The Diclonius, a mutated homosapien that is said to be selected by God and will eventually become the destruction of mankind, possess two horns on their heads and have a "sixth sense" which gives them telekinetic abilities. Due to this dangerous power, they have been captured and isolated in laboratories by the government. Lucy, a young and psychotic Diclonius, manages to break free of her confines and brutally murders most of the guards in the laboratory where she is being held, only to be shot in the head as she makes her escape. She survives, falling off a cliff into the ocean and manages to drift along to a beach where two teenagers, Kouta and Yuka, discover her. Having lost her memories, she was named after the only thing that she can now say, "Nyuu," and the two allow her to stay at Kouta's home. However, it appears that the psychotic side of Lucy is not dead just yet... 
(Source: ANN - Revised)

The story involves human mutations called "diclonii", who are born with horns on their heads and possess telekinetic powers, in the form of invisible "arms" called vectors. The power of these arms vary, but they can stop normal bullets and deflect some others. The number of them differ with each diclinous, as does their full range. 
The tendency for violence among diclonii is high, especially as they grow older. As children, their violence stems from a certain playfulness, unlike the absolute hatred of humans in their later years. Diclonii are rare, as they are the members of their species that are able to reproduce naturally. 
Silpelits are more common. They are the offspring of two humans, the male of which has been infected with the mutation. Interestingly, only males can pass on the genes, and all diclonii and silpelits turn out to be female. Certain scientists noticed an increasing number of babies with horns being born, along with those children murdering their own parents and others, and tried to contain the spreading and find out the cause by placing them in a Facility in cells where they are subject to inhumane experiments to test their abilities or where they await execution for being too dangerous. 
The main non-mutant character in the story is Kouta, who ends up becoming increasingly involved with one diclonius in particular, the main mutant character Lucy, the only pure diclonius, as she seeks a way to infect or kill all of humanity. Lucy has a cruel and unsettling past, and she has long since lost her empathy for humans, except for Kouta. 
However, Director Kakuzawa, who has diclonius ancestry although he doesn't have the vectors, has plans to mate with Lucy and start a true diclonius race. If Lucy is found and he manages to do so, humanity will be nonexistent. 
Kouta and Lucy's lives have been intertwined since their childhood, but not necessarily in a good way. And after the virus is airborne and spread across all of Japan, what is the fate of humanity and who holds all of the answers? 
Note: Chapter count includes 6 extras.

This episode takes place within episode 11 as Nana attempts to fit in the household while trying to find a chore that she can do and get used to Nyu's presence whom she only knows as Lucy. Running away after getting scolded, Nana ends up in the beach and meets Bando whom she promised to bring Lucy to later that night. Leaving the household with Nyu, it begins to rain and Nyu slips, hits her head, and is knocked unconscious. As Bando waits and everyone else worries where they might be, Nana, with an uncoscious Nyu, takes shelter as Lucy's consciousness begins to come out and dreams an old memory of how she was captured and why she doesn't attack Director Kurama. As the rain begins to let up, Kouta and the others find Nana and Lucy and takes them home. There, Nana finally finds the chore that she will be doing - feeding the dog.
 
(Source: Anime News Network)

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