The Divergent AU (Alternate Universe) portray Rapunzel Corona, Merida DunBroch, Hiccup Horrendous Haddock III and Jack Frost living in the dystopian Chicago of Divergent. Because it is not canon, ideas for this AU are shown through fanfiction, fanart, and other fan-made works. This is a sub-scenario for Sci-Fi AU.
About the AU
Based on the book series Divergent by Veronica Roth, this AU is set in the dystopian Chicago of Beatrice "Tris" Prior. In the series, when teens turns 16 years old, they have to chose a "faction". Whether they are Divergent (people who have the potential to fit into more than one faction) or not depends on the fans.
In the AU, Merida, Hiccup, Rapunzel and Jack Frost have to chose just one faction to live with for the rest of their lives. Their choices are between Dauntless (the brave), Erudite (the intelligent), Candor (the honest), Amity (the peaceful) and Abnegation (the selfless).
The Big Four are often members of different factions by born. Unlike the houses in the Hogwarts AU, they have to choose a faction rather than being sorted into one.
The Big Four
Hiccup is sometimes associated with Four (Tobias) from the original series, because he too has a difficult relationship with his father. He would quite possibly be Dauntless-born and choose Erudite because of his thirst for knowledge. Toothless often takes the form of a black dog or a cat, which Hiccup might use as a topic of study.
Jack is commonly portrayed as Candor, for his search of the truth about his past.
In some scenarios, and in order to line up with the events of Rise of the Guardians, the city government wiped his memory with the Abnegation Serum (a serum that erases part of the memory of those who cross the fence). Some fans says he crossed the fence with his sister to play in the frozen lakes where she died. Then the government discovered their walks out of the city and removed that part of Jack's memory.
Merida is often portrayed as Tris Prior; born in Abnegation and transferred to Dauntless. This is due to of Merida's reckless spirit of adventure and disregard for rules and manners. Another option for Merida's faction transfer could be Erudite, as she was able to identify the Nightshade Berries in Brave. This would be unlikely, however, as it is also shown in Brave that Merida doesn't like to study. All these qualities combined could potentially make her divergent, like Tris.
Rapunzel is generally put into Amity, because of her kind and happy personality. It is possible she would also fit in Erudite or Candor, because of her love of books or habit of always keeping promises respectively.