The classic Penrose tiles consist of two rhombi with angles 72 and 36 degrees. The edges of the rhombi are all of equal length.
If you follow a few strict rules about how to place them together, you’ll wind up with an aperiodic pattern. This means that no section of the pattern will be repeated as a unit.
There’s a fancy way to generate Penrose tile patterns like this that involves intersecting a plane at a certain angle with a five-dimensional integer lattice.
All of the faces of the five-dimensional integer lattice that lie within a certain distance of the plane are projected onto the plane, and you either wind up with a set of Penrose tiles or a really bad seizure.
That’s how I created the image above.
Now that I am able to visualize five dimensional space in my head, I’ve noticed that I get a lot of weird looks from priests and small children.
