The Mathematics of Hitomezashi Stitching Patterns

Hitomezashi patterns, which originate from traditional Japanese embroidery, are intricate arrangements of unit-length line segments called stitches. The stitches connect to form hitomezashi strands and hitomezashi loops, which divide the plane into regions. 

While these patterns have been used as prominent examples of mathematics-inspired art, their deeper mathematical properties have not been investigated until now. This talk will discuss the delicate topological and combinatorial techniques that Noah Kravitz and I developed to understand hitomezashi patterns, along with the deceptively simple-looking results that we proved using these techniques. We believe that hitomezashi patterns are fascinating mathematical objects that are ripe for exploration and generalization; I will present several potential ideas for future work.