Fourier Anim

Fourier Anim — Draw It. Transform It. Watch the Math Come Alive.
Ever wondered how engineers break down complex signals into simple sine waves? Fourier Anim turns that abstract idea into something you can draw with your finger and watch unfold in real time.
Sketch any shape — a heart, a star, your initials, a spiral, anything — and Fourier Anim instantly computes its Fourier series and Fourier transform. Then watch as a chain of rotating circles (epicycles) sums together, one harmonic at a time, to redraw your exact shape from pure sine and cosine waves.
HOW IT WORKS
Draw any open or closed shape with your finger
The app resamples your stroke and runs a Discrete Fourier Transform on it
Every harmonic becomes a rotating vector — the biggest circles anchor the shape, smaller ones add fine detail
Watch the epicycles spin and trace your shape back into existence, live
KEY FEATURES
🎨 Freehand drawing canvas — sketch anything, no limits
🌀 Real-time epicycle animation showing harmonics being summed
🎚️ Adjustable harmonics slider — see how few (or many) sine waves it takes to approximate your drawing
📊 Live stats: sample count and total harmonics available
🎥 Export and share your animation as a video, complete with a title showing exactly how many harmonics were used
🔁 Draw a new shape anytime and instantly see its own unique Fourier fingerprint
WHO IT'S FOR
Fourier Anim is built for engineering and math students studying signal processing, Fourier analysis, or systems theory — but you don't need a textbook to enjoy it. Anyone curious about how sound, images, and signals are broken down into frequencies will find this an intuitive, hands-on way to build real intuition. It's the same math behind audio compression, image processing, radio signals, and much more, made visible and interactive.
WHY FOURIER ANIM
Most explanations of Fourier series stay stuck in equations. This app flips that around: you draw first, and the math reveals itself as motion. Toggle the number of harmonics and watch the reconstruction snap from a rough approximation into a near-perfect match — an instant, visual explanation of concepts like frequency spectra, signal approximation, and why compression works the way it does.
Whether you're cramming for a signals and systems exam, prepping a classroom demo, or just love beautiful math in motion, Fourier Anim makes the Fourier series something you can see, play with, and share.
Draw something. Watch it transform. Understand Fourier series like never before.