Symmetries from Earthlinksoft Software is an interesting symmetrical vector object generator tool.
The control system is very intuitive, requring no knowledge of how to manipulate vector paths. While simplistic, it gives one a high level of control over exploring interesting symmetrical objects. I did find that there seemed to be a bit of a genre of shapes that were the calling card for this tool, but maybe I just didn’t play with it enough.
Symmetries does not generate tiled patterns, but rather single vector objects, which then can be pasted into the vector software of your choosing for futher editing. The demo mode doesn’t allow this, so I couldn’t test it.