The Sierpinsky carpet

How do you construct a Sierpinsky carpet?
Take a square (left illustration) and divide it into 9 equal squares. Take out the middle square (second illustration).
The new figure contains 8 smaller squares.
For each new square: divide the square into 9 equal squares and take out the middle square (third illustration).
Continue this process "indefinitely".

What is the dimension of the Sierpinsky carpet?
If you measure the surface area of the Sierpinsky carpet "3 times as accurate" (i.e. the side of the square that you use to measure is a third in length of the original) , the number that represents the surface area of that little square is each time 8 times as large.
As for the dimension: 3^dimension = 8.
Considering that 3^1,89279 ~ 8 , the dimension of the Sierpinsky carpet is ~1,89279.

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