me, I came looking through the comments to see if anyone else had the same observation.

@Tumbolisu 2 года назад

What if we start at level 2 and replace the big square in the middle with a wave?

@jojogape 2 года назад

This gave me inspiration for cool soundwave-blocking spells

@salaciousBastard 2 года назад

Sierpinski 4: "Tsunamis of that level have no effect on me." Tsunami 3: "You bastard!" Mangrove 4: "What am I a joke to you?"

@JustwinJBees 2 года назад

Interesting tidbit, the waves inside the carpet of level 4 looks suspiciously like the simulated random noise that the universe makes on the smallest levels.

@gtziavelis 2 года назад

the more trees we chop down, the more destructive winds there will be.

@salsamancer 2 года назад

This is stimulating pressure wave propagation, not fluid motion

@anonym3017 2 года назад

@@salsamancer yeah but we also know how good mangrove forests are at stopping and breaking up waves.

@johnassal5838 2 года назад

@@salsamancer Then why don't they construct the footings of large buildings or entire cities in earthquake zones to resemble the later versions?

@gavindillon1486 2 года назад

@@johnassal5838 ... that's a fucking EARTHQUAKE. That's the ground violently shaking, not fluid impact

@johnassal5838 2 года назад

@@gavindillon1486 both are mediums carrying a *PRESSURE WAVE.* Pressure waves are a pulse passing *through* a medium not a long distance movement of that medium. Even the biggest quake doesn't move the ground more than dozens of feet while the *seismic wave* covers thousands if not hundreds of thousands of square miles.

@cheesybutler9544 2 года назад

think it’s really cool how it charges up almost like a battery releasing the stored energy slowly

@MatthewConnellan-xc3oj 3 месяца назад

Yes.

@feynstein1004 2 месяца назад

Damn, that's a good observation. Could we use something like that to generate energy from sound/noise? 🤔

@ralfbauerfeind8236 6 часов назад

There is a Herman proverb: "Wie man in den Wald hineinruft, so schallt es heraus". (As one calls into the forest, it resounds.) Very nicely demonstrated in level 4.

@NilsBerglund 3 часа назад

Thanks. It had never occurred to me before that "Hermann" rhymes with "German". Arminia, unser Herz schlägt nur für Dich.

@okboing 2 года назад

I love the way that the wall of tiny squares, the first wall that the waves hit in level 4, they act just like a continuous wall in regards to reflecting back the wave

@rogerkearns8094 2 года назад

Double slit experimenter: Hey, where are my photons?

@canadalavearn 2 года назад

This is an advanced joke

@Zenheizer 2 года назад

@@canadalavearn Jimmy neutron lvl joke ;)

@kyototo. 2 года назад

Here// *also* here。

@alphaamoeba 3 месяца назад

Sierpinski Carpet with suspiciously photon shaped bulging cheeks: idk

@christopherrogers532 2 месяца назад

lol double slit? More like Integral Slit Experiment. XD

@MushookieMan 2 года назад

Now solve it analytically, and prove the sequence of functions converges pointwise to a limiting function.

@NilsBerglund 2 года назад

Thanks, that's a nice idea for an exam, my students will love it!

@ostsmulor 2 года назад

What have you done

@aracaniusinfinius2880 2 года назад

Formed a new method of torture, obviously

@tachikomagaming2451 2 года назад

the true face of physics

@nooneinparticular3370 2 года назад

@@NilsBerglund May God have mercy on their souls, because you certainly won't.

@GreyKnightsVenerable 2 года назад

Level 4 was beyond my expectations in its performance, if it was an acoustic barrier I would’ve heard nothing on the other side of it. (Imagining if it was 3rd dimensional of course, as 2d would only stop a fraction of the actual sound waves.)

@IEatcaTos 2 года назад

really appreciate the drum and bass in this video

@NilsBerglund 2 года назад

A nice track by Jeremy Blake, aka Red Means Recording ru-vid.com

@kristadzive 2 года назад

I have no idea what this is, but it's kinda beautifull

@NilsBerglund 2 года назад

Thanks. It represents a wave encountering a fractal obstacle. There is another version here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-LTsCx2T-4hA.html where the colors represent the wave's energy instead of its height.

@Andreas-zm9tg 2 года назад

I feel ya m8

@1997CWR 2 года назад

It's interesting to see that the wave appears to stimulate a resonant mode in the grid that only very slowly decays. Is Energy conserved in your simulation sceme?

