# Is an Inverse Menger Sponge a fractal?

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.

-
What do you mean by “inverse”? The set complement of the points in the sponge? –  Kevin Reid Oct 6 '11 at 22:42
There's a "description" of the Inverse Menger Sponge at minecraftonline.com/wiki/Menger_Sponge but I don't understand it. It may also be the object pictured at flickr.com/photos/friends_of_folding/98165798 –  Gerry Myerson Oct 6 '11 at 23:47
This seems to be the two-dimensional version of what you want... –  Guess who it is. Oct 7 '11 at 0:18
I 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. –  GEdgar Oct 7 '11 at 0:37