Python Turtle Harmonograph Setup

So recently I've been entertaining the idea of making a harmonograph, but I'm not sure where to start. A harmonograph is basically "a mechanical apparatus that employs pendulums to create a geometric image."

For libraries, I'm guessing turtle, math, and probably random will need to be included, but I'm completely with the actual calculation aspect of it. The random library would be mostly for creating a new image each time.

I would want the user to choose their background color, for the program to be under 100 lines and to watch it draw, not just instantly create the harmonograph.