@NilsBerglund 2 года назад

No, I put "absorbing" boundary conditions on the large rectangle to reduce reflections on the boundary without having to simulate a larger domain. These boundary conditions absorb part of the energy in the course of time.

@medtherockstar820 2 года назад

@@NilsBerglund what happens when there is no energy absorption by the large rectangles? ... Did you consider putting in a non-absorbing/absorbing boundary outside both the wave and carpet - in other words a second source of reflection (either circular or rectangular)?.... it was very very VERY COOL! - good job!

@NilsBerglund 2 года назад

@@medtherockstar820 Thanks! If I put reflecting boundary conditions on the large rectangle (around the picture), there will be more reflections and energy will be conserved. I could try varying the boundary conditions, though I'm not sure it would be a good physical model. Another thing I may consider is replacing the scatterers by regions where the wave speed is different, causing refraction (like here ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Q8P4iL6ZafQ.html ).

@nomoturtle1788 26 дней назад

It's cool how the waves linger within the carpet

@NilsBerglund 26 дней назад

It's also useful, because it allows to spread the energy over a large time span, making the wave less destructive.

@derpderp9281 2 года назад

Wow I don't fully understand what's going on or what this means for physics, but this video made me really curious to see how much of the wave the shapes could stop

@NilsBerglund 2 года назад

Glad you like it. There is a slightly different version here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-LTsCx2T-4hA.html

@psymar 3 месяца назад

It means mangroves/forests help stop Tsunamis from wrecking shit further inland

@malachistone88 2 года назад

Love the drum and base!!!!

@benbowland Месяц назад

1:30 The way you made the beat line up with the jump cut is so satisfying

@ToyKeeper 2 месяца назад

It's wild seeing this for the first time in 2024, because I wrote an extremely similar program in the mid-90s... then dusted it off in 2022 to get it running on modern computers, where I now use it as a screensaver. But I didn't build it for stopping waves; I built it mostly just to make a cool-looking interactive physics simulation. Thinking about maybe building a game on top of it, because the water is fun to play with.

@josesantos2603 2 года назад

A sierpienski carpet would be very useful to protect a city against a tsunami

@alterego3734 2 года назад

Even better to protect an island: a configuration that makes an invisibility cloak. There has been some research on this.

@PhamThanhLoan311 2 года назад

That’s a lot of ripples. Really vibrant looking indeed!

@gonderage 2 года назад

ah yes, the non copyright music. always a pleasure to hear this in yet another video.

@Monorat Месяц назад

This is really good for blazed watching material

@poisonhemlock 3 месяца назад

This is why I always answer my cell phone with "It's a miracle."

@beyondtherice8277 2 года назад

Ladies and gentlemen, I present to you, the algorithm

@Ticbow 2 месяца назад

I didn't expect such banger music on this video

@cyberyogicowindler2448 2 месяца назад

I remember a TV docu about Stonehenge, which originally contained additional stone pilars forming rings those are now missing. They built a fullsize styrofoam model to test the acoustics, and explained that the echo inside was very special. So as a religious temple it certainly contributed to the mystical experience of visiting people if the high priest would sing or play instruments inside.

@potatocouch3709 2 года назад

Everyone here in the comments is talking about actual practical shit, and here I am thinking about how good of a screensaver this would be

@idropgp8052 2 года назад

1: impossible for anything *NOT* to pass through 2: a little stronger but still hella bad 3: stronk i guess but waves can tunnel through the holes if they aren't trapped 4: nothing gets through

@LeafsStudio 8 дней назад

i love how near the end most of it is just a goosebumps wall

@ToastStealer1332 24 дня назад

This is actually the same way that radar-scattering paints use to reduce the radar cross section of an aircraft. They have many points to randomly deflect the waves and in turn weaken the wave that returns to the source.

@matthewkendrick8280 2 месяца назад

Ok I love the frog music, but what is a Sierpinski carpet and why is it useful?

@NilsBerglund 2 месяца назад

A Sierpinski carpet is a fractal, made my dividing a square into 9 equal squares, removing the central square, and repeating the same ad infinitum with the remaining square. What is used here is rather the complement of the fractal, that is, the squares that are removed when making the carpet. The design appears to be quite useful for insulation (from waves or sound).

