Can I create an drawing using epicycles with Matlab?

I have been watching a lot of youtube videos about the Fourier Series and epicycles. I think drawings created with the FS and the epicycles are really cool and I wanted to create my own. I am not sure how to go about this or where to begin, but any advice on how to start or if it is possible with Matlab? I would like it to be similiar to the video below.

https://www.youtube.com/watch?v=QVuU2YCwHjw

This is the recreation of a Homer Simposon's drawing using epicycles.