3D standing waves next! I just have no idea how to do it. The sponsor is Jane Street. If you're interested in an internship, check them out: bit.ly/janestreet-stevemould
In a zero gravity environment, use a 3-dimensional shell which can be statically charged to attract particles in a way similar to if the shell had its own weak-gravity, and control the pressure inside of the shell with pneumatics or hydraulics set to a variable frequency?
It makes sense that a story set in the early days of the world of Tolkien would use standing vibration waves pushing matter around as a visual motif. The entire world was sung into existence...
I feel like Chladni figures are a good visual example of electron fields. The way they interchange particles due to movement from an external force. Pretty neat!
They are a nice visual representation of some of the MATHEMATICS of the solutions to the partial differential equations of physics. They are also - obviously - visual representations of what sand actually does in response to the surface of the plate. As a physicist I can tell you that the picture here only has a loose correspondence to some of the analogous mathematics that describes the quantum mechanical behavior of a electron subject to certain forces and boundary conditions. What is actually "going on", in as much as that question even means anything in the quantum mechanical context, is not very analogous. One example would be in quantum mechanics the nodes (places where the amplitude of wave function vanishes) are places where the electron ain't, not places where it would be especially likely to be found as with the case of the sand. Still, the different discrete "normal modes" that you see ARE analogous to the discrete states of quantum mechanical systems with certain boundary conditions. One of the most important examples of that are the discrete states (and the corresponding shapes of their normal functions) of electrons in atoms which ultimately is behind all of chemistry - the Ainur singing the world into existence indeed! Interestingly, even partial differential equations for physical systems that never behave in this interesting way - the diffusion of gas in a box is a simple example - also have a countably infinite discrete solutions like the one pictured in the video, but the real behavior is always superposition of many of these, and the behavior of the gas does what you expect it to do which is to spread out until it has the same density everywhere, so a lot more boring. But very similar math.
Even if it wasn't actually made with Chladni figures, the visual motif to look like them is such a cool and unique idea for a title sequence, and whoever brought up the idea deserves a raise.
@@kiruthikpranav5047 Meh, that always happens with adapted things, they hated on the movies back in the day too, don't think it means that much. I really liked the show, particularly how they handled the various species. Especially the elves I think comes trough much better in this show than in the movies, dwarves and humans too. The whole hierarchy from most ethereal to least ethereal shines trough in everything from visuals to dialog to symbolism trough out the whole show, and I really liked that they put so much effort into keeping that consistent trough out even though it's not something that is very noticeable on the surface level. Really took the whole world building ideas Tolkien is known for to the next level. Unlike many other adaptations, this one along with Foundation are some of the best adaptations ever created in my opinion, despite what many fans and critics might say. Besides, I know of many fans that actually liked the series, they're just not crying about it on the internet all day. Jess of the Shire, a YT channel, seemed to mostly like it, and she's definitely a big fan, so it's not all negative, it's just that the media likes to amplify negative voices.
I feel like there's an important possibility you missed here Steve, the patterns could have been generated on a stationary plate, destroyed by Chladni figure generating vibrations, and played in reverse. That's not to say the CGI possibility isn't also highly likely, but since it's basically brownian motion between the node lines and generating these patterns would be a pain in the a** by hand.
2016 Steve made me feel like a genius when I saw the opening for Rings of Power. So glad to see you come back to it here in 2022 in light of the new intro! I don't have enough thumbs to like this video.
You make a scarily convincing Gollum. I don't know if that's a good thing or not, but I had to say something about it. I enjoyed your revisit to the world of Chladni figures. I can't wait for you to take this to the next step - three dimensions.
But wouldn’t that require a 4th spatial dimension for the anti nodes to jiggle in? A standing wave on a string requires the 2nd dimension for the anti node sections to oscillate without affecting the position of the nodes, a cladin plate requires the 3rd dimension for the same reason. Since we can only observe and manipulate 3 spatial dimensions I don’t see how a 3d standing wave would work
@@voidify3 Steve's pinned comment was "3D standing waves next", so even though he didn't know how he would do it when he wrote that, at least he's considering it. Of course, that was 7 months ago, so maybe he has been stuck trying to figure out that pesky 4th dimension issue all this time.
@@voidify3i don't know anything about these things so correct all that is wrong bUt the 'dimension' doesn't have to be spatial, sound waves obviously travel through 3d space and the extra bit of information, the additional 'dimension' is local pressure in earthquakes you can also see different waves that can form, i think they are based on sideways displacement of the earth lots of things can propagate waves through 3d space, the trouble would obviously have to be whether any can be visualised in a small system for a 3d version, the first thing i'd think of is sound travelling through water sprinkled with some filings of a material of similar density, but i don't know if that would work
I haven't seen it mentioned (yet), but the Stormlight Archive series from Brandon Sanderson has some interplay with Chladni figures and the way the world works
I mean, I think so! I'd probably start with another series of his to see if you actually enjoy his work, but if you're not intimidated absolutely give Stormlight a go
I've just watched the trailer of power of rings. For me it look, if they had drawn some of the patterns by hand first and then started the vibration to transition it to a real chladni pattern. Then just played the footage in reverse. so it looks, like this floral patterns created naturally. Make it look very mysterious. Good job explaining and a beautiful trailer remake, by the way.
