Mathematical specification of hitomezashi designs

TL;DR

This paper explores the mathematical structure of hitomezashi, a traditional Japanese stitching art, focusing on encoding designs with binary words and duality, introducing new self-dual patterns related to Fibonacci snowflakes.

Contribution

It introduces a novel mathematical framework for hitomezashi, including binary encoding, duality concepts, and new self-dual designs linked to Fibonacci snowflakes, which are previously undocumented.

Findings

Analysis of traditional hitomezashi using binary encoding and duality.

Introduction of Pell persimmon polyomino patterns related to Fibonacci snowflakes.

Identification of new binary words and self-dual designs in hitomezashi.

Abstract

Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two ideas. Self-dual hitomezashi designs related to Fibonacci snowflakes, which we term Pell persimmon polyomino patterns, are proposed. Both these designs and the binary words used to generate them appear to be new to their respective literatures.