One of the parts of math that I always found neat was the pretty pictures you can make with plots. It started in algebra with the quadratic and cubic functions and continued in college with the Fourier series. In high school, I got interested in mechanically making some curved art for a design and architecture class, which led me to spirographs. Spirographs, or drawing machines, are how this art is made. An example of a professional in spirograph art is James Nolan Gandy, I have one of his prints in my apartment, his gallery is linked here: https://www.jamesnolangandy.com/new-gallery.
My plans are to make my own proper spirograph machine and with the help of the software to pre-check the linkages and speeds, make some nice-looking prints!
My most recent work with spirographs was in college in an advanced mechanisms design course taught by Dr. Eric Constans. He is the author of a textbook on linkage design using numerical methods and constraint equations to model linkages. We applied the equations to the basic spirograph linkage set and got the following results!
My first attempt at a spirograph was in 2017 using a LEGO NXT robot and motors, with 3D printed linkages. This is the result:
