iTessellate

An iPad app for designing, customizing, and sharing custom full-color tessellation patterns based on any of the 17 wallpaper groups.

iTessellate is designed with many purposes in mind:

Learn about the 17 wallpaper groups (a mathematical description of the set of all possible ways to tile the plane with a single motif), and how they are related to the fundamental plane symmetries: translate, reflect, rotate (and, from composing the first two, glide-reflect).
Choose one of the wallpaper groups from a drop-down menu and begin your Design with a simple lattice of tessellating “simple” polygons, e.g. rhombuses or hexagons. Drag points along the edges and at the corners of the central tile in order to customize its shape — the new pattern is reflected through the plane using the appropriate symmetries. Design templates can be stored in the user’s Portfolio or shared as an SVG file.
Add some color to your design template using Paint, where pre-designed templates can be chosen from the user’s Portfolio. It’s only necessary to paint one of the tiles — the pattern’s symmetries will distribute the pattern seamlessly throughout the plane! WWMCET (What would M.C. Escher think)?
Share your unique design with the world in the user Gallery, or export it to your device in the format of your choice. Use the design to make custom wallpaper, unique fabrics, or frame-able prints.