Cantor dust, named after the mathematician Georg Cantor, is the two-dimensional version of the Cantor set.

In the limit, starting from a square the construction 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 three-dimensional form of this is called the Menger sponge. An alternate generalization of the Cantor set produces the Sierpinski carpet.

See also: fractal