the simplest quasiperiodic tiling
By adding a third dimension to the lattice, it is possible to use the cut and project method to generate 2D tilings. This 3D lattice is intersected by a 2D 8 window, which is at an angle of θ to both the x–axis and the y–axis. By rotating the accepted points onto the x–y plane, the vertices of the Fibonacci square tiling are formed
The vertices of a section of the 1D Fibonacci sequence can be created by intersecting a 1D slice at an angle to the x–axis of \(\Theta = \tan^{-1}(\cfrac{1}{\tau})\) with a 2D lattice. The fibonacci sequence then follows by projection.