(W)hole in One (Sierpinski Carpet)

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This design is based on the idea of a Sierpinski Carpet, a fractal image generated by an iterative process of dividing an unit square into nine equal parts and deleting the central square. This process is repeated over and over again leaving behind a finely filigreed square full of holes. It can be mathematically proved that the area of the hole is equal to the area of the original square—even though there are remnants of the original square left behind!

In other words, the area of the holes (taking away just 1/9th of a square at a time is equal to the area of the unit square! How crazy is that! Thus the hole is equal to the whole!

This seemingly contradictory statement has inspired the following design—where the words whole and hole are mapped onto a square – with the letter o representing the hole in the Sierpinski carpet. Of course as you zoom in, the whole and hole keep interchanging. We call this design (w)hole in One (in keeping with the idea the area of the hole is equal to the whole of the unit square).

whole-hole-sierpinski

Click image to enlarge (opens in a new window).