Using the three plots of Infinite Jest as the vertices doesn't really work, there is nothing fractal like about the plot itself and plot is not the structure. How I see it is that the vertices would be family, education, and society, which are all deeply interrelated. For the majority of the characters we learn their relation to these three things, in Hal and Gately we get a very well developed view of it, not so much for Marathe and Steeply where the family and education aspect is abbreviated and I think this is where the mentioned mercy cuts happened.

I don't think I would say Infinite Jest has three plots, it feels like it does because the plot never happens, we get the setup and then it is dropped right when it actually starts. We can view it as three plots but those plots don't provide anything useful towards understanding. They would be more accurately viewed as triangles, they are containers for information.

Edit: I also don't think we can fully interpret Infinite Jest through the Sierpinski structure, that was the structure of the first draft which was something like 500 pages longer and had the bulk of the novel in the end notes. It has been too long since I last read it to say what the structure of the final form of the novel is but I think he may have just made the gasket more linear; he keeps repeating the full triangle but each time he goes a bit deeper with the iterations.

Ah, maybe I made my claim unclear. So my claim is that the 3 vertices are the institutions (ETA, Ennet House, the Wheelchair Assassins), not plots. I agree that IJ is kind of plotless, and that to me is what the voids in the Sierpinski Gasket could represent, but this article was more about the two-ways-to-construct-the-triangle thing.

But I like your vertices (family, education, and society).

You're making me think that there's something to the fact that you could 'seed' the Gasket with different vertices as well. Something I learn when re-reading is that you can bring so many interpretations and perspectives to this novel and still come out with an entertaining and valid experience of it. In that respect, I like the idea that you can use different triplets to seed the Gasket!

You're correct that we can't lean fully on the Sierpinski idea. Wallace mentions in his interview that after those edits, the book became more like a 'lopsided' Sierpinski Gasket "it looks basically like a pyramid on acid" (https://www.kcrw.com/shows/bookworm/stories/david-foster-wal...).

Separate from the Gasket thing, but I like your point about the footnotes. I wish people spent more time on those. I've heard commentary on the structure of those. Some folks talk about the 'self referentiality', as text (obviously) references footnotes, and there are even instances of footnotes referencing the main text! I've also heard that the back-and-forth emulates the back-and-forth in a tennis match, although that one seems less interesting.

Edits: fixed spelling mistakes Edit: I added your 3 vertices idea and the fact you can invert the 3 vertices to the post, thank you! I attributed back to this thread.