Noah Iliinsky, an expert in data visualization and communications, has put together what he calls a "spoiler-ific timeline" for Looper in which he charts all the various paths taken by the film's characters. But as Iliinsky notes, it also shows how the film defies standard time-travel conventions. Now, the diagram does indeed contain spoilers, so you have been duly warned.
Iliinsky argues that there are basically two kinds of time-travel stories, those that feature an immutable past (where events cannot be altered) and those that feature a malleable history (in which previous events can be altered, thus spawning an entirely new set of timelines).
But Looper, says Iliinsky is a time-travel movie that "keeps us guessing with aspects of both archetypal plotlines." He writes:
Regardless of how we classify it, the key question Looper presents is: Can modifying the past significantly affect the future, or are some outcomes inevitable? While some aspects of the film clearly indicate that we can change our futures by changing our pasts, the open question we're left with is whether Joe really is able to successfully alter a probable future?