Works of fiction containing non-related but constantly alternating narrative streams?

Question

Chapter is set in a particular period in time, having four - at the time - in no way related characters, each of them with their own separate story. My best feeling is these stories should be presented in an alternating way, while never directly interfering with each other: short fragment of one (about 3 standard pages or even less than 1 s.p. short) followed by short fragment of another and so on - not necessarily keeping strict order.

I don't really know how to take on on that. Problem is probably deeper than pure formatting, or organization, or composition (to paragraph each passage, to title it or not to, to order them in a certain way etc; although I don't reject any advice on that matter, neither), it's, I imagine, more to the subtleties in the very body of text, which make that kind of narrative convincing, and, having not read anything similar myself, I'd be thankful if you can come up with an example, if you can name a book, recommend a novel which uses, in any part, structure roughly similar to the one I described here, so I can study it myself.

Edit:

(One character is in 1st person (a child, btw, who is also the narrator, which, when I think of it better, probably makes the schema so problematic, tricky to convincingly shift between characters), others in 3rd person. It's set in the past (two decades before main story line taking place), and is imagined to be more of a character backgrounding, catching the zeitgeist, atmosphere of time and places, less of a real action, which it can't be in all truth, because it would lead nowhere as 4 parts are separate all the way, mixing at no point, except on symbolic level. Also, idea is for it to be the middle chapter of 3 in total. Luckily, though, I haven't written a word yet, so I'm pretty flexible in every respect, and Psicofrenia's answer and Lauren Ipsum's comment have opened some perspectives for me.)

Answer 1

Something like Cloud Atlas, you mean?

Indeed this is basically Nonlinear narrative. I use it a lot when I write because it can be great -- if well done -- to generate expectation and mystery.

For me, the key of nonlinear narrative is to leave roles that the users can't fill at that point. You can use other chapters to get back to the loose ends and help the readers to understand. You won't follow a right line, but you will move from different perspectives to create that line.

What you need to take real care is to drop breadcrumbs along the way, because if the readers goes for too long completely lost they will loose the interest in your story. Even not being the right time to explain everything, you need to drop small clues that will keep the readers focused.