Sierpinski carpet

The image above we see a portrait of Wacław Sierpiński, which was created by a student of Oberlin College Andrew Pike. It reminds us zoomed newspaper photos, when we can see particular dots of various size. But it's unusual image, because every element in it is not a simple dot, but one of several generations of the Sierpinski carpet fractal, which was first described by Wacław Sierpiński in 1916.

The forming of the Sierpinski carpet is like to forming of the Sierpinski triangle fractal, because the next generation of the fractal sets up by cutting removing elements from the source shape. Generation of the Sierpinski carpet begins from the square. Then it being divided into nine rectangles, and the center rectangle removed. This procedure continues for each of eight rest squares. You can see several first generations of the fractal on the image below.

Andrew Pike used two series of several generations of the fractal. The one series began from the black color, and another from white. He designed a computer program, which divided a photo of Wacław Sierpiński into squares of various values of grey color. To avoid strong color changing he used dithering technique.

So, the inventor of the fractal was pictured with his fractal.

The Sierpinski carpet is a two dimensional generalization of the one dimensional fractal Cantor dust. Also, there's generalization of the Sierpinski carpet into three dimensions, which named Menger sponge.

The image by Andrew Pike was found at http://www.bridgesmathart.org/art-exhibits/jmm08/pike.html