I'll preface this by saying I haven't watched Rings of Power But I do find the idea that they used something like this as their intro actually quite interesting. One of the themes in Tolkien's work is essentially that God / Eru Ilúvatar who along with his Angels / Ainur sang the world into existence By showing something like this in the intro they could very well be showing a practical example of how something like that is possible. Music is just vibrations after all and this is using vibrations to create ordered structure out of chaos. You could even go so far to have it explain how a deity could influence the world sending vibrations that make it easier to settle in places that are in the pattern that it chooses.
7:50 - oooohh! It just clicked how wind instruments actually work. By opening and closing ports, you are setting or removing boundary conditions at various lengths.
3:38 I think they could use high-tech CGI called reverse the tape. First form this Triskelion, then induce vibration to smear the sand. Reverse the tape and you have chaos sand forming a shape. Another explaination is using some putty under the plate to act as dampener?
Love this we use a lot of RNA vibrating conveying systems at work using moving 'standing' waves to move parts with out rollers is a common thing in industry.
This is awesome - I love seeing the "real" version of a clearly cg thing! that said, this title sequence got my brain going too. for years (probably since I saw your first video about these) I've wanted to build an arbitrary chaldni generator. here are a handful of ways you could do it, playing with boundary conditions, using multiple actuators, driving with more complex waveforms, or in the least-dynamic mode, modifying the sheet's springiness or mass locally, but regardless any of these requires a LOT of math... Since this would necessarily require a huge pile of simulation, I'm curious about your simulated patterns not lining up with the actual ones - did you glean any idea of why/how they failed to predict the nodal lines? My gut would say that the equation assumed the actuator in the center of the plate was the center of a tall antinode but based on your 1d strip example, that didn't entirely pan out?
@@armstrong.r I will have to check but I think the particles in the opening sequence move towards a point and then appear to vanish. That is a bit of a CG give away. Very good nonetheless.
@@2BadgersBlue that could be just some compositing magic but I agree that when I looked at it, it seemed to be at least partly CGI with very good reference shots.
@@armstrong.r the weird symmetries that Steve pointed out along with the more complicated shapes like the tree don’t feel very physical unless played backwards as others have said, and then the exact same style of particle starts doing the “flow” thing without evidence of an obvious driver like a magnet, so I assumed the whole thing was rendered. Where did you see it said practical? I’d love to know how it was done!
I didn't see your first video back then, but here this one is: great, extraordinary, exceptional, outstanding, remarkable, ... Thank you for making educational videos like this fun and easy to understand. Have a nice day!
This is actually a surprisingly good introduction to many of the topics you would see in a structural dynamics course. This is quite refreshing considering the overall quality of most edutainment-type stuff on RU-vid. Granted, you left out the derivation of those equations, but that's a graduate-level topic requiring a semester or more of study.
I recognize one of these resonance patterns, also in metal, stamped tin ceiling in my house. Crazy part it, house is surrounded on all sides by fright trains in the air. I'm wondering if it had vibration suppressing properties, only a few rooms still have it, but and oddly the plaster survived better in the rooms with the ceiling.
Wish you would of included the frequency used for each pattern. As regards to your circle pattern, I have found two. I need to find my notebook, will post the numbers when I find it
i think the thing to remember with the title sequence is that there's no way to know if they're being shown in reverse or not, therefore they could be setting up a shape they want (such as the rotating spiral) and then vibrate the plate to have it break down and play it in reverse
What if there are more than one fixed points (not constrained to the edge) and more than one vibrating points (not necessarily at the middle or edge) at more than one frequency. It seems like you could get an infinite number of patterns if you did that.
There are indeed an infinite number of patterns - but the more complex the pattern, the higher the frequency you need to input. Fundamentally, what you're proposing changing the boundary conditions, which makes it an entirely different system - just like changing the shape of the plate would be.
This is very similar to the idea behind the Fourier Expansion, and Fourier Series, in mathematics. Essentially, any function can be described as an infinite sum of sinusoidal functions with proper coefficients. Taking the first several terms in the sum is a good approximation of the original function, and is sometimes easier to work with in calculus.
Part of it might be where the material starts. For example if there was a “node” in the middle and no material inward of that “node” or between the “node” or the next “anti node” then surely it wouldn’t collect at the “node”. And then obviously each pattern shifts the material, so it may be possible to create a sequence of patterns that depend on the patterns that come before.
Is this what we’re seeing when looking at the arrangement and connections of galactic super clusters? The vibrational arrangement of matter in the universe. The harmony of the spheres.
