Looks like Halameda. Do a google pic search for Halameda and see if the pics look like what you have. From what I see on the left and the edge of the rock on the right it looks like Halameda to me. It thrives on calcium and turns white when lights are out. If it is Halameda it's a good macro.
LOL...ok. Funny you say that. My first thought was that it wasn't a macro algae but something attached to the rock that algae has grown on. The stuff in the middle looks like threads or fibers almost like it is woven or something.
Can you take some off and put it in a container with detergent an try scrubbing the algae off? You may get a better idea of what it is by attempting to see it in it's natural form.
Maybe it is one of those fake ornamental silk plants. Where did you get that rock