SIERPINSKI FRACTALS AND GCDS

The Sierpinski triangle, carpet, and pyramid, along with the Menger sp onge, are well known two- and three-dimensional fractals. The fact tha t these fractals are constructed in a similar fashion is made evident by showing that discrete versions of these all arise using inner produ cts involving greatest common divisors and least common multiples on m atrices involving base two and three addresses. These constructions ad mit generalization to arbitrary dimension and base.