Menger's sponge

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.

st 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.

st 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.

st 1 and  2

And one more small sponge level 1 built of 72 modules.

small st 1

Sponge under construction.

under construction under construction

Commision of the work.

Kasia i g¹bka

The level 3 sponge is under construction now.

st 3 st 3

I see you !

st 3

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