hckrnws

> Distorting the shapes of the tile edges a tiny bit is enough to prevent the unwanted extra tilings, and produce a tile which rules out all but single-handedness non-periodic tilings of the plane by its shape alone.

> The distortion can be anything you like: the precise shapes don’t matter, as long as they match.

My favourite way to do this is to make each of the original edges the hypotenuse of a 1-by-2 right-angled triangle. This results in a 27-sided shape with only two different edge lengths and lots of rectangular 'tabs' and 'slots' to help fit the tiles together. Image: https://mathstodon.xyz/@OscarCunningham/110488184680656303

The 4-coloring is interesting.

Here is an example of what you can do. You could have 4 designs, say sheep in field, lost shepherd, barn, and lost sheep dog. The even and odd edges could have paths lined up to go a bit to the side of the edge, with fences. And now you get a pastoral scene that your eye gets to wander over and never quite see the pattern to.

I wonder how hard it would be to actually tile a wall or floor with a design like this?

I've been inspired by the linked article and your comment to draw a vector file of the chiral monotile and get that lasered out of plywood.

There's a shop down the road here that cuts out your vector drawings with a laser, it's pretty nifty. I want to get at least 50-100 of these tiles, paint them in 4 distinct colors... sounds like a wonderful cool thing to do together with the kids.