Menger Sponge by lgp692000

Bryce • (none) • posted on May 03, 2005

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Description

Construction of a Menger sponge can be visualized as follows: 1.Begin with a cube. 2.Shrink the cube to 1 / 3 of its original size and make 20 copies of it. 3.Place the copies so they will form a new cube of the same size as the original one but lacking the centerparts. Repeat the process from step 2 for each of the remaining smaller cubes. After an infinite number of iterations, a Menger sponge will remain. Properties of a Manger sponge Each face of the Menger sponge is a Sierpinski carpet; furthermore, any intersection of the Menger sponge with a diagonal or medium of the initial cube M0 is a Cantor set. The Menger sponge is a closed set; since it is also bounded, the Heine-Borel theorem yields that it is compact. Furthermore, the Menger sponge is uncountable and has Lebesgue measure 0. As Peitgen, J

Comments (9)

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electric

1:11PM | Tue, 03 May 2005

hi mark,,,nice to see your art again.. excellent mats, nice concept,, boolean compound..

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lgp692000

1:16PM | Tue, 03 May 2005

Actually, each cube is created just like the description above. I cannot tell you how many cubes are in each sponge, but it was so many that I used Rhino to put it together because I could not get Bryce to leave it looking like a solid mass. Mark

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lgp692000

1:25PM | Tue, 03 May 2005

Ok! The first level Menger sponge contains 20 cubes. So for every level you go up you raise 20 to the next power (you can easily count the level of the sponge by the different size holes in the sponge, in this case there is 3 different sizes). This is a third level Menger sponge, so it is 20^3 or 202020=8000 cubes per each of the sponges in this image. Hope this helps! Tee-hee!

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Burpee

3:43PM | Tue, 03 May 2005

You're a masochist! 8000 cubes? Oh my! Unbelievably cool though. Could you reduce the poly count and put it in freestuff :D ;)

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jocko500

8:30PM | Tue, 03 May 2005

real cool work

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Stoner

2:01AM | Wed, 04 May 2005

Not just my head, my whole body is in pain reading this. I love images with some thought in it and you have that in this and its also very well executed.

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