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Fourier Epicycles Drawing Machine — Draw a Path, See the DFT Redraw It
Draw any closed path with your mouse and watch a chain of rotating vectors — epicycles, sized and timed by a Discrete Fourier Transform of your drawing — trace it back out in real time. It is a direct visual demonstration of the same idea Joseph Fourier proved centuries ago: any periodic curve, no matter how complex, can be built from a sum of simple rotating circles.
How to use Fourier Epicycles Drawing Machine
- Draw a closed path with your mouse.
- Watch the DFT compute the epicycle vectors from your drawing.
- See the chain of rotating circles retrace your path.
- Adjust how many epicycles are used and watch the fidelity change.
Frequently asked questions
- What is an epicycle in this context?
- A vector rotating at a constant speed around the tip of another rotating vector — chaining many of them together, each sized and timed by the Fourier transform of your drawing, reconstructs the original path.
- Is this the actual Fourier transform, or a visual approximation?
- It is a real Discrete Fourier Transform of the path you draw, decomposed into frequency components that are then visualised as the rotating epicycle vectors — not a simplified stand-in animation.
- Why does using fewer epicycles make the drawing less accurate?
- Each epicycle corresponds to one frequency component; dropping the higher-frequency (finer-detail) components for speed leaves only the broad shape, the same trade-off any Fourier-based compression makes.
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