Originally Posted by La Mer

KV. And before you ask:

Definition of the Sierpinski Carpet
Start with a solid (filled) square. Divide this into 9 smaller congruent squares. Remove the interior of the center square (that is, do not remove the boundary). Now subdivide each of the eight remaining solid squares into 9 congruent squares and remove the center square from each. Continue to repeat the construction to obtain a decreasing sequence of sets

The Sierpinski carpet is the intersection of all the sets in this sequence, that is, the set of points that remain after this construction is repeated infintely often.

And if you don't understand what the above is all about, don't worry, not knowing will not have any affect on your punting.