Enumeration and Identification by Elimination of Weave Families of Given Repeat Size
R. M. Dawson · Textile Research Journal · 2000
An algorithm to identify all families of weaves of given repeat size is outlined. It is based on a numbering of all possible black and white colorings of a rectangular block of squares, but only a small proportion of these colorings need be considered individually. For the cases investigated, however, the number of weave families increases almost exponentially with repeat size, and so necessarily does the number of colorings considered individually. If this is always so, any algorithm is only practicable over a range of small repeat sizes. The algorithm, in Pc-program form, is used for (ends per repeat × picks per repeat) values of up to 18. Numbers that specify the repeat of the highest numbered member of each weave family are listed for repeat sizes of 2 to 8 X 2, 3 to 6 × 3, and 4 × 4.