Welcome to Fran McConville's Harmonograph Page
Harmonographs are simple yet fascinating devices that can reveal to us some of the complex,
mysterious and beautiful patterns that lie hidden in simple harmonic motion, such as pendulums and rotating wheels. Wikipedia offers an excellent write-up on the topic and provides a list of references for further reading.
On this page you can find photographs, video clips and sample images produced by some of the
harmonographs that I have built.
This is a simple harmonograph consisting of two pendulums (pendula?) swinging at 90 degrees to one another. Below is a sample of some of the figures I've produced with my lateral harmonograph, a photo and video of the harmonograph (videos are best played with the free VLC player), as well as a link to an Excel spreadsheet that simulates the lateral harmonograph and a selection of some of the types of figures that one can theoretically produce with it. .......
Karl Sims provides complete instructions for making a three-pendulum harmonograph, with sample outputs, here.
A pintograph is a specific type of harmonograph that is based on the rotation of two wheels (the name was coined by my daughter and is a clever variation on 'pantograph' and also brings to mind the little wheels of the Ford Pinto). This particular model was inspired by the 'drawing machines' of Alfred Hoehn in Switzerland (see also). It consists of two disks about 4cm in diameter. One rotates clockwise at a fixed speed of 10rpm, the other is equipped with a speed controller and can operate from 0-10 rpm in either direction. The other variable in the mix is the relative diameters of the disks, as each disk has a series of pivot points to which the drawing arms can be attached.
Photos, a video, and sample printouts are provided below, along with the Excel spreadsheet model (not a trivial exercise!) and examples of some of the type of figures that can be produced.
This machine is a pintograph in which by means of a third motor, the drawing surface also rotates 360°. By varying the relative speeds of the paper and the drawing wheels, their direction, and their starting positions, you can create untold numbers of designs. Change pens halfway through and make multi-colored patterns. Note that the most pleasing patterns come from operating only one of the drawing wheels while rotating the paper. Producing something meaningful from the operation of all three motors at once requires very precise speed control, something that I haven't been able to achieve with the inexpensive hobby motors I'm using. Below are samples of some of the figures I've produced with my rotary pintograph, as well as a photo and video of the device in action.