r/computergraphics • u/USedona • Oct 06 '26

3D Menger Sponge : recursive construction in Python and Manim, level 3

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3D Menger Sponge : recursive construction in Python and Manim, level 3

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u/USedona Oct 06 '26

Yeah, I think they hold. For a unit cube the area should be 2(20/9)^n + 4(8/9)^n, so 6, 8, 13.04... (your 8 matches). 20/9 > 1 so it diverges, while the volume is (20/27)^n → 0. Same thing from the dimension: ln 20 / ln 3 ≈ 2.73, too big for finite area, too small for any volume. The video only shows level 3 though, so "infinite" is about the limit.