Carpet Walk

At first glance, this print looks like the classical fractal known as the Sierpinski carpet, carried through five generations. Topologically, that would be an object with 1 + 8 + 8^2 + 8^3 + 8^4 = 4,681 holes. On closer examination, however, the print shows a nonintersecting closed path that topologically is identical to a circle; i.e., an object with one hole. To see how this works, click here for the early construction stages and a high-resolution detail of the print. The path traverses all of the "points" (small squares) that comprise the carpet. This iterative construction could be continued through any number of generations. "Carpet Walk" is a limited edition of 50 digital prints executed in 2015. The image size is 15" x 15".

Artwork showing a Sierpinski carpet created from a single closed curve.

Copyright 2015 Robert Fathauer