Harmonograph Maker

A harmonograph is a machine that draws with pendulums. This page draws an idealized one: set how each pendulum swings, and the pen traces the resulting curve. Download the drawing as SVG for a pen plotter or laser cutter, or as PNG.

Drawing

Presets

Pendulums

Adds this amount to the frequency of pendulum 2 and subtracts it from pendulum 3. Small values make each loop shift slightly.

Line

How many seconds of swinging the pen records.

How it works

Pendulum 1 moves the pen left and right. Pendulum 2 moves it forward and back. Pendulum 3, when used, swings the paper table in a circle. Each swing follows a sine wave that slowly dies out. The drawing is the path of the pen across the paper:

x(t) = A1 sin(2πf1t + p1) e−d1t + A3 sin(2πf3t + p3) e−d3t

y(t) = A2 sin(2πf2t + p2) e−d2t + A3 cos(2πf3t + p3) e−d3t

For each pendulum, A is the amplitude (how far it swings), f is the frequency (swings per second), p is the phase (where in its swing it starts), and d is the damping (how quickly the swing dies out). t is time in seconds. Without pendulum 3, the second term of each line is zero.

When two frequencies form a whole-number ratio, such as 2 : 3, the curve repeats the same loops. A slightly different ratio makes each loop shift a little, which builds up layered bands. Damping makes the loops shrink toward the center.