Cantor dust
Cantor dust, named after the mathematician Georg Cantor, is the diadic
(two-dimensional) version of the Cantor set.
In the limit, starting from a square, this produces a set with an infinite number
of square sections each having zero area--the sum of all areas also decreases to zero
in the limit.
The triadic (three-dimensional) form of this is called the Menger sponge.
An alternate diadic generalization of the Cantor set produces the Sierpinski carpet.
See also: fractal