Fun with Menger's Sponge!

[Roman Legion]

Ok, so I was doing research for a math paper, and while I was looking for hyper-pyramids, I happened to wander by this thing called a Menger's Sponge... A rather nice 3D fractal, which requires an infinite surface area to enclose zero volume.

Anyway, I decided to make my own! A few hours later, and I had a lovely four or five iterations of Menger's Sponge floating in space. Take a look!

http://www.toonzone.net/romey/temp/sm_mengersponge1.jpg (http://www.toonzone.net/romey/temp/mengersponge1.jpg) http://www.toonzone.net/romey/temp/sm_mengersponge2.jpg (http://www.toonzone.net/romey/temp/mengersponge2.jpg)

--Romey

[Dante Bunny]

OOOOOOhhh....3-D!! :yakko: :wakko: :dot:

Dante Bunny

[Roman Legion]

Hmm... you got me thinking...

For anyone who'd like to see this in true 3D, and for anyone who has good control over their own depth focus, give this a try:

http://www.toonzone.net/romey/temp/menger3d.gif

I'd recommend viewing at 1024x768 resolution, to get it to appear small enough on the screen to avoid eye strain. ;-)

--Romey

[Feslmogh]

Where do you get this program and how advance in math doyou have to be?

[Roman Legion]

Aaaaaactually, I just built the whole thing out of polygons, by hand. Start with a cube, and duplicate it as necessary to obtain the first iteration (20 cubes). Then I merged the cubes, deleted unnecessary polygons, scaled the new cube down, and repeated the process.

It's basically just a 3D version of a Sierpinski Carpet, which progresses like this:




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X X
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X X X X
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X XX XX X
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X XX XX XX XX XX XX XX XX X
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XXX XXXXXX XXXXXX XXX
X X X XX X X XX X X X
XXX XXXXXX XXXXXX XXX
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X XX XX XX XX XX XX XX XX X
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X XX XX X X XX XX X
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XXX XXX XXX XXX
X X X X X X X X
XXX XXX XXX XXX
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X XX XX X X XX XX X
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X XX XX XX XX XX XX XX XX X
XXXXXXXXXXXXXXXXXXXXXXXXXXX
XXX XXXXXX XXXXXX XXX
X X X XX X X XX X X X
XXX XXXXXX XXXXXX XXX
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X XX XX XX XX XX XX XX XX X
XXXXXXXXXXXXXXXXXXXXXXXXXXX

Even after removing as many unnecessary polygons as possible, the final object had 260,200 polys. Total file size was 47.6 megs. =X

Could probably write a script to automatically generate Menger's Sponges to render in something like Blender, and it wouldn't suprise me if someone has already done so...

--Romey

[Narfpinky]

Ah, yes, the Bor-- ...er, sponge thing-ey you showed me. ;)

I like the 3D pic you posted.

Just looking at it makes me all wobble-wobble, hehha, poit.

Yet another reminder to get back on a certain project I've been away from.