Simulating Harmonographs

pendulum 1 - x axis

pendulum 2 - x axis

pendulum 3 - y axis

pendulum 4 - y axis

frequency

coarse tuning

1

fine tuning

0

phase

π

2

damping factor

0.02

activate

time

100

max recursion

10

show axes

A harmonograph is a mechanical device that uses pendulums to create geometrical patterns. For example, to create a two-pendulum harmonograph, you might use one pendulum to oscillate a pen along the

y

axis and another to oscillate the paper along the

x

axis. Harmonographs were quite popular around 100 years ago and were often found in people's homes. You can simulate a harmonograph by using sums of sinusoids, where each sinusoid represents an individual pendulum. This Demonstration is capable of simulating several different kinds of harmonograph using up to four independent pendulums.

In this Demonstration, the sliders control the selected pendulum. You can turn the selected pendulum on or off by selecting the activate checkbox.