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Interactive Fourier Visualizer

Draw a shape or pick a preset — watch the Fourier series reconstruct it with spinning epicycles.

Click and drag to draw a shape

or choose a preset below

Preset Shapes

Controls

Frequency Spectrum

Hover for amplitude values. Height = contribution to shape.

Embed This Tool

Copy the code below to embed this visualizer on your site:

Cite This Page

APA:

Fourier Tools. (2026). Interactive Fourier Visualizer. https://fourier.tools/visualizer

BibTeX: 
@misc{ fouriertools2026,
  title={Interactive Fourier Visualizer},
  url={https://fourier.tools/visualizer},
  year={2026}
}
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Frequently Asked Questions

What am I seeing?

Each spinning circle (epicycle) represents one term in the Fourier series. Together they trace out your drawn shape.

Why are there circles?

The Fourier Transform decomposes any path into a sum of rotating vectors (complex exponentials). Each vector traces a circle.

What controls the accuracy?

The number of harmonics slider controls how many Fourier terms are used. More harmonics = better approximation.

Can I use this for audio?

This visualizer works with 2D shapes. For audio frequency analysis, try our FFT Calculator or Spectrogram tool.

What are the color themes?

Choose from Neon, Sunset, Ocean, Matrix, and Vapor color schemes to change the look of the epicycles and trail.

Can I export my visualization?

Yes! Use the Export PNG button to save the current frame as an image, or use the Embed code to share it on your website.