Here is a compilation of animations made from plotting three sine waves together, rotating them and changing the appearance in various ways – an interpretation of the Harmonograph concept.
In a real system, there is a damping effect as the pendulums gradually lose energy. My approximation is to simply reduce the plotted radius over time. The X (left to right) and Y (up and down) axes are plotted, with the Z axis providing the colour or line thickness changes. However three different rotations can take place, including the involvement of the Z axis, which is why the plot occasionally gives the impression of being in 3D.
I’ve been remaking my Harmonograph system in C++ using Cinder, and the resulting animations are much smoother than Java. Of course a lot of detail is lost in an online video, as it’s been through two compression algorithms, but you can watch it fullscreen and it doesn’t look too bad. (Don’t forget to click on HD!)
The track is from a batch I made last year, partly from a few studio squatting sessions, hence the analogue palette.
Here are a few links to other computer generated Harmonograhs:
http://thomas.home.fmf.nl/harmonograph/ (from The Typethinker)
links via (and initial harmonograph awareness thanks to) http://boingboing.net/2010/01/02/harmonographs.html