While exploring symmetry I got interested in Wallpaper Groups and how these were generated. There are 17 different plane groups:
I worked on a shader based implementation of them that could generate nice patterns like the one below:
You can access the app by clicking on this link. Remember that you need to have a WebGL enabled browser.
I recommend you that before using the app you watch this quick tutorial on how to use the tool to create your own wallpapers here: