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.

Edit:

Re: flickering flames:

Just looked it up:

"Rational ratios produce closed (connected) or "still" figures, while irrational ratios produce figures that appear to rotate."

From:

https://en.m.wikipedia.org/wiki/Lissajous_curve

Years later I blogged this:

Lissajous hippo, retrocomputing and the IBM PC Jr.:

https://jugad2.blogspot.com/2012/09/lissajous-hippo.html?m=0