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That's pretty much a defining feature of all (infinitely iterated) fractals [1] [1] https://en.wikipedia.org/wiki/Fractal https://en.wikipedia.org/wiki/Fractal
by ttttannenbaum 12y ago
That's pretty much a defining feature of all (infinitely iterated) fractals [1]
[1] https://en.wikipedia.org/wiki/Fractal https://en.wikipedia.org/wiki/Fractal
- gballan 12y agoCool! I didn't appreciate that. I think its interesting to see that behavior in an everyday Fourier series though.
- jey 12y agoI'm not sure that I'd call something with an infinite number of non-zero Fourier coefficients an "everyday" Fourier series. :)
- gballan 12y agoHeh. I hear you. But but on the other hand, a sawtooth is perfectly everyday with an infinite series of coeffs: http://en.wikipedia.org/wiki/Triangle_wave http://en.wikipedia.org/wiki/Triangle_wave .
- astrange 12y agoAny sharp edge in an image has an infinite number of frequencies once Fourier transformed. This is why images get blurry when resized up! For some reason better algorithms never seem to become popular.
- SamReidHughes 12y agoEvery function with a Fourier series will have an infinite number of non-zero Fourier coefficients unless it's merely a finite sum of sinusoids. (Like, obviously.) So yeah, those are "everyday" Fourier series.