What are fractals? In simplest term, a fractal is a rough or fragmented geometric shape that can be split into parts, each of which is approximately a reduced-size copy of the whole. The Sierpinski carpet is a well-known example of a plane fractal first described by Polish mathematician Wacław Sierpiński in 1916.
Thank you to Anabeth Dollins for graciously sharing a photo of her quilt based on the Sierpinski carpet. The construction of the Sierpinski carpet begins with a square. The square is cut into 9 congruent sub-squares in a 3-by-3 grid, and the central sub-square is removed, resulting in a Nine-patch quilt block. The same procedure is then applied recursively to the remaining 8 sub-squares, ad infinitum.
What a wonderful quilt design! Make it any size, any color palette, or any fabrics to give the quilt your own spin. Here’s how Anabeth made hers:
“Each week for several weeks I took a pile of fabrics to quilt group—one week reds, one week oranges, one week blues, and so on. I cut two 1" x 8" strips from each of the fabrics that read mostly solid, omitting plaids, florals, and multicolors. At home, I'd choose eight strips that sort of went together in value and color and then make eight 1.5" Nine-patches, using sky fabric as the middle piece. Then I made a 4.5" Nine-patch out of these, using sky as the middle. The 4.5" blocks that satisfy me the least are the ones in which the eight fabrics have too much contrast. I think the trick is to keep the fabrics similar in value.“
Anabeth continues, “Eventually I had 64 different 4.5" Nine-patches to play with. I spent a lot of time arranging them on the design wall, taking one photo after another to record my arrangements. I finally said ‘Stop thinking!’ and put the 64 squares into eight 13.5" Nine-patches, with sky in the middle, and put the eight big squares into a large Nine-patch.
The 512 smallest Nine-patches have half-inch finished blocks. All of the fabrics came from my stash, but since the blocks use so little fabric there's NO visible change in the size of my stash!”
Another variation is the Sierpinski triangle, also a wonderful quilt design. I’ve started my own Sierpinski carpet variation, in which the smallest squares finish three-fourths of an inch. I love this project because it can be done in small snippets of time, and it has endless design and color possibilities. Use your computer’s search engine to find many more examples of quilts based on mathematics. You can see more of Anabeth’s quilts at http://anabeth.dollins.org/qlt.html.