Infinite Fractionation?

I stumbled upon this interview with David Foster Wallace, author of Infinite Jest, a book I've been meaning to read for a while, but haven't quite gotten around to. I thought it was interesting for another writer to express the idea of branching we discussed in class in such familiar terms:

MICHAEL SILVERBLATT: I don't know how, exactly, to talk about this book, so I'm going to be reliant upon you to kind of guide me. But something came into my head that may be entirely imaginary, which seemed to be that the book was written in fractals.

DAVID FOSTER WALLACE: Expand on that.

MS: It occurred to me that the way in which the material is presented allows for a subject to be announced in a small form, then there seems to be a fan of subject matter, other subjects, and then it comes back in a second form containing the other subjects in small, and then comes back again as if what were being described were -- and I don't know this kind of science, but it just -- I said to myself this must be fractals.

DFW: It's -- I've heard you were an acute reader. That's one of the things, structurally, that's going on. It's actually structured like something called a Sierpinski Gasket, which is a very primitive kind of pyramidical fractal, although what was structured as a Sierpinski Gasket was the first- was the draft that I delivered to Michael in '94, and it went through some I think 'mercy cuts', so it's probably kind of a lopsided Sierpinski Gasket now. But it's interesting, that's one of the structural ways that it's supposed to kind of come together.

MS: "Michael" is Michael Pietsche, the editor at Little, Brown. What is a Sierpinski Gasket?

DFW: It would be almost im- ... I would almost have to show you. It's kind of a design that a man named Sierpinski I believe developed -- it was quite a bit before the introduction of fractals and before any of the kind of technologies that fractals are a really useful metaphor for. But it looks basically like a pyramid on acid --

To answer Silverblatt's question, a Sierpinski Gasket is constructed by taking a triangle, removing a triangle-shaped piece out of the middle, then doing the same for the remaining pieces, and so on and so forth, like so:

The result is an object of infinite boundary and zero area -- almost literally everything and nothing at the same time. A Sierpinski Gasket is also self-similar...any smaller triangular portion is an exact replica of the whole gasket. You can see why Wallace would have wanted to structure his novel in this fashion.

Totally cool! This reminds me of what I discussed one evening after class with Professor Moss about formlessness and attainment of such in the material world. It seems like in the language of mathematics, this ubiquity is not only permitted but prevalent. I like how Wallace translates/transcribes this body/instrument/illustration/poam of mathematics into the realm of language and an expression more relevant/ubiquitous (words keep branching off their neighbors) to general human living.

So with an infinite boundary, are dead ends possible? One could keep expanding forever, yet still be contained within this indescribable boundary...the end of infinity would be the dead end, an end one cannot technically reach.