Is the Inverse of a Menger Sponge a fractal? I know a Menger sponge is fractal in nature, and it seems to me that the inverted form of it would be fractal as well, but I don't know.
Is an Inverse Menger Sponge a fractal?
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fractals
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5What do you mean by “inverse”? The set complement of the points in the sponge? – 2011-10-06
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0There's a "description" of the Inverse Menger Sponge at http://minecraftonline.com/wiki/Menger_Sponge but I don't understand it. It may also be the object pictured at http://www.flickr.com/photos/friends_of_folding/98165798/ – 2011-10-06
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0[This](http://math.stackexchange.com/questions/7412) seems to be the two-dimensional version of what you want... – 2011-10-07
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3I guess "the inverse Menger sponge" is what mathematicians would call "the complement of the Menger sponge" in the containing cube. If so, then it is an open set in three-space, and thus not a "fractal" in the sense of Mandelbrot. – 2011-10-07