PlaneTiling is a Mathematica package that draws any of the 17 wallpaper patterns. This page shows some of examples of what this package can do.
The function WallpaperPlot allows plotting of any periodic wallpaper design. User specifies the symmetry type and motif. This means that it'll plot any periodic tilings, Islamic patterns, or Celtic knots designs
WallpaperPlot can also plot the symmetry diagram of wallpapers. Shown here are wallpaper groups with 3-fold symmetries. Any symmetry element graphics can be user specified. For example, the last image displays the rotation elements of group *632 (p6m), using numbers instead of traditional symbols.
Assorted graphics manipulation functions lets you transform or cut graphics.
Assorted functions generates lattices or networks colored regularly. Here are some examples of triangular network with regularly directed edges.