I had forgotten what these were called or that your channel was where I'd learned about them back in the day but I was hoping that one of my educational youtube subscriptions would tackle this and you did it better than I could've hoped for. And the Gollum bit, hahahaha! Thanks :)
I'm pretty sure that there is another clue that the title sequence is not from a real Chladni plate: real nodelines cannot terminate on the plate. They either terminate at the edge or for loops.
It took me 3 episodes to realize the intro sequence was a visualization of the song of creation, when the valar are singing in harmony with illuvatar until melkor slips in his dissonance
How I imagine it: *someone in the studio planning the intro* "How do we make particles of gold dance or move on their own?" *2nd guy* "What about that old video on Chladni figures by Steve Mould..." *1st guy* "Mould... like the Mould effect?"
There's an additional element you may have missed - you are using plates that are a homogeneous material and only focusing on the geometry. Plates that have a composite construction (ie, portions of the plate are a different material/alloy mix) would propagate the wave differently leading to different resonant patterns on those portions of the plate. A combination of geometry and material variation could lead to some quite complex patterns. And some Chladni plates are made by using multiple points of vibrational input (like periodically spaced speakers attached at the edges, rather than a central vibration point) which can also lead to some more fine-controlled vibration across the plate.
You never experimented with different plate shapes with the vibration generator! I wonder if that one you were trying to recreate from Rings of Power might have been easier on an octagonal plate (or even octagrammal? Is that a word?). You'd also be able to get higher modes if you used a larger plate, since it would have lower resonant frequencies. I also wonder now about other boundary conditions--what if you forced the plate at multiple points, with different phase relations? Or even different frequencies (probably in simple rational ratios like 2:1 or 3:2)? I bet with a whole array of transducers around the edge of a plate, you might be able to use phased-array techniques to put all sorts of patterns on the interior...
It's amazing how well you're able to describe things, I'm sure I've seen your other views explaining it, but going in I was expecting a 10 minute explanation why this works, but I completely understand after like a 2 minute explanation, same with all your other videos
You already did 3D standing waves, Steve. There was this square transparent container filled with water and you put it on pistons and it kept moving the container up/down while the water was stationary, you even tested a little boat on the underside of the floating water. There were even two volumes of water in that container, one above the other.
The symmetry never drops to one, you are merely constraining the output within the shape of your plate. If you were to follow that line to some point you will intersect with another symmetry line, and that point will be a node. Your plate is limited by the suspension point as a forced node. All symmetry lines connect nodes, even if one of them is at infinity.
I actually think it is possible to get all shapes by applying a 2D Fourier transform to find the frequencies you would need to play to get the correct node shapes.
Really cool! When I first saw the intro to the show I went back and rewatched your old video on Cladney figures - this one is certainly more cinematic :)
Possible to do with multiple sources of audio / multiple frequencies. One just has to work out the interference pattern. This is basically the backbone of mobile phone communication using 'beamforming'
Every time that opening started I thought: I bet whoever made this is a Steve Mould viewer. Also, if any of it was practical effects or it was all rendered.
SO COOL!!!! I thought it looked kind of like it could have been a practical effect, but I could tell parts of it were CGI, so I assumed the whole thing was invented. I never expected it to be so based on a real phenomenon that looks SO SIMILAR!! Awesome video Steve!!!!! ✨✨✨
The greatest thing I love about the rings of power intro is how baddly it demolishes the compression algorithm especially just before the episode actually starts
I learned about this in university referred to as "cymatics" (or rather the study of this phenomenon). It was a music course so it was cool they taught us about that.
Once again I am astonished about the thought and work put in this video, bravo! The first time I saw the title sequence I decided to use it as an example for my students. And a few weeks later you give us this perfect video, thank you this will make preparing the lesson so much easier. :)
it was obviously done digitally, but in theory it should be possible to create any imaginable chladni pattern using wave field synthesis. Basically have a large number of transducers that are driven at just the right frequencies to generate the wanted standing wave pattern
I've been watching RU-vid for a long time now and the one thing that always resurfaces every few years is this. I think the first time i saw a youtube video on this was 2009.
Possibly, for some of the complex images, such as the two trees, the pattern was sculpted on the plate, then erased by vibrating it, then shown in reverse.
Speaking of resonate frequencies, my day-to-day vocal range (what I normally sound like while talking) happens to include the resonate frequencies of several plastics and woods so I often vibrate surfaces around me when I talk.
I find it hilarious that you even considered the title sequence not being CGI. I can think of an easy way to simulate the effect but get any node lines you want. You basically have a line drawing and then the grains bounce around randomly with a vector that pushes that random motion towards the nearest line. The farther from a line, the bigger the motion. This'll give you any shape you want even impossible ones.
I recall them saying the whole intro WAS done in-camera. So if it wasn’t this specific technique, it is some real practical effect. But I bet it was exactly this
It seems like some of the shots from TROP use the old "arrange the sand into an intricate design, then jiggle the board to make it all spread out, then play the recording back in reverse" trick.
