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A Menger Sponge ist a fractal curve with a surface area approching \infty while the volume approches 0 for higher order Merger sponges.
This seemed interesting, so I built one out of paper.
Fold 72 sonobe:
Insert the individual sonobe together to form the merger sponge:
Next step: Build a level 2 menger sponge (left as an exercise for the reader).
A sturdier variant can be build using blank business cards:
The amount of cards needed can be calculated using one of the formulas described in A212596, for example
f(n) = 4 * (8^n + 2 * 20^n)
(cube)
#
12 cards
(cube with a hole made out of cubes)
### # # ###
192 cards
(cube with a hole made out of cubes with hole made out of cubes)
######### # ## ## # ######### # # # # ######### # ## ## # #########
3456 cards source
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emile - 1655834893.652401s
