A systematic way to generate quasiperiodic tilings of the plane is to take a lattice in higher dimensions and slice it at a funny angle. Greg Egan has created an applet that generates quasiperiodic tilings by projecting selected triangles from an $n$-dimensional lattice called the $\mathrm{A}_n$ lattice onto a plane. This particular picture comes from the $\mathrm{A}_4$ lattice.