One of the aspects of math that has always appealed to me is the pretty pictures you can make with plots. I first ran across these plots in high school algebra with the quadratic and cubic functions and then later, again, in college with the Fourier series. In high school, I got interested in mechanically making curved art for a design and architecture class, which led me to spirographs. Spirographs, or drawing machines, are used to make this type of art. An example of a professional in spirograph art is James Nolan Gandy; I have one of his prints in my apartment. Here’s a link to his gallery: https://www.jamesnolangandy.com/new-gallery.
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 results shown below.
I plan to make my own spirograph machine and then, with the help of software to check the linkages and speeds pre-production, create some nice-looking prints!
My first attempt at a spirograph was in 2017 using a LEGO NXT robot and motors, with 3D printed linkages. This is the result:
