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
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.