Example output from Symmetry Tile
Symmetry Tile is a plugin for GIMP, a wonderful image manipulation program.
The Symmetry Tile plugin (avaliable here) takes the user's selection ("cell") from an image and produces a new image according to one of the 17 plane symmetry groups . These are also known as wallpaper groups or plane crystallographic groups.
Basically it rotates and or flips copies of the cell, combines them to form a tile and then copies that tile to fill a new image.
More information on the plug-in can be found here
Each image in the individual example galleries was produced from the same base image using the plug-in options:
Symmetry group : 17 groups
Multiple images : Yes