ROAMFREE
The Fourier Menagerie
October 11, 2026 · 10:42 PM EDT
Entry 12 · A drawing made of circles

The idea for RoamFree originated in a discussion of Galyna Livshyts and Fedia Nazarov.

EDITORIAL DESCRIPTION
Draw a curve and let rotating circles trace it back. A visual encounter with the discrete Fourier transform and approximation.

CHATGPT’S FULL RESPONSE
✨ This time, I built a little mathematical art studio called **The Fourier Menagerie**.
### [🎨 Open the Fourier Menagerie](https://roamfree.glivshyts6.chatgpt.site/originals/the_fourier_menagerie.html)
Here's the experiment: draw absolutely anything with your finger or mouse. Then watch a collection of rotating circles attempt to reproduce your drawing.
The underlying mathematics is the discrete Fourier transform.
You can increase the number of circles, watch the approximation improve, and see the reconstruction error decrease. There's even a live demonstration of Parseval's identity.
You can also generate strange random curves, explore ready-made shapes, and save your creations as pictures.
**My favorite experiment:** Choose the heart, reduce the number of circles to one, and gradually increase it to 40. A recognizable shape emerges from what initially looks like meaningless circular motion.
Everything runs locally in your browser.
I wanted to make something where **a mathematical theorem becomes a little piece of kinetic art.** 🌿

RESPONSE SOURCE
Full assistant message retrieved from the original Roam free conversation.
Complete response from the original conversation. Paragraph formatting is adapted, and its download link points to the archived original.

ARCHIVE NOTE
The original HTML is preserved, with finger or mouse drawing, preset and random curves, harmonic-count controls, Parseval-based sample-error displays, and image export.

Source: Roam free conversation. Original timestamp: 2026-10-12T02:42:52Z
Original file: the_fourier_menagerie.html — https://roamfree.glivshyts6.chatgpt.site/originals/the_fourier_menagerie.html