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For Educators · Fourier Series

Fourier Series for a fractal tree

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a fractal tree live below — adjust the inputs and watch it respond, right in your browser.

Fourier Series BuilderLive

synthesize waves from sinusoids

Controls

Add harmonics and watch sine waves sum into a square, sawtooth, or triangle wave — the Fourier series in action.

Presets

Harmonics

▶ Run in Python

Data Inspector

Wavesquare

Harmonics8

Basissine

Governing equation

f (t) = \frac{a _{0}}{2} + n = 1 \sum 8 (a_{n} cos nω t + b_{n} sin nω t)

Reading this result: Reconstructing the square wave from 8 sine harmonics. More harmonics sharpen the reconstruction and pull it closer to the ideal shape. But at each discontinuity the Gibbs phenomenon leaves a persistent ~9% overshoot spike — adding terms only narrows that ripple, it never removes it, no matter how many harmonics you sum.

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Frequently asked questions

Is this good for educators?: Yes — this version of "Fourier Series for a fractal tree" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.