I started a new math art project today and just couldn’t stop. Basically I’m dreading going back to school soon, but didn’t want to mope all day and waste it. So the day turned into a day of learning new things.

Right now my project is drying so I don’t have a final photo yet. Here it is before I got it wet. (It still has the water-soluble transfer paper on it in the photo.)

Update: Here’s the photo now that I’ve removed the water soluble transfer paper.

Earlier today I typed “embroidery math” in Google and a site called Threaded Theorems popped up. Nary a second passed before I was on the site. With a website name like that! I saw the instructions for embroidering the aperiodic monotile called the “hat tile.”

Here’s a Scientific American article that explains the math and is very accessible: https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/

Technically what I embroidered uses a slight variant of the “hat tile,” because that tile requires the shape and its reflection when filling the plane, and this variation in the embroidery does not require its reflection. Just a single tile, repeated over and over again, but creating something that fills the plane but doesn’t have translational symmetry! (The variant tile is known as “the spectre.”) And this is modern math! It only was discovered in 2023!

Here’s the website with instructions: https://www.threadedtheorems.com/aperiodic-tiling

I literally know nothing about embroidery so I’m learning and doing things on the fly. In this project the instructions had me learn the backstitch and satin stitch.

And if you want more technical definition of aperiodic tilings, and some really pretty pictures, here’s the wikipedia page!