emile.space

# Menger Sponge

Menger Sponge
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).



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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# ## ## #
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3456 cards source

———
emile - 1655834893.652401s