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LostInParadise's avatar

What do you think it would be like to walk through a structure shaped like a Menger Sponge 3D fractal?

Asked by LostInParadise (31914points) March 3rd, 2013

Assuming that such a structure could be built that could safely hold people in it. Three or four iterations of the design process should be enough to make it interesting. I thought It might be a fun and educational idea for a museum. It is one thing to look at a 2 dimensional fractal, but it would be something else to have to travel inside of a 3D one. I am not sure what would be the best way to get from one level to the next. There could either be stairs on the outside of the cubes or you could pull your way up like a 3 dimensional jungle gym. What do you think a cat would think of such a structure?

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6 Answers

ragingloli's avatar

It reminds me of the movie “Cube”. I would not want to enter such a construct.

Brian1946's avatar

I would feel safer climbing it than I would walking through it.

gasman's avatar

Just slap on a Serpienski gasket & sprinkle a little Cantor dust, lol. Decorate with stairs like this. Actually, @LostInParadise, that’s an excellent video with very nice graphics.

LostInParadise's avatar

On second thought, considering how quickly the number of cubes grows, it would not be feasible to actually build such a structure. It would not be hard, though, to design a game program for something like Wii that could simulate moving through it

wundayatta's avatar

Get a very large 3-d printer and you shouldn’t have much problem constructing it.

I’m not sure how interesting it would be to play in it without the diagonal cuts. You’re just running along boxlike corridors.

ETpro's avatar

@LostInParadise Thanks for a fascinating tour of a Menger Sponge 3D fractal. Try to imagine typical 2D fractals translated into 3D. Nature routinely does it.

As to cat exploring a Menger Sponge, Spoony THE Cat would love to, but it would take her an eternity to mark every passage with her scent.

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