Two of my favorite things are math and knitting. Perhaps surprisingly, there is a fair amount of overlap between them. On Ravelry, my favorite knitting site, I have seen patterns for everything from lacy triangular shawls meant to look like Sierpinski’s gasket to seamless single-sided cowls that double as Möbius strips. Dr. Sarah-Marie Belcastro, a mathematician with Smith College and Clark University, maintains The Home of Mathematical Knitting, where the fiber arts on display include handmade Klein bottles and projective planes. She also provides links to a variety of resources on the topic.
Last spring, I started getting interested in fractals and decided I would like to knit some. I couldn’t find any patterns I liked for fractal-print hats, so I drew up a color chart of my own. My favorite hat pattern is Keiyla’s Basic Beanie, by Renee Peterson, so I adapted the sizing to fit my chart and get a number of stitches that would be compatible with iterating the fractal. After a bit of trial and error, I got the hat in the picture. It’s a little hard to see, but the triangular shapes are the type 1 quadratic Koch curve at four iterations. I had some extra space left at the top, so I added some stripes representing the first few terms of the Fibonacci sequence. It was a fun experiment in combining two of my interests!