An article by Ralph Griswold on using residue sequences (integer sequences reduced by modular arithmetic) to design weaving threading and treadling sequences. It explains periodicity, grid plots, and how to compute residues on the fly, then converts 0-based residues to 1-based shaft numbers and introduces pivot-based draws. Two worked examples are given, a Fibonacci threading (mod 15) and a Wythoff point twill (mod 9), followed by areas to explore and an appendix of Fibonacci residue repeats for moduli 4 through 16.