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Waclaw Sierpinski

Waclaw Sierpinski was a Polish mathematician who lived from the late 19th to early 20th centuries C.E. In addition to his many contributions to set theory, number theory, and topology, he discovered three well known fractals the Sierpinski Gasket, Sierpinski Carpet, and Sierpinski Curve.

For the 2008 Joint Mathematics Meeting in San Diego, California, I created a picture of Sierpinski using iterations of the Sierpinski carpet. Eight different iterations were used, four each from a white and black square.

Using Java, I took the source image, averaged over 4x4 squares of pixels, and replaced each square of pixels with the iteration of the Sierpinski carpet which most closely approximated the grayscale value of the pixels it would replace. After placing a square, I diffused the error over the nearby squares using a Floyd-Steinberg based algorithm. I created a similar portrait using Sierpinski gaskets and the pair of portraits were displayed at the 2009 Bridges Math Art meeting.


I can provide higher resolution images on request. Here is a detail of the Sierpinski Carpet picture showing a number of iterations: