The Menger fractal


How do you construct a Menger fractal?
Take a cube (first illustration), divide the cube into 27 equal cubes and take out 7 cubes (second illustration).
The resulting figure consists of 20 smaller cubes (second illustration). Now for each new, smaller cube: divide the cube into 27 equal cubes and take out 7 cubes. Ad infinitum.

What is the dimension of the Menger fractal?
If you measure the content of the Menger-fractal "3 times as exact" (i.e. the side of the cube to measure the content with is one third of the original cube), the result found for the content each time is one twentieth.
As for the dimension: 3^dimension = 20.
Considering that 3^2,72683 ~ 20, the dimension of the Menger fractal is ~2,72683.

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