Spirograph Inventor Denys Fisher (1977) [video]
laughingsquid.com
laughingsquid.com
Spirograph truly was brilliant — a kind harmonograph you could fit in a Trapper Keeper. I would love to see something that does indeed more closely replicate the elaborate machines that engrave currency. I suspect it won't be nearly as minimalist though as the Spirograph.
I think you may refer to a rose engine, which in operation is very close to a dimensional spirograph. A modern variant might be a core-xy open etch-a-sketch using those LCD writing tablets and a set of physical gears and pins that would control the stylus' motion, maybe powered by a folding handcrank like the Panic Playdate. It might even be a tool for teaching the Fourier series.
rose engine: https://www.youtube.com/watch?v=Gw3aCAQjC88
core-xy: https://corexy.com/
LCD writing tablet: https://www.mi.com/global/product/mi-lcd-writing-tablet/
Panic Playdate: https://en.wikipedia.org/wiki/Playdate_(console)
Teaching Fourier series: https://www.youtube.com/watch?v=qS4H6PEcCCA
Also, projects on Hackaday: https://hackaday.com/tag/spirograph/
The watch manufacture Breguet (part of Swatch Group) still uses rose engines to make guilloché dials by hand, the effect is visually stunning.
Strangely enough, you can get a precious metal Breguet watch with a guilloché dial for less than the secondary market price of some steel Rolex sports watches.
Article: https://revolutionwatch.com/the-breguet-guilloche/
Video: https://youtu.be/aTo3ff9fzdU