Harmonograph

Two pendulums move the pen, two move the paper. Set them swinging at a simple ratio and the friction does the rest.

Fig. 1 Ratio — Friction — Swing left —

Set the machine

Side to side

Both pendulums push the pen left and right. Near-equal speeds make the figure slowly twist.

Pendulum A speed

Pendulum B speed

Start angle

Front to back

The same again, at right angles, moving the paper under the pen.

Pendulum C speed

Pendulum D speed

Start angle

Friction

How quickly the swings die away and the spiral closes in.

Decay

A real harmonograph is a table, a pen arm, and a set of weighted pendulums. Nothing computes the curve — the pen simply records where two swings happen to meet, thousands of times, while friction pulls the whole figure inward. Victorian audiences watched them draw in parlours and lecture halls. This one keeps the same arithmetic: two sine waves for each axis, each fading on its own exponential.

Plate drawn in your browser, ink still wet.