Drawing with Circles
// The Fourier Transform
Any shape — any shape at all — can be drawn by circles rotating on circles, each spinning at its own fixed speed. That is the essence of the Fourier transform: every signal is a sum of simple rotations.
f(t) = Σ cₙ · e^(i·n·t) — each circle is one term of the series
draw any shape on the canvas — the circles will redraw it · fewer circles = rougher approximation
Everywhere
JPEG images, MP3 audio, MRI scans, WiFi, noise-cancelling headphones — all of them run on the Fourier transform.
Epicycles Reborn
Ancient astronomers used circles-on-circles to model planetary orbits. They were accidentally doing Fourier analysis — 2000 years early.
More Circles, More Detail
Slide the circle count down and watch the drawing blur into a rough ghost. Every extra circle adds a finer level of detail — that's compression in a nutshell.