Geometric Drawings · How-to · Math and Book Arts

Moires: A Reason to Tile

Balloon with Moire
Balloon with Moire

Just before Valentines Day the usual group of suspects who capture my attention with their outrageously playful exploration of ideas once again were posting images that stopped me in my tracks.  I have to say that when I saw what they were doing I made a decision not to participate because I was busy-with-other-things.  But then they started using HEARTS in their images and I just couldn’t resist. What they were doing was  creating moire patterns, mostly digitally. Moire patterns are that cool effect you see when two identical screens are laid on top of each other, then shifted.  I started out making some with my Illustrator program, then my attention shifted towards making them in the real world, engineering paper rather than working on the computer.

Moire patterns can start with a repeating tile, a tessellation, which is a shape that can be repeated forever. Here’s a photo of one of the explorations that I saw going on, by Mike Lawler’s family:

Tesselating in the Living Room
Tessellating in the Living Room

Then Dan Anderson started doing a series of outrageously beautiful interactive images on his Open Processing page:

Dan's Moire
Dan’s Moire

Then Martin aka GHS Maths started making moires with straight lines in the on-line graph program Desmos.

You really must visit some of these links in order to get the full sense of how stunning these images are.

My first response to these image was to make a  few gifs myself.

My Illustrator Heart Moire
My Illustrator Heart Moire (click on image to see the gif)

What I wanted to do, though, is make some movable paper structures. I didn’t really know how to do this, but I know someone who does: book artist extraordinaire  and paper engineer Ed Hutchins. The biggest deterrent for me was that it seemed that it would include lots and lots of paper cutting and I don’t feel like doing that right now. Destiny interceded: I came across some transparency paper for copy machines at the local thrift store (50 cents!) and now I was almost ready to proceed.  Most of the rest of this post is one way of making the copy, cut and paste moire pictured at the top of this post.

Moire Materials
Moire Materials

I wasn’t truly sure that using transparency paper and prints would work, but, as it happened, Dan Anderson invited me to visit his tech lab at the high school that he works at, which is just a short drive from my house (amazing good luck for me, considering the other two conspirators collaborators live thousands of miles away). He printed up some of his images on transparency papers and we were able to immediately see how well this worked.

A Repeating Pattern : Tiling; Tesselation
A Repeating Pattern : Tiling; tessellation

I came home and tried out, oh, about 15 different kinds of images, some in color and some in black and white, and settled on a hexagon kind of tiling. Dan had done some colored moires, which , when on the computer screen, knocked my socks, but the yellows and oranges faded out in real life. There were things I could do to work with color but I chose to work with black and white for now, but then shamelessly decided to use screenshots of Dan’s work as part of the background for my moire.

Moire from D.Anderson's OP
Moire from D.Anderson’s OP

Nice, huh?!!

Circle Rectangle Card Compass
Circle Rectangle Card Compass

First thing I did was cut a four-inch circle from the paper that my tiling was printed on, then I cut a my card from the glorious image above (about 4″ x 8″), and cut a 3 7/8″ x 6″ rectangle from the printed transparency paper.

Shapes to start with
Shapes to start with: 1 inch circle, 1-3/8″ square with a 1″ hole cut out, 2.5″ circle, and an egg cup to hold my straight pin.

I am also unbelievable fortunate to live near Ed Hutchins, who graciously agreed to show my how to do the paper engineering for moires. I thought that it would be a quick kind of thing, that he would just be able to say “snip here, glue there” and we’d be done. Three hours after sitting down with him I sort of had the idea of what to do. Honestly, what I am writing here is mostly so that I can remember how to create what I went to learn. Ed’s skill with cutting tools is far beyond my ability, so I’ve altered what he showed me. There is one major concept that remains intact,the hub; exactly  how to make and insert it is a matter of preference.  So I started with the tools above. The hub is the  little bright green circle in the center. This is the basis of a spinning hub. My hub is a one-inch diameter circle.


The hub fits into a smaller hole, which in this case is 5/8″ wide. There are four snips in the hub, cut just so that it fits snugly into the hole  and can turn without wiggle room or too much friction.

Hub Balloons
Hub Balloons

I made some hubs with a square, some with balloon shapes. There just needs to be enough room around the hub so that the larger piece can be glued down without interfering with the ability of the round piece to turn.

One and five-eighths away from the edge
One and five-eighths away from the edge

After the hub is together I put a straight pin through the center of the circle to help me get everything else centered together. I also cut a hole through my card, large enough to allow the hub to show through, but small enough so that the piece around the hub can be glued to the back of the card.

The Hub showing through
The Hub showing through

Here’s how the inside of the card looks. My egg cup is waiting there for my straight pin, so that it doesn’t land on the floor then in my foot. But for now, the pin stays in the card, waiting to pierce the center of the dark circle. The dark circle will be glued on the hub only, which still turns freely.

Adding the Moire
Now the 4 inch patterned circle will be glued on to the smaller circle


A word about the papers I am using: for the hub I need something that is strong , and that folds and glues well. I started out using regular copy paper but was unhappy with how it behaved, so I switched to using some thin but sturdy wallpaper paper, from a sample book that I had around. The dark circle is also a strong, lightweight paper. This piece may not even be necessary, but I decided I wanted a lighter paper to glue to the hub, because my printed paper, which is heavy Hammermill 80 lb color copy digital cover paper, seemed like it would stress out the structure. I could be wrong, but this was my work flow.

Almost Moire
Almost Moire

Now the printed pattern of hexagons is glued on. I used the straight pin to make sure all the centers were lined up. The pin in now back in the egg cup. You can see I added a cut-out on the front of the card. I like the way a cut-out shape frames the pattern when the card is shut.


Now, with some white glue I glued down the transparency paper. You can’t see the full effect of the moire in a static picture. Here’s a link to the video I uploaded of this. You can’t hear much of what I say, but don’t try: I’m giving instructions to my husband on how to hold the card while I am holding the camera. If you don’t want to watch a video, here’s the front, middle, and back of the cards…

three cards
Enter a caption


…and here’s another of my gifs:

Click image tp animate
Click image to animate

And, finally,

here’s the video that started this round of visual explorations, a Numberphile video called Freaky Dot Patterns

another fine example of moires in desmos by Martin

and a video that shows what the Lawler family did with their moire-that-wasn’t








4 thoughts on “Moires: A Reason to Tile

  1. Absolutely. Working with the paper in hand brings up different kinds of questions that I hadn’t anticipated, and also easily allows doing translations as well as rotations, which makes very different kinds of images! Also, Dan noticed, when doing translations that the image moved at a different rate than the paper. Really interesting. At every step of this process new questions kept suggesting themselves. It was like a rabbit hole. The possibilities for noticing and devising relationships just keep coming.


  2. Paula, I’m loving your posts! You have such an amazing brain and I’m so impressed with your imagination and willingness to go down those rabbit holes! My day is so much better having followed you down the rabbit hole…so inspiring! 💕

    Liked by 1 person

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