The QuasiTiler tiling generator is a part of the Geometry Center at the ScienceU web site. (See separate review of Geometry Center.) It provides an interactive exploration of quasitiling and crystal patterns -- Penrose tilings and their generalizations. There is a rather detailed explanation of how this occurs and the mathematics behind the scenes.
Please also see the related reviews of the main Science U-Geometry Center site, and another of its subsites, Kali: Wallpaper Patterns.