The Ammann-Beenker tiling is a quasiperiodic tiling with 8-fold rotational symmetry. It uses two tile types: squares and 45° rhombi.
The substitution factor is 1 + √2 ≈ 2.414 (the "silver mean"). Unlike periodic tilings, it never repeats but still has long-range order.
The diffraction pattern shows the characteristic 8-fold symmetric Bragg peaks that proved quasicrystals exist in nature (Nobel Prize 2011).