@rotkehlchen2920 2 месяца назад

I swear there is a hidden message in the subtitles... "so so so... one great foreign..." LIKE WHAT??? TELL ME WHAT GREAT FOREIGN AAAH

@soyo0126 Месяц назад

Not entirely sure why, but this was the perfect music choice for this video

@flamencoprof 2 года назад

Pretty much an irresistible title for me. I like waves, and sound, and fractals, and graphics. I was not disappointed. Music reminds me rhythmically of "Oh Yeah " from the Can LP Tago Mago (1971).

@retepbocaj4272 2 года назад

cornfields make more sense to me now. thank you

@unfa00 2 года назад

I love the music.

@camronchlarson3767 Месяц назад

I got distracted for a few seconds and actually caught myself backing up to see what I missed lol

@TetyLike3 24 дня назад

this song brings back memories i don't even remember

@aracaniusinfinius2880 2 года назад

Lol I watched this to fall asleep for some reason Weird dreams came with it though

@WorriedTheif 2 года назад

Examples?

@JNJNRobin1337 2 года назад

Yeah Wait What Examples Of Weird Dreams

@mostlime12195 2 месяца назад

May I ask where I can listen to this music? I love it.

@NilsBerglund 2 месяца назад

You can find it for instance here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-H_i-AcebAAI.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5SRIvvFLyTw.html The artist is Jeremy Blake, www.youtube.com/@RedMeansRecording

@anotherdamn6c 3 месяца назад

Now imagine the smaller objects flexing as they both bounce and absorb the energy. This is why you want your sound baffles made from natural fibers and not plastic. Nice soundtrack.

@NilsBerglund 3 месяца назад

I actually later made some versions with mobile "mangroves", see for instance ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eIwX5Z6jf2s.html or ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XVHmrd7emy4.html

@ThatOpalGuy 5 месяцев назад

Interesting and absolutely incredible to watch.

@trueandonlyfandre 2 года назад

What happens, when you remove the larger squares and replace them with smaler ones?

@notquitehadouken 2 года назад

you get a grid

@boonewalker3973 2 года назад

More square

@gaaraheater44 2 года назад

You get a nonfractal grid

@darkfllame 2 месяца назад

now you know why we cannot se through everything.

@waylonk2453 Месяц назад

I love the music in this video. Reminds me of the game music to Gare: Sapphire Mechs

@IWasAlwaysNeverAnywhere Месяц назад

I love imagining things from the perspwctive of higher dimensions. Envisioning that the cause of these waves are actually the shifting of an object in higher dimensions.

@deephorizon1365 2 года назад

Trippy!

@whatitmeans 2 года назад

Should try using a 2D gaussian attenuation function for the edges of the simulation frame so you can issolate the frontwave effects from the spourious eccoes of the bounds of the wavefront on the borders of the simulation window

@John-yr1ww 2 года назад

this sounds like meaningless gibberish, so it must be smart math thing

@whatitmeans 2 года назад

@@John-yr1ww is something you can do when, because of finite size windows, spourious effects appears when implementing some algorithms, like the eccoes in the waves of the video, or, as other common example, when doing 2D convolutions and circulation effects happens on the boundaries. A tight unitary 2D Gaussian envelope supress these edge-effects without introducing ripples because of their own response as a filter in the simulated system. If you have already reach this video and see my post, I hope someday you will use this comments as a tool in your own research.... nowadays, every new mind suck out of ignorance will lead as to a brighther future. Hope you the best.

@BlackSoap361 2 месяца назад

All those small squares reminding me of acoustic crystals. Regularly arranged round objects, that can allow 1 frequency through but block other frequencies, based only on the spacing.

@billiam_bob 7 дней назад

The MOAD-Mother of all diffusers

@hjfreyer 2 года назад

Can you use this setup to simulate what hearing an echo bouncing off of this would sound like?

@patrikcath1025 2 года назад

"Squares together strong"

@joshcoffey6923 2 года назад

It would be interesting to me to see this with constant wave sources rather than a single impulse! Great simulation!

@douchopotamus3755 2 года назад

Man, this is a great video to have on in the background at parties

@NilsBerglund 2 года назад

Glad you think so!

@ARBB1 2 года назад

Very reminiscent of photonic crystals.

@kallekivimaki7825 2 месяца назад

Stop kidnapping waves

@judet2992 3 месяца назад

This track is fire 🔥

@lightknightgames 2 года назад

Someone @ me when this inevitably gets made into a screen saver simulation.

@pje723 2 года назад

So much deep learning going on here...

@Hexanitrobenzene 2 года назад

I'm sorry but this has nothing to do with deep learning. It's good old numerical analysis.

