Elfen Lied

The Diclonius is a mutated homo sapiens that reportedly has two horns on its head, a "sixth sense" that grants it telekinetic abilities, and is supposed to have been chosen by God to be the end of mankind. They were caught by the authorities and isolated in labs because of their potentially harmful power. A young, unstable Diclonius named Lucy manages to escape her constraints and viciously murder the majority of the lab guards before being fatally shot as she attempts to flee. She manages to live and drift to a beach, where she is found by two teens named Kouta and Yuka. She was given the name "Nyuu," the only word she can now utter after losing her memories, and the two let her stay at Kouta's house. It seems, though, that the truly horrible "Lucy" is still alive.