GoKawiilBlog post explains drawing shapes like a llama using Fourier epicycles
A technical blog post walks through how the Fourier transform can be used to reconstruct a hand-drawn path, such as a llama, by summing rotating vectors (epicycles) of different frequencies, radii, and starting angles connected tip to tail. The author shows progressively complex examples, from a straight line and square to a fish, culminating in a llama drawn using 1024 circles.
GoKawiil's interpretation of the reporting above, not reported fact.
The post illustrates a visual, intuitive way to understand the Fourier transform, a mathematical tool with wide-ranging uses in audio processing, image compression, and filtering. By showing that adding more circles yields more detailed drawings, it demonstrates the general principle that more frequency components allow closer approximation of any signal or shape.
- Fourier transforms convert signals between time and frequency domains and underpin technologies like JPEG compression and audio filtering.
- Any closed curve can theoretically be approximated by summing enough rotating circles (epicycles) of varying frequency and radius.
- The complexity of the reproduced drawing increases with the number of circles used, as shown by a llama rendered from 1024 circles.
Source: adekau.github.io, 2026-09-24
Published there as: “Fourier Analysis: Drawing Llamas with Circles”
Read the original report → The summary and analysis above are GoKawiil's own, written from reporting by the source above. Facts and quotes belong to the original publisher.