Interlude: tiling the dinner table with aperiodic cookies
Epistemic status: delicious
As we all know, you are a total nerd. So you probably already know all about aperiodic tilings. You’ve also heard about the recent technological developments making it possible to tile the plane aperiodically with only one type of tile.
[If you haven’t, here’s a very quick rundown: tiling the plane means it’s possible to cover the entire Euclidian plane by putting the tiles next to each other (for example, hexagons in a honeycomb pattern). However, unlike the hexagons, an aperiodic tiling never repeats itself – as you add new bricks, it always generates new configurations. The most famous is Penrose’s tiling, which is a mixture of two types tiles. Of course there’s a whole world of recreational mathematics with aperiodic tiles, such as running cellular automata on them.]
The freshly-discovered single-tile aperiodic tiling looks like this:
So I took the next logical step and made a 3D-printable cookie-cutter:
I recommended making sablés cookies. Mix 220g of salted butter with 50g of granulated sugar, then add two egg yolks. Mix more. Add 250g of sifted flour then 60g of icing sugar and hand-mix until you get a nice dough. Spread on a floured surface to make a 5mm-thick layer, cut it into an infinite non-repeating fractal pattern of einstein-tiles, and let it rest for 30 min in the fridge. Bake at 190°C until it’s gold (~15 min) and let the cookies cool down so they solidify.
Notice that, in order to work, the tiling must include the mirror image of the basic tile. For our plans, it’s not a problem: just flip the cookie.
The SCAD and STL files for 3D-printing are available here.