Menger's sponge is a well known example of 3 D (more accurate 2.73 D) fractal. It's a spatial counterpart of the Sierpinski carpet.
To obtain the Menger sponge perform the following steps:
Get a cube. You obtain a sponge level 0.
Divide each face of a cube into 9 squares (3 x 3). Hollow every face through the center quare. You obtain 3 holes in perpendicular directions. It's a Menger sponge level 1.
Each side consists of 8 squares. Divide each square once mores into 9 equal parts and hollow once more at the center square. It's a Menger sponge level 2.
Repeat this operation infitely. The result is the Menger sponge. It's a spatial, bounded geometrical figure with infinite surface and null volume. It's fractal dimension equals log 20 / log 3, approximately 2.73
Following photo shows Menger sponges built of Sonobe modules. The sponge level 1 consist of 648 modules. The sponge level 2 consist of 1056 modules.
And one more small sponge level 1 built of 72 modules.
Sponge under construction.
Commision of the work.
The level 3 sponge is under construction now.
I see you !