Our Apps‎ > ‎

Harmonograph for iPad


A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890's, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor. 

A simple, so-called 'lateral' harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency of the pendulums relative to one another (and phase) different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures. 

More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example hanging one pendulum off another), or involve rotary motion in which one or more pendulms is mounted on gimbals to allow movement in any direction. 
(source: http://harmonograph.askdefine.com)

* * *

This app simulates a four pendulums harmonograph. But in contrast to other digital harmonographs it shows the pendulums’ motion and drawing in the real-time. That means the picture develops, as you would have observed it being drawn by a real, mechanical harmonograph. It gets changed every second. 

The curves drawn by the harmonograph, called sometimes harmonograms, are described by a system of parametric equations: 

where x1, x2, y1 and y2 represent the movements of four damped pendulums. The movement of a single damped pendulum is given by the following equation: 


A – amplitude, ƒ – frequency and φ - phase shift, d - damping factor. 

All parameters (A, f, φ, d) are fully adjustable so you can control each pendulum separately (decoupled mode). Alternatively you can bind x-y pendulums creating one, which either rotates or follows the diagonal (rotary or linear mode).


Try then some YouTube video demonstrating a real harmonograph: http://www.youtube.com/results?search_query=Harmonograph

You migh also want to look at the screenshots ot see the Harmonograph for iPad in action on this short video:


Please have a look at the included examples. This is the quickest way to learn how the harmongraph works and what is the meaning of the parameters. 

After you are done, your great harmonograms can be easily saved to Bookmarks, sent to iPad's Photos Album or shared with you friends via email. Enjoy!