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Can anyone explain why they bothered with the fractal at all, instead of using a 3 dimensional grid? Doesn't a grid of the appropriate resolution provide the exact same? Or is it to show that they can do everything within even a subset of a 3D grid limited in this way?

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The 3D grid result is well known, perhaps it would be fair to call it trivial (you can even throw away all but 2 layers of one of your dimensions). As you say, the Menger Sponge is a subset of the 3D grid, so the students had to find a construction which dodges the holes. To me, the result isn't surprising, but it is pleasing. But the really cool part of the article in my mind is the open problem at the end: can you embed every knot in the Sierpiński tetrahedron?

Thanks, I think that helps me understand the 'why' a lot more! That's kind of cool, and I do hope they can keep making progress in that effort!

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