Harmonographs are mechanical devices that employ coupled pendula (aka: “pendulums”) to control the movement of a pen relative to a drawing surface (e.g., a sheet of paper). The pen’s motion can produce some strikingly beautiful curves.
I had never heard of harmonographs until I read Mike Croucher’s post: Simulating Harmonographs. Instead of building a physical apparatus, Mike simulated harmonographs with Mathematica. The resulting drawings are indeed most aesthetically pleasing:
[ image courtesy of Mike Croucher ]
Drawings produced with harmonographs remind me of the drawings I used to make with the Spirograph toy when I was a kid. They also remind me of the Lissajous curves I liked to visualize on the oscilloscope when I was an undergraduate student and spent countless hours in the electronics laboratory.
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Some links:
Tags: Art, Harmonograph, Mathematical Art, Recreational Physics
August 30, 2008 at 16:10 |
Hi
I’m glad you enjoyed the post. Its interesting that you think that the harmonograph images remind you of lissajous and spirograph curves because it turns out that the parametric equations describing harmonograph curves also describe both lissajous figures (using only 2 pendula and no damping) and spirographs (by playing with the relative phases a bit).
Cheers,
Mike
August 30, 2008 at 16:32 |
Mike,
I read on your post that harmonographs could draw Lissajous figures, and I was not particularly surprised. Intuition suggested that was the case, though intuition is often misleading.
I would like to derive the parametric equations that describe the harmonograph curves, and play with them for a while, to see what comes out of it. As soon as I have some time…
August 30, 2008 at 19:26 |
You know, I’ve been thinking about changing the image at the top of my blog for some time now… So I think I might try this out (in Maple, as I don’t have Mathematica on my system) just for a logo.
August 30, 2008 at 20:12 |
Robert,
Guess what? The very same thought crossed my mind ;-) I have also been thinking of changing this blog’s header image, and when I saw the Harmonograph curves, I fell in love with them and then thought those would indeed be perfect images for a header.
August 30, 2008 at 23:45 |
Hi guys
You don’t need Mathematica to generate new harmonograph images – you could run the applet I wrote by using the free Mathematica player application (links in my blog post). I’ll have a look at implementing it in Maple next week though to see how easy (or otherwise) that is.
Cheers,
Mike
March 8, 2009 at 04:12 |
Just in case you haven’t read it? I’m sure you have, have a look at woodenbooks.com. there’s a great small book about harmonographs.
Harmonograph – Anthony Ashton
I’m planning to build one and decided to start with an internet search and found stochastix (on a side not i used to work for a company called astix).
cheers for now
Gid
March 16, 2009 at 01:24 |
I didn’t know that book. Thanks for the suggestion! If you build an harmonograph, please publish your work online (if you have time) so others can learn from your experience.
September 22, 2009 at 14:01 |
Lovely images Mike.
Wonder if this could be combined with the maths of Strange Attractors?
I remember seeing some fantastic images that came out of those.
Cheers
Lee
March 8, 2010 at 17:20 |
I found this cool online harmonograph from Swantesson Interactive to produce captivating pictures
http://swantesson.com/harmonograph.html