Every key is a thread. At the front of the loom each key stands in its slot of the array, on a wire as high as its value, and its thread runs back from there. Seen from the front (Bars) the loom is the familiar bar chart; seen from above (Weave) it is the whole history of the sort.

Every comparison weaves one row. A gold pick joins the two keys compared, then the cloth draws back a row. When keys change places their threads bend and cross, so the length of a cloth is the number of comparisons its sort made. Weave all six runs every sort on the same threads: the O(n²) sorts weave long cloths, the O(n log n) ones short, and the gap grows with n.

Stable means equal keys keep the order they came in. Choose Twins to give every value a twin, 3a and 3b, at the same height. A stable sort never lets twins cross; an unstable one ties a red knot where they do.