This is called a Resurrection Fern. It's an air plant that grows in the trees around here and gets its nourishment from the air and what accumulates in the bark. It doesn't hurt the host tree, so I don't think it qualifies as a parasite. This clump is growing on a piece of firewood from the big oak branch that came down almost two years age (see here).
It gets its name from its response to drought. It will dry up and shrivel away to almost nothing, a brown clump of dead looking leaves, but then with even a small sprinkle of rain, it will revive instantly (resurrect) and turn into a lush green cloak for the tree branches.