Uploaded February 2022 | Updated September 2026, 2 weeks ago
Made in Python & FFmpeg.
svg file downloaded from svgrepo.
Music by @gpcbass - a longer version of the song Gravity_Y, previously used in another of our videos.
Made in Python & FFmpeg.
svg file downloaded from svgrepo.
Music by @gpcbass - a longer version of the song Gravity_Y, previously used in another of our videos.
![Fourier expansion of simple geometries [+MWE Python code]](https://i.ytimg.com/vi/V6bQoEjnCKk/mqdefault.jpg "Fourier expansion of simple geometries [+MWE Python code]
Shown is some simple geometries drawn by epicycles, i.e., represented by Fourier series. See pinned comment for a minimal working example code (Python).
The ellipse of course only needs two rods to coincide with the exact solution. However, I was a bit surprised that the square and the triangle were so well approximated using only two rods. When representing the three (disconnected) geometries by a single basis set the number of basis functions must be large. The discontinuities naturally induce Gibbs phenomenon. Ive cheated a bit here, and removed a small portion of the traces in connection with the discontinuities.
Reuse of the fantastic song Vanessa, made by @gpcbass. See https://www.youtube.com/watch?v=yE8G0kmfzjc for the full version.")
