alhambra
Alhambra is a program that implements two such design technique for Islamic star patterns. The first technique is based largely on the work of Hankin [1] in the early part of the twentieth century and on a more recent paper by A.J. Lee [2]. The technique was further refined by Craig S Kaplan [3]. In a nutshell, we start with a tiling of plane made up at least in part of regular polygons. The polygons are filled with radially symmetric motifs like those found in the Islamic tradition. The tiles forming the gaps between the regular polygons are then filled in by finding natural extensions of the lines meeting their boundaries. The result is a network of lines that has nice graph-theoretic properties. The graph structure enables it to be coloured in various ways, or even rendered as a weave, or interlacing, as were many of the original designs.
The second technique is based on work by Peter J. Lu and Paul J. Steinhardt of Harvard University [5]. It centers on the realization that many classical Islamic tilings are based on a small set of tiles with equilateral sides, now dubbed Girih tiles. When each tile is decorated with a particular set of lines, they can be assembled to produce many of the intricate designs found in mediaval Islamic architecture.
Alhambra has a library of built-in tilings that can be used to construct many famous Islamic designs. Even better, the construction of these designs is parameterized in certain ways, so you can use Alhambra as a vehicle for exploration of the vast space of Islamic designs.
