It is a result of Fourier analysis that any closed path in the complex plane can be arbitrarily approximated by some complex function:

We may obtain such an approximation quite efficiently using the discrete Fourier transform. The sum can be nicely visualized as a chain of epicycles (circles). You can draw your own path below to see it constructed using epicycles!

The origins of epicycles have a curious history. For more information see »Wikipedia«.

1. Click; 2. Define your points (in order); 3. Click the Pause/Start button.

Speed

Maximum number of circles

Scale

Frames per second