An Infinity of Nine-Patches -- A Sierpinski Carpet


2010. Machine-pieced, hand-quilted. 41.5 inches square
Detail

If you’re a quilter:
1) Begin with a square.
2) Divide the square into a nine-patch and remove the center square. (The sky shows through.)
3) Divide the remaining eight squares into nine-patches and remove the center square of each.
4) Divide the remaining 64 squares into nine-patches and remove the center square of each.
5) Divide the remaining 512 squares into nine-patches and remove the center square of each.
6) Keep going. (I stopped after completing Step 4.)

If you’re a mathematician:
This is the third iteration of a Sierpinski Carpet, a plane fractal named after Polish mathematician Waclaw Sierpinski in the early 20th Century.
FRACTAL DIMENSION: In the fractal, there are 8 identical figures, each of which has to be magnified 3 times to get the entire figure. The fractal dimension (or Hausdorff dimension) is log 8 / log 3, which is approximately 1.89.
AREA: After every iteration, we leave 8/9 of the area of the figure. To find the area of the figure after n iterations, we have to raise 8/9 to n. After an infinite number of iterations, the area will be 0.


This quilt has been pictured in these publications:
American Quilter Magazine blog from March 22, 2010
Found Math, a gallery of mathematical objects, November 2011, at the Mathematical Association of America website.
XlaTangente (Italian), December 2011
Images des Mathematiques, May 2012

The quilt was displayed at the following quilt shows:
Three Rivers Quilters Quilt Show, Pittsburgh, Pennsylvania, March 2010
American Quilters Society, Des Moines, Iowa, 2011
Pacific International Quilt Festival, Santa Clara, California, 2011


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