Well sort of...it looks like the remains of macroalgae to me. It's white, so it's dead, and not likely to sprout new.
A little about macroalgae:
Macroalgae is not a bad thing, but it has to be pruned (called harvesting) to keep it under control. Many people keep it in a refugium, copepods and amphipods love it. It will absorb nitrates and phosphates to grow...then when you harvest it (prune it) you remove the NO4 and NO3 out of the system, keeping your water pristine.
There are free floating macros, which are good for growing in a refugium, the anchored macros make great hitching posts for seahorses, and are decorative, Red, gold and green, adding color to the tank. If you want corals I wouldn't recommend macros in the display, it can cover over corals, the more unstable the system the faster it grows. For fish only systems it makes great snacks for algae eating fish, and like I said...copepods and amphipods love it, and the fish love hunting down and snacking on those too....AKA: FREE FOOD!!!
It looks to me like a type of algae called Branching Coralline. No common animal, including pods, in the hobby will eat it. A Parrot fish would eat it but not a lot of people have the ability to keep one of those.
Blah...LOL...I thought it was just dried dead branches, if it's spreading it isn't dead, and it isn't a macro. If it's coralline as Bang Guy said...isn't it a desired thing to have in the tank? The only thing I know that eats coralline are urchins, but branching coralline...I don't know, since I have no knowledge of it.