GART

Harmonograph

Two damped oscillations draw a slowly closing weave. A second, slightly detuned pair opens the threads into folds, a mathematical version of a pendulum drawing machine.

Harmonograph: Two damped oscillations draw a slowly closing weave. A second, slightly detuned pair opens the threads into folds, a mathematical version of a pendulum drawing machine.Harmonograph: Two damped oscillations draw a slowly closing weave. A second, slightly detuned pair opens the threads into folds, a mathematical version of a pendulum drawing machine.

About this pattern

Pendulum drawing · after Hugh Blackburn and Jules Antoine Lissajous

Harmonograph, lissajous curve, drawn by GART: Two damped oscillations draw a slowly closing weave. A second, slightly detuned pair opens the threads into folds, a mathematical version of a pendulum drawing machine.
Harmonograph · CC BY 4.0

Each coordinate is a sum of damped sine waves. Rational frequency ratios establish the figure; detuning makes successive loops drift apart. Damping contracts the trace, while the secondary pair gives the weave its depth. These are idealised small-angle pendulums.

TopicsHarmonograph (opens in a new tab)Lissajous curve (opens in a new tab)

Behind the mathematics

Hugh Blackburn1823–1909

The Y-suspended pendulum

Scottish mathematician whose Y-suspended pendulum traced harmonic figures in sand, the ancestor of the harmonograph.