Harmonograph (Lissajous)
Harmonograph — damped two-pendulum Lissajous figure
x and y are each a sum of two exponentially-damped sinusoids, traced as a single 60,000-sample continuous pen stroke. The slowly-tightening envelope is the pendulums losing energy.
Paper / citationJ. A. Lissajous, “Mémoire sur l’étude optique des mouvements vibratoires,” Ann. Chim. Phys. 51:147–231 (1857); harmonograph device attr. Hugh Blackburn (~1844).
https://gallica.bnf.fr/
https://gallica.bnf.fr/
◈Made by real computation — every vertex is produced by the algorithm’s own math, integrated or iterated from the paper’s equations. No tracing, no decoration, no image model.