Menger sponge

The construction of a Menger sponge can be described as follows:

The topological dimension of the Menger sponge is one, the same as any curve.

The 3D analogue of this is the Menger sponge.

In mathematics, the Menger sponge is a fractal curve.

Number of cards required to build a Menger sponge of level n in origami.

However, it is not the Menger Sponge complement.

The Menger sponge itself is the limit of this process after an infinite number of iterations.

The Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume.

This is a level-1 Menger sponge (resembling a Void Cube).

It was just that: a huge, articulated cube 600 kilometres on a side hanging in the vacuum like a poor physical rendering of a Menger sponge.

One is the Menger Sponge, where every cube is replaced by a three dimensional ring of cubes.

The Mystery of the Menger Sponge.

It is related to the Smith-Volterra-Cantor set and the Menger Sponge.

The Menger sponge constructed in three dimensions extends this idea to graphs that are not planar, and might be embedded in any number of dimensions.

For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge, a higher-dimensional generalization.

Margaret Wertheim A Field Guide to the Business Card Menger Sponge (2006)

The Menger sponge is a closed set; since it is also bounded, the Heine-Borel theorem implies that it is compact.

Every cube is divided into 27 smaller cubes and the center cross is retained, which is the opposite of the Menger sponge where the cross is removed.

His most famous popular contribution was the Menger sponge (mistakenly known as Sierpinski's sponge), a three-dimensional version of Sierpinski's carpet.

Menger Sponge Animations - Menger sponge animations up to level 9, discussion of optimization for 3d.

In August 2006 the IFF curated an exhibition on the Business Card Menger Sponge, a giant origami fractal made by engineer Jeannine Mosely.

With computer graphics of stunning beauty, we are conducted through the weird world of Koch curves, Seirpinski carpets, Menger sponges, Fatou dusts, self-squared dragons, and Apollonian gaskets.

The Void Cube is a 3-D mechanical puzzle similar to a Rubik's Cube, with the notable difference being that the center "cubes" are missing, which causes the puzzle to resemble a level 1 Menger sponge.

Level 3 Menger Sponge made of Business Cards - A level-3 Menger sponge built by students at Mississippi State University out of 48,000 folded business cards.

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 M is a Cantor set.