1. Menger Sponge

1. Menger Sponge
1.1. using blank business cards
1.2. cards needed
1.2.1. level 0
1.2.2. level 1
1.2.3. 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).

1.1. using blank business cards

A sturdier variant can be build using blank business cards:

1.2. 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)

1.2.1. level 0

(cube)

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12 cards

1.2.2. level 1

(cube with a hole made out of cubes)

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192 cards

1.2.3. level 2

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

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3456 cards source




        

emile - 1734444931.0615s - generated using vokobe "0.1.3"