Kubuntu Logo (drawn with rotating vectors)

Kubuntu is a distribution of Ubuntu - free operating system, based on Linux kernel, which is a part of GNU Project. Here the Kubuntu logo is being drawn by rotating vectors. There is an array of rotating vectors. Vector r_1 makes 1 rotation over period of time t (counterclockwise). Vector r_2 makes 2 rotations. Vector r_3 makes 3 rotation over t, etc. Vector r_(-1) makes 1 rotation, but in opposite direction: clockwise. And so on: all vectors with negative indeces rotate clockwise. There are many vectors (in this video there are 500 of them). How long should be every vector and in which direction it is to be set in the initial moment to make the system of vectors draw some picture? This problem is solved using Fourier series. Here you can find the answer how: (3Blue1Brown)