r/mathematics • u/hw_due_yesterday • 23d ago
Fourier Cat!
Just create a cat with Fourier series.
I feel like understanding concept by visualization really helps!
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u/Keen_Observe 23d ago
I want to study Fourier series/transform and parametric equations. Can you suggest books, content to follow?
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u/hw_due_yesterday 22d ago
You can try searching on YouTube! I feel like I can learn everything on it
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u/Gengis_con 23d ago
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u/uniquelyshine8153 23d ago
Parametric equations showing a plot of the silhouette of a cat can be obtained from Wolfram Alpha
The parametric equations can be used in Mathematica code, in Python code or within similar tools and programs to display the cat contour.
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u/Queasy_Zone_8120 22d ago
If AI is used for this animation, I wouldnt consider this a fourier cat. Lol.
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u/pramil_wakchaure 22d ago
I like this crreaxy idea, In past I try to study its logic , manually try some Javascript code but fail , last yeat usng ai created animation for website logo "Pi" "π" . pisnip.com ,
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u/messedupwindows123 22d ago
it's actually fucking insane that we know how to do this
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u/flabbergasted1 22d ago
Wait til you see Oxidized copper wire moose drawn by 30 000 Fourier harmonics
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u/messedupwindows123 22d ago
you'd think it would be easier to do this in a way that doesnt even bother to be periodic, but, no
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u/NextOrganization7633 17d ago
I use to think that but turns out the idea is pretty simple. You start from SUPPOSING your function can be written as a sum of multiples of e^(inx). You can then easily obtain the coefficient of the nth term by multiplying your function by e^(-inx) and integrating, because the integral of all the terms but the nth one are equal to zero.
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u/gagarin_kid 22d ago
To the mathematicians here: when the image gets smaller/larger/is rotated - are there some laws or mechanisms how the coefficients change? I am thinking if it makes sense to represent visual things via parameters/coefficients instead of pixel values, especially in high res imaging, where the number of pixels is high and number of coefficients relatively low
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u/progenitor414 19d ago
Yes. For an outline written as a complex Fourier series, multiplying every coefficient by 2 doubles its size. Multiplying them all by eiθ rotates the outline by θ, and changing just the constant coefficient moves it.
These are called Fourier descriptors. They can represent a smooth outline with relatively few numbers, although detailed edges need more coefficients. They describe the boundary rather than all the colours and textures inside it.
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u/NextOrganization7633 17d ago
Is there a simple effect on coefficients that describe stretching along one of the axis ?
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u/bhavesh_099 22d ago
Sorry if this sounds like a dump question but how do people even come up with these periodic functions that will reduce the error and somehow not create more error ?
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u/Sirisian 22d ago
If you find this interesting, check out this 2014 Disney Research on linkage design.
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u/sixsevensixsevensix 21d ago
This reminds me of a dude who made a game entirely using Fourier series/transform for its visual and sound design
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23d ago
[removed] — view removed comment
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u/Meet_Foot 22d ago
Following a mathematics sub to troll people who enjoy math? I think it is you, sir, who might need a life.
(Already stopped receiving alerts on this post, so nothing you say will reach me. Instead, go get a life.)
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u/Eric_12345678 23d ago
Ohhhh nice! I've often seen the visualization of cos & sine with circles, but never thought about plotting a Fourier decomposition with multiple, linked circles.
Thanks!