Wallpaper functions

Instead of making wallpaper by repeating copies of a motif, we construct wallpaper functions. These are functions on 2 that are invariant under the action of one of the 17 planar crystallographic groups. We also construct functions with antisymmetries, and offer a complete analysis of types. Techniques include exhibiting bases for various spaces of wallpaper functions, and an algebraic definition of equivalence of pattern type.