I have some ground cover in my back yard that I have always thought of as weeds, but the more I look at them I like there texture and no need to mow. I'm 12 miles north of Atlanta, GA. In this plant grows in shade better than full sun, but there are a few that survive around the edges of full sun. ( photo / image / picture from rd42's Garden )
Wood violets is what this look like to me. They bloom in white, bi-color purple and white, purple and yellow up here.