Spirograph Designs Compilation:
Wild Gears: Triangle Gear 120 in Ring 210 with Birdsong
There is a relationship between the Spirograph toy -- and Fourier Series:
"But what is a Fourier series? From heat flow to circle drawings (3Blue1Brown)":
PDS: Also, if I were to go for "full crackpot" (which I will, because I usually do! <g>) -- I'd speculate that fields, such as atomic, and subatomic fields (all particles -- because particles are basically all fields which act as particles) are "Spirographic"/Fourier Series in nature...
Yeah, I know...
"You're a crackpot!"
(Oh, an even more crackpot conjecture... I'd bet you could derive all of the quantum particles... from Spirographic designs/Fourier Series...)
Drawing Spirograph curves in Python - https://news.ycombinator.com/item?id=17883187 - Aug 2018 (10 comments)
Spirograph Simulator (2014) - https://news.ycombinator.com/item?id=13256222 - Dec 2016 (40 comments)
Spirograph drawing - https://news.ycombinator.com/item?id=11026525 - Feb 2016 (1 comment)
Spirograph: Circles on circles rotating in opposite directions - https://news.ycombinator.com/item?id=6959404 - Dec 2013 (1 comment)
Spirograph in HTML 5 - https://news.ycombinator.com/item?id=5505467 - April 2013 (20 comments)
The mathematics of spirograph art - https://news.ycombinator.com/item?id=3777536 - March 2012 (2 comments)
In a calculus class, I once gave a demonstration and then derived the parametric equations on the board.
In an introductory number theory class, I tasked my students with figuring out how to predict how many points a figure would have before drawing it.
I ended up with like three of them. They were fun, but I don’t think I needed three.
I first discovered them in a math book, early on, in a phase when I had a craze for computer graphics programming. Plotted conics, sine and cosine, Lissajous, derived curves of all kinds, independently discovered an algorithm to draw Spirograph-like curves, etc. Some Lissajous figures I drew looked like yellow flickering flames. Good fun.
Re: flickering flames:
Just looked it up:
"Rational ratios produce closed (connected) or "still" figures, while irrational ratios produce figures that appear to rotate."
Years later I blogged this:
Lissajous hippo, retrocomputing and the IBM PC Jr.: