Mathematics · Study 055
Harmonograph
A simulated harmonograph: four damped pendulums steer one pen, tracing a looping figure that spirals inward as the swings die away.
What you're looking at
Two pendulums move the pen left and right, two move it up and down. Each has its own frequency, phase and rate of decay. The frequencies are close to simple whole number ratios but slightly off, so the figure slowly precesses instead of retracing itself, and friction shrinks every loop a little.
The idea behind it
Harmonographs were a Victorian parlour instrument, usually credited to the Scottish mathematician Hugh Blackburn in the 1840s. A table and a pen arm each hung from a heavy pendulum. The small detuning between them is what turns a plain Lissajous figure into a drawing with apparent depth.
Try this
Click or tap to stop the current drawing and release a new set of pendulums.
