shape:circles:
🌀 Fourier Epicycles — What's going on?
Imagine drawing any shape using only spinning circles.
A big circle spins slowly and gets you roughly close to the shape.
A smaller circle sits on top, spinning faster, correcting the path.
An even smaller one sits on that, spinning faster still...
Stack enough spinning circles and their combined tip traces your shape perfectly.
This is what the Fourier Transform does: it takes any path and figures out
exactly which circles (how big, how fast, what starting angle) recreate it.
Each circle is one "frequency component":
- Size → amplitude
- Speed → frequency
- Start → phase
The DFT (Discrete Fourier Transform) computes all of these from your path.
Real-world uses: MP3 audio compression, JPEG images, radio signals, MRI machines.