Three-Pendulum Harmonograph #2 – an improved version

Hi! Here is an improved (faster and cleaner) version of the harmonograph. The worksheet has three different areas, the physical machine (a photo of the machine build out of wood by Karl Sims), the virtual machine (which is a 2D chart with a top view of a model showing the three pendulum ends, the drawing table, and the linkage mechanism which connects pendulum #1, pendulum #2 and the pencil) and the detailed curve area.

Feel free to navigate between the three areas while the model is running. Cell M14 prints a warning if the strokes (amplitudes) of the pendulums are too large and the length of the linkage cannot accommodate the movement. In this case just reduce Amplitude #1, Amplitude #2 or both. There are a total of 100 different configurations out of which the first sixteen are created by myself and the rest of 84 are empty.

To upload a configuration, dial in the address of the configuration in “Setup #”,  hit “Upload” and then click “Reset” and “Start-Pause” to run the drawing. If you want to save a configuration you’ve just created, you can change the “Setup #”, then hit “Save”.

Play with the damping time and simulation time too. Choose a small simulation time if you want to see the “virtual machine” animation well.  The photos below show how the drawings for each configuration look like. Because of speed reasons, I recommend that you use versions of Excel previous to year 2007 with this particular model. Your feedback is appreciated.

Good luck,



  1. Author

    Thanks, Miles, for the free advertisement. It’s not necessary but in general I prefer credit to mainly in the video comment, the reason being that, in this way search engines get it and then people will then be able to come over an rummage through my site. Please don’t change anything. Thanks again, George.

  2. Thanks, Ali, I’m just modeling what other people did 100 years ago. Cheers, George

  3. Great and generous work, George. It is a great illustration of chaos that allows hands on experience

  4. Hi Andy, It is really slow for me. In the best case 2003 it is 3-5 times faster. In the worst case (here) it’s like 30 times faster. You might have a better PC. Thanks for commenting. George

  5. This is really slick George.

    This actually runs pretty well on E2007, animation and all. Or, possibly, it runs adequately and I don’t know what I’m missing (^:

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