Sierpinski carpet (nonfiction)

The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is one generalization of the Cantor set to two dimensions; another is the Cantor dust.

The technique of subdividing a shape into smaller copies of itself, removing one or more copies, and continuing recursively can be extended to other shapes. For instance, subdividing an equilateral triangle into four equilateral triangles, removing the middle triangle, and recursing leads to the Sierpinski triangle. In three dimensions, a similar construction based on cubes is known as the Menger sponge.