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Lissajous Swing


  • Image of Lissajous Swing
  • Image of Lissajous Swing
  • Image of Lissajous Swing
  • Image of Lissajous Swing
  • Image of Lissajous Swing

Ultra Precise. Loads of Fun. No Math!

This harmonograph is unlike any of my other drawing machines. Setup is quick and easy. There aren't any gears. Making wonderful harmonogram drawings is a breeze.


Miron Padowicz invented the first version of this toy harmonograph in 1971. Over the years this moving platform with a fixed position pen on top has been the basis of a number of other toy versions and several large installations at science museums. This harmonograph traces its lineage even farther back in time to the Blackburn’s Pendulum from 1844. All of these versions are considered a one plane harmonograph. They depend on linear momentum (back and forth) and torsional momentum (twisting) to make interesting patterns.

My New and Improved Version

I've had one of the Swing-o-Graph toys in my drawing machine collection for years. I also purchased the mini-Gravity Graph—both Padowicz's designs. Even though I collected them I never actually spent time playing with them. Last Spring, I finally gave the Swing-o-Graph a spin and had a blast with it.

The Swing-o-Graph had some usual problems found in a 50 year old toy like a broken counterweight and dried pens. I bought another one in better condition on eBay and kept playing with it. This led me to wonder about fixing some of the underlying issues inherent in the mass produced toy.

A number of parts seemed like they could be improved. My new homage to the original design includes:

• Penholder that can accommodate a broad range of pens and makes it easy to change colored pens
• Added more weight to the paper platform to overcome friction
• Used a steel weight instead of sand so there is no sand leaking all over over your table
• Improved pen counterweight for easy adjustment and fine tuning
• Steel top on the paper platform allowing for smaller sheets of paper to be held down with magnets
• Expandable design allows for increasing the height by using longer 3/4 inch dowels (not included but available at any hardware store)
• Indents on the paper platform and on the string hanger to allow for increased torsional momentum making more swirling drawings

Lissajous Swing in Action

My new Lissajous Swing is a very simple tool which can help you produce wonderful designs. It includes several very subtle adjustments that none of the other simliar machines possessed. That said much of the variations in your drawings are based on how you swing the paper platform. Numerous drawings can be overlayed to make more complex designs. Pens can be changed between drawings for multi-color designs. And very importantly the pen counterweight can be easily adjusted to alter the spacing between the lines of the drawing. Drawing time can last from 40 seconds to over 2 minutes.


The Lissajous Swing can be put together in under a minute! It is the least complicated harmonograph I've ever seen. There are only 7 parts which are held together with large plastic screws. (These are reinforced with steel for added durability.) The Lissajous Swing is easy to set up and then store back in its box for later play.

Safe for Kids?

No! The paper platform weighs over 4 pounds and can swing pretty violently if pushed hard. The pen holder is delicate and sensitive. The Lissajous Swing will make a great toy for adults to use with kids or for older children but it is definitely not for kids under 12 to use on their own.


The basic color scheme is translucent green for the paper platform, the sides, penholder, the arch and hangar at the top. The screws, pen counterweight, and string adjuster are printed in a bright orange.

You can select a translucent blue version with clear screws if you prefer.

What's in the box?

• Basic machine
• Printed instruction sheet
• 60 sheets of coated paper
• 4 assorted color Staedler Triplus Broadliner pens
• level bubbles
• Alignment blocks
• Extra screw
• String with easy adjustment clamp

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