Harmonograph

Two pendulums painting beautiful shells

In Short

The harmonograph draws beautiful geometric images with a pencil by using the interaction of pendulums. You will be surprised at the figures that can be created by their simple back and forth movements.

Details and Theory

A swinging pendulum is a simple example of a harmonic oscillator: it is an oscillation from left to right. It is approximately harmonic because the swinging has only one frequency. This is an idealisation; in reality there are many disrupting factors like the wind or the string’s elasticity, but they do not prevent our harmonograph from showing the desired visual effect: how multiple oscillations look when they are superimposed on each other.


In the harmonograph, pendulums control the movement of a pen. If only one pendulum is used for drawing on a paper that is moved at right angles to the swinging, one would draw a simple wave. Our harmonograph uses three pendulums. Two of them move the pen along two (x and y) axes. The paper itself is mounted on a gimbal, allowing it to move in any direction and thus act as a third pendulum. The resulting drawing is a superposition of the waves that each single pendulum would draw on its own. The frequency – the time a pendulum needs to swing back and forth once – and the phase – the starting time of each pendulum – vary, creating remarkable structures.