It's definitely a carpet. Actually it looks like it might be a really cool carpet. The colour looks pretty cool, is it as blue as it looks in the picture?
If you can manage a picture of the underside, or at least take a look at the underside, it will help to cinch an ID.
Based on what we can see already, this could be a
Stichodactyla haddoni or
Stichodactyla gigantea. I'm sort of leaning towards haddoni although it's showing characteristics of gigantea by perching up high on a rock like that and the oral disk folding like that (haddoni tends to settle near the rock/sand interface, and tends to lay flat). Although two things, first of all it's really small, which means it's juvenile, and haddoni juveniles tend to attach to rock up high at first, with the tendency toward moving toward the rock/sand interface when they get larger (in my experience it seemed to happen around when the anemone got to about 10".) The other thing to consider is that this guy is newly introduced to your tank and could just take a week or two to settle in.
As to looking at the underside, what we want to see is the verrucae. Verrucae are the little dots on the pedal disk sides that the anemone uses as holdfasts (sticky points that help attach to substrate) when the oral disk is spread out. Haddoni has verrucae that are subtle or even invisible (same colour as the pedal disk) and regularly shaped. Gigantea has irregularly shaped verrucae that are usually of a high contrasting colour (eg. purple) that are more dense at the top. There is another species of carpet,
S. mertensii that has them as red dots uniformly dense from top to bottom.
Here's a picture of
S. gigantea's verrucae. This is the underside of one my two gigantea carpets.
I don't have haddoni anymore (sold it, got too large - haddoni carpets can reach 24" in diameter
) and I can't find any good pics I can link to. Offsite linking to RC is strictly verboten by RC so I can't show the image I want to show you here. But if you go to this thread:
http://www.reefcentral.com/forums/pr...5&pagenumber=5
.. and then search on "
Stichodactyla haddoni verrucae" you will see a picture by Gary Majchrzak that has a great example (actually the verrucae are a bit raised in the photo, they're not always that obvious, but if you see the picture you will see what I'm getting at).
For completeness, here's a picture of mertensii's verrucae:
http://www.wetwebmedia.com/Cnidarian...rtensiiQLD.jpg
Couple of items to note. First, carpets can be kind of dicey the first few weeks. Due to stress incurred during collection/wholesale/retail and all the shipping in between, they come to us compromised - not all will survive. Those that do, tend to be very hardy and undemanding reef citizens. But "getting there" is not guaranteed, in fact, probably more of an exception than the actual rule. The other thing is that, if it's haddoni, once they start to get a bit bigger, they are known fish-eaters. (Just something to be mindful of.)
Anyhow sorry for the large brain dump but I hope some of this info is helpful.