Enclave Depth in Hitomezashi Stitchery
D. Jacob Wildstrom

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 357–360
Short Papers

Abstract

The patterns of closed or open shapes produced by interleaving horizontal and vertical dashed lines, some of which are offset by a half period, are the fundamental designs behind the art of hitomezashi, the “one-stitch” style of the sashiko embroidery technique. These same patterns also appear in the AA Weaving technique developed by Ahmed. An “enclave” in a division of a finite canvas is a region which is wholly enclosed by other regions. The order or depth of an enclave is the number of regions one must pass through to reach the edge of the canvas. Some hitomezashi patterns possess very deep enclaves, but in general, the maximum depth of an enclave, even in fractal or random designs, is sharply limited.

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