Connections between Hitomezashi Patterns and Truchet Tiling
David A. Reimann

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 457–460
Short Papers

Abstract

Many visual patterns are often created on an underlying grid of squares. Truchet tiles are squares decorated with two quarter-circle arcs that can be used to create fields of meandering patterns. Hitomezashi is a type of traditional Japanese sashiko embroidery, often white thread on blue fabric, where large running stitches follow orthogonal grid lines to create regular patterns. Hitomezashi forms two complementary patterns, one on each side of the fabric. Interestingly, one can overlay Truchet curves on a hitomezashi pattern such that half of the Truchet arcs follow the hitomezashi pattern and the other half of the Truchet arcs follow the obverse hitomezashi pattern. However, an arbitrary Truchet pattern will not always have a corresponding hitomezashi pattern. Examples of each pattern type and relationships are shown and discussed.

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