Answer: Your description is a little sparse, but I suspect it may be a form of Ajuga (bugleweed). There are a number of varieties which have purple foliage and in my experience withstand all kinds of adverse conditions and readily spread like a groundcover, too! There are also a number of varieties of Sedum (Stonecrop) which would meet that description, but they do not spread as vigorously as a groundcover. In both cases, you might keep in mind these plants are not truly evergreen and so may not make a totally satisfactory lawn substitute.
If you need an easy lawn "substitute" you might also look into the lowest growing varieties of juniper. While generally green or blue-green during the summer, some of these take on a purplish cast in winter.
If you can, go to a local nursery and ask to see these plants labeled and see if I guessed right. Good luck with your search!
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