Clifford A. Reiter, Sierpinski Fractals and GCDs, Computers & Graphics, 18 6 (1994) 885-891.

The Sierpinski triangle, carpet and pyramid, along with the Menger sponge are well known 2-d and 3-d fractals. The fact that these fractals are constructed in a similar fashion is made evident by showing that discrete versions of these all arise using inner products involving greatest common divisors and least common multiples on matrices involving base 2 and 3 addresses. These consructions admit generalization to arbitrary dimension and base.

See also: · Some images related to the paper [Images] · A paper focusing on Sierpinski Fractals from inner products [Abstract mv_1993] · A paper on Sierpinski Fractals in high dimension [Abstract mv_1995b] · · A paper on various ways to implement the Sierpinski Triangle in J [Abstract ci_1997a]