Einstein and Truchet

As you probably know, we now have an aperiodic monotile! I was particularly intrigued by an example patch given towards the end of the great introduction found on aperiodcal.com . Here a post is shared where Dan Piker overlays the new tile with a Truchet pattern.

I wanted to see a larger patch of that pattern, and I really wanted to see it overlaid on the "fylfots" described in the paper. These seem to define a very pretty structure of interlocking trees on their own, and I wanted to see how it interacts with the Truchet pattern.

So, I have been expanding the interactive patch constructor found on the paper website to support drawing the truchet pattern. You can play with the expanded tool here. I will be submitting a pull request to the original tool, so hopefully it will also soon be available there.

If you want to expand further yourself, you can find the source on github. I put some effort into improving the documentation and comments of the original repo while reading along in the paper.