Felix' Workshop

Fourier Atelier

Drop an SVG here or press to choose a file Anything with shapes in it — a drawing, a logo, a portrait Every shape in the file is joined into one closed curve first, because a chain of circles can only ever draw one line. Nothing is uploaded.

The function

f(t) = Σ c_n e^{2πi n t}

That is the drawing — not a description of it. t runs from 0 to 1, one lap of the pen. Each term is one circle: n is how many turns it makes in that lap, and c_n is a complex number saying how big it is and where it starts. Add them up at a given t and you have the point the pen is on. Everything else in this tool is machinery for choosing the c_n.

rank	n	radius	phase	share

How the file became one line

A chain of circles draws one closed curve and nothing else, so the shapes in the file have to be joined before the transform ever sees them. They are joined along a minimum spanning tree, walked depth first, with every bridge travelled out and back again. The joins are still visible as lines between shapes — retracing does not hide them. What it buys is that the line returns the way it came instead of wandering on to the next shape, so a join reads as one stroke rather than two, and the spanning tree keeps them short. It is also what closes the curve: a walk that retraces every edge finishes where it started.