Kluckel Fibiri

Kluckel Fibiri is a hands-on Fourier lab that turns any closed outline into a mesmerizing train of rotating circles. Draw a loop with your finger or pick one of the built-in shapes, and watch 👀 a chain of "epicycles" — one rotating circle riding on the tip 💡 of the next — reconstruct your curve in real time ⏱️. It is equal parts toy, teaching tool 🛠️ and signal-analysis workbench.

Under the hood every drawing is resampled into hundreds of points and run through a Discrete Fourier Transform, right on your device 📱. Each Fourier coefficient becomes a phasor with its own radius, frequency and phase; summed tip 💡-to-tip, their final point traces your original path. A term-count slider keeps only the strongest terms, so you can watch 👀 a shape converge from a rough blob into a faithful outline, while a convergence chart 📊 plots the reconstruction error against the number of terms.

What you can do:
• Draw any closed contour by hand, or load a preset — circle, star, heart, gear, spiral, polygons and more
• Trace a shape from a photo 📸 — import 📥 a picture from your camera 📷 or gallery 🖼️ and turn its outline into a contour
• Scrub, speed ⚡ up or slow down the epicycle animation 🎬 and watch 👀 the tip 💡 draw the curve
• Analyze the spectrum: inspect each coefficient's frequency, radius and phase, and dial the term count up or down
• Read the convergence chart 📊 to see 👀 exactly how detail improves as you add terms
• Save 💾 your studies to a local library 📚, then reopen, compare ⚖️ and refine them anytime

The core mathematics 🧮 — resampling, the Fourier transform, the epicycle reconstruction and the error ❌ analysis — all run locally on your device 📱. There are no accounts to create and no ads. Your saved studies live in local storage on your phone, and a one-tap 👆 "Reset all data" control clears everything back to a fresh start whenever you want.

Kluckel Fibiri does use a network connection in a couple of places: at launch it checks your connectivity and shows a retry screen if you are offline 📴, and the Privacy Policy and Terms are opened live from the web inside the app 📱. Everything else — the drawing, the transform and the animation 🎬 — happens on your device.

Whether you are a student trying to build 🔨 real intuition for the Fourier transform, a maker curious about how "drawing with circles" works, or just someone who enjoys watching mathematics 🧮 turn into motion, Kluckel Fibiri gives you a genuine, tactile signal-analysis lab in your pocket.