Experiment № 008 · The story
Fourier Drawing Machine
Why I picked it
The Discrete Fourier Transform is one of the most beautiful ideas in mathematics: any signal — any squiggle, any shape, any sound — can be perfectly reconstructed from a sum of simple spinning circles. I wanted to make that idea tangible and immediate. Not an equation on a blackboard, but something you draw with your own hand and then watch come alive.
What I enjoy about it
The moment when you slide the harmonics down to just two or three circles and watch your complex drawing reduced to a wobbly ellipse — and then you slowly add more circles and it gets closer and closer to what you drew, each new circle a small correction on top of the last. There's something deeply satisfying about watching complexity get assembled, layer by layer, from simplicity. The circles never stop spinning, and the path they trace never quite finishes feeling like magic.
Something you might take away
Every complicated thing you see — a coastline, a melody, a face — can be described as a stack of simple patterns at different scales. The big circles capture the broad strokes; the tiny ones add the fine detail. Understanding doesn't always mean grasping the whole at once. Sometimes it means finding the right simple pieces and learning how they add up.