Uploaded April 2023 | Updated September 2026, 2 weeks ago
Similar to the video youtube.com/watch?v=0zmWEzrtvJA, but here with only two balls each, and including graphs over incremental separation between balls over time. For the parabola, the initial separation is 1e-3 length units, while for the circle the initial separation is much smaller, 1e-7 length units. For reference, the radius of the circle is 1 length unit.
For the chaotic system, i.e., the circle, the distance between the balls exhibits a quite clear exponential increase over time, while for the non-chaotic system, the parabola, the distance increases on average linearly.
Song made by @gpcbass, called Bounce it.
Visuals in Python and FFmpeg.
Similar to the video youtube.com/watch?v=0zmWEzrtvJA, but here with only two balls each, and including graphs over incremental separation between balls over time. For the parabola, the initial separation is 1e-3 length units, while for the circle the initial separation is much smaller, 1e-7 length units. For reference, the radius of the circle is 1 length unit.
For the chaotic system, i.e., the circle, the distance between the balls exhibits a quite clear exponential increase over time, while for the non-chaotic system, the parabola, the distance increases on average linearly.
Song made by @gpcbass, called Bounce it.
Visuals in Python and FFmpeg.
![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.")
