The Penrose tiling pattern is a type of quasicrystal, which means that it has an ordered yet never-repeating structure. The pattern, composed of two shapes, is a 2D projection of a 5D square lattice.

Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up ...