The Federation Square buildings in Melbourne, Australia feature an aperiodic pinwheel tiling attributed to Charles Radin. This tiling starts with a 1-2 right triangle, then divides it into 5 identical triangles, thus illustrating an order-5 rep-tile (a tile that can replicate itself).
E. Pegg Jr. "Melbourne, City of Math." MAA Online. (Sep 5, 2006) http://www.maa.org/editorial/mathgames/mathgames_09_05_06.html.