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Menger Sponge

Menger Sponge
    using blank business cards
    cards needed
       level 0
       level 1
       level 2

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).

using blank business cards

A sturdier variant can be build using blank business cards:



cards needed

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)

level 0

(cube)

#

12 cards

level 1

(cube with a hole made out of cubes)

###
# #
###

192 cards

level 2

(cube with a hole made out of cubes with hole made out of cubes)

#########
# ## ## #
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# #   # #
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# ## ## #
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3456 cards source



——— emile - 1655834893.652401s