I have a vague childhood memory of visiting a museum and seeing some Victorian contraption of pendulums and pulleys that would produce lovely swirling, swooshing designs from the pen clamped at its center. The designs weren't Lissajous figures, they were far more complex than that. What were they? And what were the devices that produced them?
Sand pendulums? No, I think that was from "Vision On" with Tony Hart. But searching for "sand pendulums" did take me to the archive of the Bridges Organization, which "oversees the annual Bridges conference on mathematical connections in art, music, architecture, education, and culture". OK, I feel I should have known about that and am ashamed that I did not. Moving on…
My point of entry into the archive was a paper by Douglas McKenna, "From Lissajous to Pas de Deux to Tattoo: The Graphic Life of a Beautiful Loop". Victory! It mentions the device I was trying to recall. The harmonograph. Yes, those are the patterns I remember, those are the devices.
Googling for examples is much easier now I know what the things are called. It turns out that several artists are working in this space and producing delightful work. Here's an example from Rick Hall (it's also the source of the image at the top of this post):
Now I just need to work out how to build one of these creatures.