shapes - Illustrator: how to create a spirograph?

I am trying to create a spirograph in Illustrator, as per attachment. How do I do this? Where do I start?

Answer

Ok, so a spirograph is just a function and I have made a function drawing script called jooGraphFunction. With this tool at hand we can go and plot

cos(2*t)*(10*cos(12*t)) -sin(2*t)*(26*sin(12*t)) 
sin(2*t)*(10* cos(12*t)) +cos(2*t)*(26*sin(12*t)) 

over range 0 to PI with stepping PI/24 and you get. Where 12 is the number of lobes.

Image 2: Screenshot of jooGraphFunction GUI and a few alternate versions with different number of lobes.

Image 2: And drawing with same number of lobes as yours (36) made with same technique.

You can also dissect the script for a starting point for your own learning.