The Fourier Transform is a mathematical technique that decomposes a function into its frequencies. The machine takes points (x, y) as an input (by clicking anywhere) and creates a function in polar coordinates, transformed into a function of frequencies using the DFT. Then it creates circles that have these frequencies/radial velocities. Appended to each other, the result becomes an approximate function that goes through all input points. For a more detailed explanation, have a look at Mathologers and 3Blue1Browns videos:

Open Processing: https://www.openprocessing.org/sketch/943646