The Fringe (Symbol)
Both Tris and Tobias take trips into the fringe at different points in the story. Tobias goes with Nita in order to meet Mary and Rafi, while Tris goes with Amar and George to do surveillance. The fringe represents the sprawl and depravity caused by genetically damaged people living with no rules. There is no government in the fringe, it is the areas between metropolitan areas; it's basically a violent shantytown that isn't safe for anyone. Tris and Tobias take their experiences in the fringe to mean that something has to be done about how GDs are treated. If they are treated so poorly that they prefer the lawlessness, danger, and poverty of the fringe to city life, then something is wrong. The fringe represents what happens when the Bureau's viewpoint toward GDs is allowed to reign free and unopposed.
The Factionless and GDs (Symbol)
Before Evelyn and the factionless overthrew the faction system in the city, the factionless lived in poverty, having failed out of their chosen faction's initiation (or choosing to exile themselves). They don't eat enough, living in hordes, forced to do the dirty work of the city. They are the lowest-ranking citizens. In the compound, there is a similar social dynamic. The scientists, researchers, and council are GPs, while the GDs work in maintenance and other menial jobs. Tris and Tobias quickly equate the factionless in their city to the GDs in the Bureau. Zoe and David say that it is not the same, that everyone in the bureau is treated the same, but this is not the really the case. Once again, this dynamic between GD/GP and factionless/part of a faction represents the terrible consequences of the Bureau's mindset toward GDs.
The Faction System (Motif)
Similarly, Tris, Tobias, and their friends find that the faction system that they had become so accustomed to over the years relates to their life outside the city at the Bureau. They find that the genetic manipulation experiments from before the Purity War aimed to do genetically exactly what the factions tried to do behaviorally. The genetic manipulations tried to delete a bad gene, while the factions simply tried to suppress that gene so it was never seen in a person's behavior. Tris quickly realizes that the same things that went wrong in the city were what went wrong with genetic manipulation experiments. When you suppress a bad behavior trait so much, it only makes way for an even worse behavior trait to shine through. Thinking about the genetic manipulations in terms of their faction system helps the city-dwellers to understand the implications of the outside world.
Geography (Motif)
Location serves a primary role in this story. People in the city experiments are mostly GDs whose ancestors signed away their rights to participate in the experiments. The only genetically pure individuals are known as Divergent. In the fringe, almost 100% of inhabitants are GD. No GP would willingly choose to live in the fringe. In the Bureau, a huge population of GPs works and lives, aided by the GD maintenance population. In the metropolitan areas/cities ruled by the government, there is a mixture of both GPs and GDs, but the GDs are terribly mistreated, often leading to their evacuation into the fringe (out of desperation). These different spatial geographical locations have different population layouts, which is a critical motif throughout the story.
The Serums (Motif)
The serums are one thing that connects the characters' past life in the city experiment to their new existence outside the city in the Bureau. Before leaving the city, Johanna tells them about how each faction has a serum -- the Abnegation's is the memory serum, the Erudite's the death serum, the Candor's the truth serum, and so on. Once outside the city, these serums continue to play a huge role. The death serum is used to protect the Weapons Lab from an intruder, and Nita unsuccessfully attempts to break in and release it on the Bureau. At the same time, Evelyn is prepared to use the death serum on the Allegiant rebels in the city. The memory serum is almost used by the leadership of the Bureau to completely reset the Chicago experiment, but Tris instead resets the Bureau itself. In the past, in the city, the memory serum had been used to wipe the memories of people who left the city, and to cover up secret deaths to cover up evacuation of the Divergent. The characters from the city have at least one thing to rely on to play a huge role in their lives both inside and outside the city -- and that is the serums.
The Sculpture in the Bureau (Symbol)
The huge sculpture in the bureau that Tris finds to be especially interesting is a symbol of the Bureau's patient approach to healing genetic damage. The sculpture is a large slab of stone with a tank of water suspended above it. Drops of water run out of the tank and onto the rock periodically, forming a small divot of change in the rock. The slab of rock is meant to represent the problem of genetic damage, the tank of water is the Bureau's ability to fix the problem, and the tiny drop of water is what they're actually able to do. Tris doesn't agree with the sculpture. She thinks it'd be more effective to unleash all of the water at once to attempt to fix the genetic problem.