## Making Art with Harmonographs

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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### 9 Responses to “Making Art with Harmonographs”

1. Mike Says:

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

2. Rod Carvalho Says:

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…

3. Robert Says:

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.

4. Rod Carvalho Says:

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.

5. Mike Croucher Says:

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

6. Gid Says:

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

• Rod Carvalho Says:

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.

7. leelcampbell Says:

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

8. James Swanson Says:

I found this cool online harmonograph from Swantesson Interactive to produce captivating pictures

http://swantesson.com/harmonograph.html