I think it is just a square piece of fabric, draped. Think of holding up a bed sheet by the corners ... then move your hands in across the top 18" from each corner and letting those sides "drape" down. The way it's draping it appears to be a very heavy fabric -- when I first saw it I thought "animal hide", but I suspect it is just heavy weight fabric.

I don't care for it at all from this angle, but I'd be interested in seeing it from straight on.

Brenda is right about the way it drapes. Note that to replicate the look, you need reversible fabric, because it need to look goo from both sides. Also, you could not drape lined fabric in this way. Another consideration is the side seams, because heavy fabric would not drape so smoothly with turned seams, the folds would have a lot more volume. I believe it is probably satin, because of the soft sheen.

maybe the corners tie together to "close" the curtains. I kind of like it; it's original.

Sstarr93... that's what I thought... original. A good look for a garden room or some such casual room. I've got a whole house to drape and most of the windows will require 108" length draperies. I'm desperate for ideas! Most of the windows are for decor only and not for light reduction.

I think I might see a track, perhaps they are traversing panels?

emjfla, I would not put in a whole house full of curtains, these days. It's gone out of style. I would do only a couple of rooms, like this one, in an interesting fabric window treatment.

funny it looks like a version of a Reatoration Hardware catalog!...LOL...love the look