The director is Christopher Nolan, and the film is Following. Based on an idea Nolan thought up after his home had been burgled (hence, I suspect, the "twisted") and shot over the course of a year for barely $6,000 (hence, obviously, the "ultra low-budget" claim) by a student of English Literature who never formally studied film (which, I would argue, is where the "twisty because unconventional" comes from), it's an astonishingly confident, competent, and remarkably stylish film And it's on NETFLIX INSTANT.
A claustrophobic neo-noir film about an odd young man who's obsessed with following people.
Because the film is part of the wonderful Criterion Collection's...um...collection, there's a really thoughtful, cleverly-named essay by Scott Foundas -- then of The Film Society of Lincoln Center, now of Amazon Studios -- on their site called "Following: Nolan Begins." This is probably my favorite bit, because it reflects my own thoughts on the film (and its director):
To revisit—or discover—Following today is, at least in part, to marvel at how rapidly Nolan has ascended from these humble beginnings to the very top of the big-studio food chain, and how he has managed to do so without compromising his vision. Indeed, he is an anomalous figure: the creator of cerebral blockbusters that make big demands on audiences’ supposedly modest intelligence and ever-dwindling attention span; a stalwart proponent of celluloid in the digital era; and a rather private figure who keeps the precise details of his biography close to the vest.