Fungia sp, or Mushroom coral, is a solitary coral that does not attach to the the reef nor does it bud off new polyps to make a colony.  It has a central mouth with radiated septa (the ridges) around it.  When you're out on the reef, take a close look because the size of the Mushroom coral (usually about 15cm) makes them a great way to learn about the structure of the usually much smaller polyps that are in the larger colonies (like Staghorn, Honeycomb, Boulder or Brain corals).  They sit on the reef floor - sometimes scattered like giant copper coins - and are great at colonising loose coral rubble slopes.  You'll almost definitely see one snorkelling out on the Great Barrier Reef from Port Douglas.