Veronica Roth had several sources of inspiration for Divergent. Some were super serious sources, like psychological ideas about exposure therapy. And some were less serious, like an Evanescence song and a billboard of a person jumping off a building. (Source.)
In fact, besides that Evanescence song, Veronica Roth had a whole playlist that she wrote to. And—how nice of them—the official Facebook page for the book lists all the songs and what they mean to Roth.
People don't just read books these days—they make art and jewelry about their favorite books. And then they try to sell that art. Check out this fan's collection of the best fan-made Divergent merchandise.