On 3-Harness Weaving: Cataloging Designs Generated by Fundamental Blocks Having Distinct Rows and Columns

A weaving drawdown is a rectangular grid of black and white squares with at least one black and one white square in each row and column. A pattern results from vertical and horizontal translations of the defining grid. Any such grid defines a tiling pattern. However, from a weaving point of view, some of these grids define actual fabrics while others correspond to collections of threads that fall apart. This article addresses that issue, along with a discussion of binary representations of fabric structures. The article also catalogs all weaving (or tiling) patterns defined by grids having three distinct columns and three to six distinct rows, and groups these patterns into design families based on weaving symmetries.