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.

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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