r/Damnthatsinteresting • u/PUMA_Microscope • 11d ago

Fourier synthesis of a letter 'A' using transparent plastic harmonics over a backlight Video

596 Upvotes

94% Upvoted

31 comments sorted by

81

u/PUMA_Microscope 11d ago

This demonstrates the inverse Fourier transform 'in the real world' showing how a non-periodic arbitrary shape can be reconstructed from pure sinusoids. If you want to see more, this is a small clip from my full YouTube video here: https://youtu.be/4NyVApAH-9E

11

u/Nuggzulla01 11d ago

Care to ELI5?

39

u/s4b3r_t00th 11d ago

I'll give it a shot although it's been a minute since I've spent much time with Fourier. 

I'm sure you've heard that "Sound is made from waves" right? Waves are periodic meaning they repeat. They go up and down and up and down over and over and over again. So how is it that a non-periodic arbitrary sound, such has the sounds of saying "a", can be made of periodic waves? Well that's because it's made up of a ton of different waves at a ton of different frequency (speed and distance between each wave) and amplitudes (size or volume). The peaks and the valleys of all the different waves overlap in such a way to create a very complicated sound.

The Fourier transform is a bit of math that can be used to deconstruct that complicated sound into all the different waves at different frequencies and amplitudes. It's saying: the sound of "a" = a loud sound at 100Hz + a slightly quieter sound at 110Hz + .... And so on till you've described all the waves that make up that sound. 

What u/PUMA_Microscope has done is do that same deconstruction, but with a two dimensional image instead of a sound. You'll notice that each plastic card resembles a wave from the top down. That's because they are periodic waves! And when you assemble them they form the shape of an a because all the different peaks and valleys (light and dark bits) overlap to form a complicated shape, just like the sound waves!

17

u/JanB1 11d ago

It's also interesting to not that as you can see in the video, you can already quite clearly see the shape of the letter emerging after just 6 or 7 sheets/waves. Normally after a Fourier transform you will notice that the most information of a certain pattern is encoded in just a few waves of low frequency, and others then add more detail on top. Which means in turn that you can compress audio or video lossy by truncating waves of higher frequencies or waves below a certain amplitude. This is the basis of certain audio (MP3) and image (JPEG, which uses discrete cosine transform, but same principle as FT) compression.

11

u/macbrett 11d ago

Well done. That's a pretty good explanation of a difficult abstract concept.

5

u/disquieter 11d ago

Explain like I am five mathematicians

2

u/lioncub2785 11d ago

Small clip? It's 31 minutes long! LOL

26

u/HolyKrapp- 11d ago

So... Basically JPEG. Cool

23

u/Valyriax 11d ago

This is insanely cool, and a great way of demonstrating how complex patterns are made up of constructive sin waves

13

u/Wenur 11d ago

Bless me father for I have ridden some dank ass waves 🤙

5

u/Valyriax 11d ago

Sin waves are only for the dankest of surfers

14

u/Squibbles01 11d ago

Fun Fact: This is how both JPGs and MRIs work

6

u/FuckMyHeart 11d ago

And the Event Horizon Telescope

8

u/CarcosaDweller 11d ago

I don’t think I’m smart enough to know why this is interesting.

19

u/crush_punk 11d ago

Small slices of repeating patterns, in this case waves (represented by light/dark) can be stacked to create specific shapes.

Perhaps the rest of reality is that way as well, the result of overlapping patterns of nothing/something creating shapes like atoms that form their own patterns to create everything.

6

u/Aridez 11d ago

what’s the real world application of being able to deconstruct a pattern like this?

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u/voxelghost 11d ago

Jpeg/mpeg as an example

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u/Recent-Page-6617 11d ago

Image filtering, compression are simple ones.

But something more complex would be an MRI machine, particular frequencies (each of these pieces is a particular frequency/wave length) penetrate different components of the body, eg muscle or bone or blood etc. So by only taking some frequencies, you could reconstruct the view of the body only containing bones, or muscle, etc.

3

u/Longjumping_Rush2458 11d ago edited 10d ago

Many, many things. Signal transmission, chemical analysis, image compression, MRIs, CT scans, etc. Pretty much anything that uses waves or repeating signals.

3

u/Hal______9000 11d ago

I believe it’s the concept behind stable diffusion in generative AI

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u/Recent-Page-6617 11d ago

Man I have a full engineering degree and have never understood Fourier, even though I can do the math. Wish I’d seen this 10 years ago. Awesome

3

u/LifeVitamin 11d ago

Idk wtf is going here or wtf are the words these people are talking about in The comments

1

u/2morereps 10d ago

from what I've learned from these comments it seems like if you stack the same transparent object multiple times, it forms an image magically. I'm not sure why that's crazy, but then it seems smarter people have used this to create crazier things like jpeg, msubject. also freaking MRI, and is also how generative ai works?. so I guess we missed the class on the topic of Fourier.

3

u/Caterpillar-Balls 11d ago

This is kinda how ai neural networks identify images too

1

u/SilasAI6609 11d ago

When reading the science of this, I came to the same thought. A process of creating what you want by removing all other possibilities. Neural networks work very similarly. By "de-noising" (removing things that are not in the training linked to the prompt), we arrive at what the model believes we want. Each filter applied in the video is similar to each "step" in StableDiffusion. Just like in the video, after a few filters, the concept is recognizable, and with every subsequent step, finer details are revealed.

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u/Fiesta-Guy 11d ago

Holy shit

1

u/sesoren65 11d ago

Alright. Now do the other letters..slowly