This project was inspired by this video.
The basic idea behind this program is to go around a spiral and draw a dot every 0.5, 0.3. etc rotations.

In this example this can be seen with the value 0.05.
The dots order themselves according to the nearest fraction. If you enter for example 0.33, the one can see three branches because 0.33 approximates 1/3. This is different though for the golden ratio, since this is not a rational number.
For a more detailed description I recommend to watch the this video by numberphile.