Most likely it is nothing about the rock itself that is growing. The growth could be a some sort of moss or lichen. Some fungus will even grow close together to look like grass. Any growth on the rock is slowly dissolving it, so you might want to remove it.
The growth you are describing is hair algae. Every aquarium will go through various stages. The proper water parameters and lighting conditions are extremely important to cut down on the bad algae, and encourage the good. I recommend a cleaning crew, including a tang, algae eating snails, and crabs.
Caulepra or hair algae is what you have. Both of these ages have a grass like appearance and tend to grow in little clusters. These two kinds of algae is nothing to worry about. Most aquarium fish will eat at it and it can actually be good for your aquarium.