Scripting Spirographs


Since I was a kid, I was always more interested in design than the finer arts.  I was not confident or practiced at sketching, painting, or sculpting, but was attracted to and composed beautiful pieces of bead-work, dream-catchers, collage, and ornate feathered chokers and hair pieces, all before the age of 20, and I had taught myself how to do each skill.  Before all of this I had my favorite toy, the Spirograph.  I may delve into the math of spirographs later, as I focused on this last summer actually, and once I get into the flow of making art it will be hard to pull myself back, and if I reviewed the topic enough to explain it again, I would be right back in it.  However, I wanted to display this art now, as I have the venue to.  For this article I will call the art you make spirographs, from the toy Spirograph.  However, they are actually called Rhodonea Curves, being described as a sinusoid plotted according to polar coordinates; or a smooth periodic oscillation radiating around a central point.

You can use one or multiple rings inside or outside another, and their locations, sizes, amount of teeth, or relative speed indicate the differing designs, as well as whether each iteration or few meets up with itself or continues with small or large overlaps, until (according to my friend Eric and “if the advance rate is same for all the meshings”), the number of circular passes, or the periodicity of the pen in a single hole of the disc takes to repeat the pattern reaches the least common multiple of the number of teeth on one ring and the other.  You can use these properties to predict somewhat the shape of a spirograph based on the number of teeth, and so I remember that this is why geometries of prime numbers are prominent, but I’m a visual and tactile learner, and the last math I excelled at was in fact geometry, so I learned this from looking at the images, learning how to mimic them, setting a goal, and how they work by achieving a visual goal.  Its been long enough I would have to retrace my steps(i.e. viewing and making art).

All of these images are fairly grainy, as the base figures for this set were actually digitally drawn and saved by screenshot, and not scaled up.  They are an experiment in using color palettes and scripting to compose layers of single spirograph passes.  For this series I chose rhodoneaic geometry where a pass or a set of passes would evenly end up back on the originating point, so that I can treat each pass as a layer for discrete coloring.  I have also used real data such as the size and speeds of the orbits of the Earth and Venus’s to display their apparent 8-year synchronicity, which overlaps by just a day over 8 years if I remember, but that too is for another time.

What I will pause to say is how inspirational this must have been on my young mind; that it didn’t matter so much finely skilled my hand was, with my mind I could still make beautiful art, and dream while doing so.  That some cycles echo back on themselves, and others create visual effects against the others as they echo their different paths, creating a meta pattern that can have rotational and even bilateral symmetry.  The numerical patterns are heavy with significance in the natural, cultural and metaphoric realms.  For example, how many times have you seen a graphic with a 3-petaled Trillium flower on it?  This art form is perfectly suited to my personality that I have returned again to this skill and other skills for making natural patterns and displaying different geometries.

The next time I have some time I will spend a week or three generating many beautiful spirographs with different geometries and palettes of my choosing, using different online, open source, and command line tools to generate, color, modify, and combine the layers.  I also have many other simpler spirograph images I will use to art up this website, but I would like to get back into the garden tomorrow, and describe my gardening today.  I leave you with my images and the wish that you smell some real flowers soon, and view the glowing orbs in their sinusoid arcs above us, nature is always my inspiration!


I colored and combined the layers of this image in half an hour on a packed bus using command line.


Turns out 7-pointed spirographs, or rhodonea curves are more common than 6, because Math.  (Is has something to do with bi-lateral symmetry and 3)


Layers doubled with larger black border. Well that’s what that looks like.


Reminds me of the candy I ate around the same time I started making spirographs as a kid. It was my favorite past-time besides nature, biking, and beading. This image an example of “What if we feather to white?”

This one is blue. I learned how to add the watermarks yesterday, and I know they are a bit much, but I am still learning about masking out the background.


I combined 3 different symmetries in this one and carved out some negative space.


I will make more complex versions of these later for prints and shirts if need be, but this series is a test in concept, with quality of image for small sticker size. I think an image that is 4 times this resolution could be ready for a tee-shirt.