Fourier Analysis: Drawing Llamas with Circles
The Fourier transform converts signals from the time domain to the frequency domain, and it can also draw pictures. By chaining rotating vectors tip to tail, each spinning at a different frequency, you can trace any closed curve—from a simple line to a fish to a llama using 1024 circles. This article explains the math behind the Fourier series and transform, covering complex numbers, linear algebra, and inner products, to show how these epicycles recreate your sketches.
In general (most) every closed curve can be drawn using circles, called epicycles.
- phqb
Shameless plug: I made this tool years ago (predates AI) that draws arbitrary images using Fourier circles https://phqb.github.io/circle_drawing/.
- polotics
I have a bit of a hard time liking this sentence in an otherwise lovely article:
"The velocity is the same as the position but imaginary instead of real."
- TheLegend14
Well atoms are circles and llamas are made of atoms so real llamas are also made of circles i mean spheres similar thimg anyway