This series of drawings is based on the discovery by Peter J. Lu  of girih tiles , a set of decorated tiles used by Islamic architects for centuries. I’ve taken the basic girih tile set and extended it to include scaling tiles. I decorate these extra tiles with lines (girih strapwork) like the five girih tiles, but unlike the girih tiles, the scaling tiles are not equilateral. The scaling tiles lack girih lines on two sides, but otherwise preserve the angles of girih tiles.
The scaling tile sides match the sides of two sets of girih tiles. I use multiple scaled sets of the tiles to generate fractal-like drawings in which tile patches at different scales are similar.
Since this is art, not math nor archeology, I’m free to add tiles, ignore symmetry, and disregard normal restrictions on tessellations. I’m searching for interesting designs whether or not they fill the plane. I’m not attempting to stay true to the historical methods.
1. Peter J. Lu and Paul J. Steinhardt (2007). "Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture". http://peterlu.org/content/decagonal-and-quasicrystalline-tilings-medieval-islamic-architecture.
2. Wikipedia contributors, "Girih tiles," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/wiki/Girih_tiles (accessed November 11, 2010).