Penrose Tiles

I wrote a program to generate Penrose tiles.

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.

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