@pje723 2 года назад

@@Hexanitrobenzene 'deep' as in impactful, resonating or lasting...

@xyzct 22 дня назад

Level 4 is like trying to get a logical argument across to a woman.

@adreq3.05 3 месяца назад

Level 3- disperssion of waves, level 4- ideal barrier before the shock wave

@feynstein9593 Месяц назад

This is very close to being a nice visualization of refraction

@mmaldonadojr 2 года назад

Nice job! But AFAIK this fractal is a Menger class, not Sierpinski. Congrats anyway!

@derrickmelton5844 2 года назад

The Menger sponge _is_ just the Sierpinski carpet applied to three dimensions. Sierpinski is known for fractals other than the triangles too.

@il_vero_saspacifico6141 2 года назад

We whant level 12 🙌

@Duracellmumus Месяц назад

It may going to be a like a comb filter when the wavefront was paralell with first contact surface. The ONE center element is may not seem effecient in cancelling so add more same sized elements in a grid to let develop same-size but invers direction waves/beams.

@ferenccseh4037 2 месяца назад

That would be so cool as a height map! You could better see their amplitudes

@NilsBerglund 2 месяца назад

Here is a 3D rendering: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-8yddkbwrqss.html

@jeansapplebottom9291 2 года назад

Who needs homework when you have album cover material like this??

@coleozaeta6344 2 года назад

Music: Hey, this is another episode of Dead by Daylight Survivor methods, let’s get right into it. First, if you wanna evade the Trapper...

@WhyWhatWhoWhenWhyAgain 2 месяца назад

This is how ive adjusted my way of thinking since 2000. Jurassic Park and the Lost World by Micheal Crichton changed my brain. Turbulance and energy dispersion actually started to make sense.

@SoloBat32akaZJG 3 месяца назад

Idk anything about how this works but its mesmerizing

@thea.m.p.co.467 2 месяца назад

This is about 20 times longer and slower than it needs to be...

@Graeme_Lastname 2 года назад

Interesting and informative. Thanks m8.

@NilsBerglund 2 года назад

Any time!

@ComputationalModelingExpert 2 месяца назад

Beautiful! 🤩

@NilsBerglund 2 месяца назад

Thank you! 😊 You will find more recent vids like this one in the playlist ru-vid.com/group/PLAZp3rbgWLo2dIeEYz8KP2TW-Yvq8TFLx

@rosekennedy9744 2 года назад

This is magical

@NilsBerglund 2 года назад

Thanks, glad you like it!

@melchiortod29 2 месяца назад

Was it really necessary adding music that goes soo hard? Man let me enjoy my math videos, don't get me all up dancing it's 2am

@NilsBerglund 2 месяца назад

Apologies. Please get some sleep.

@ocayaro 2 года назад

Animators should be interested. You’ve just found the algorithm for the most realistic ocean simulation.

@rg3412 Месяц назад

Great sound barrier material, if you can manufacture it

@CrisEdmundson Месяц назад

Fun music choice for somwthing like this

@alissamckeighan6287 2 месяца назад

This is the god of all optical illusions

@youtubeuser6067 Месяц назад

The fractal matrix of squares has a rigid index of 1, ie inflexible. It would be interesting to lower the index of rigidity to see how wave propagation can be attenuated with flexible squares.

@kosiak10851 Месяц назад

I hate fractals

@NilsBerglund Месяц назад

There are some simulations with flexible circles on this channel. See for instance ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4UtYtM-wEkE.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XVHmrd7emy4.html and others in the playlist ru-vid.com/group/PLAZp3rbgWLo2VvXUsaiRbw33x2qMKASdF

@kjankiewicz 2 года назад

The first 30s is all you need to see to understand the rest. Re-run it in an infinite space vs spacial confinement. Reflection waves make a difference. Also run it with a central point of oscillation with scattered blocks around it. Start with one block on one side and then progress from there.

@HigherEnlightment 2 месяца назад

If the goal was to diffuse the reflected wave then level 2 did best. It would be interesting to see the same experiment but with varying wavelengths because this highlights one of the main problems with audio reproduction i.e. controlling waves of frequencies spanning four orders of magnitude.

@NilsBerglund 2 месяца назад

Here is a version with a superposition of two different wavelengths: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SXhmZ0Bqni8.html

@HigherEnlightment 2 месяца назад

@@NilsBerglund Thank you!