This alien like creature is a baby stone crab. This species can grow as big and even more intimidating than an adult blue crab. They are very aptly named as they both look like and live on rocks and stones. This young one had a purplish tint to it as did the adult I caught on my vacation. Stone crabs are edible but have very little meat in their bodies. The common practice is to break off one of their claws and allow the other to grow big. The torn off one will grow back, so causes no permanent home to the crab.  In areas near people, stone crabs occur more often than not with one claw larger than the other because of this.  The claws on a stone crab are probably the largest in comparison to body size of any crab species, which is why the claws are the most desirable part of the crab.  However, the crabs are fascinating to watch and unless you intend to eat the claw soon, it is best to just leave them be.