Fourier Circles

Line

Pick a shape.

Closing the line

The circles come back to where they started after every turn, so they can only draw closed loops. An open line is either joined end to start, or walked there and back. Auto joins it when the ends are less than 15 % of its size apart.

Circlesof 511

Energy captured> 99.99 %

Samples

Points taken along the line. It's also the most circles you can use.

Animation

Speed1.0×

ShowCirclesRadius armsOriginal lineWhole curve

What am I looking at?

Each circle turns at a steady speed — a whole number of times per loop, clockwise or anticlockwise — and rides on the rim of the one before it. The pen at the end of the chain draws your line. The sizes and starting angles come from the discrete Fourier transform of the line: the biggest circles go first, and the more you add, the closer the copy.