Sponge-a-rific!

THE SPORG WILL ASSIMILATE YOU

Yeah, the Borg were pretty tough customers … but they merely traveled around in a simple geometric cube. The Sporg travel around in a freakin’ Menger-Sierpinski sponge, with infinite surface area and enclosing zero volume! In case you can’t comprehend that, human, here is the mathematical representation:

So clearly, resistance is futile despite the relative simplicity of the Sporg Sponge. I mean, after all, it’s quite simple: “the Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume. In spite of this, there exists a homeomorphism of the cube having finite distortion that “squeezes the sponge” in the sense that the holes in the sponge go to a Cantor set of zero measure … The sponge has a Hausdorff dimension of (log 20) / (log 3) (approximately 2.726833).”

Just pray to your puny gods that the Spongoronites don’t show up on your doorstep … they travel in a Sierpinski tetrahedron.

wikipedia

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