Generator

8-end satin, move 3

A satin, drawn from its move. Almost the whole surface is warp, broken by one weft point per pick, and those points are placed so that no diagonal forms — which is what distinguishes a satin from a twill of the same float length.

3 essays call satin. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

Which satins exist. For each order, the moves that give a satin — a step coprime with the order, and not the steps of one and one less which give a twill instead. Four and six admit none, so no regular satin exists on four ends or on six.

Weaves

There is no satin on six ends

Weavers have known it as a rule for centuries. It is a theorem with a one-line proof about common factors, and it rules out four ends as well.

$What a float limit of 4 leaves. For each repeat, the fraction of the distinct twills on it whose longest float is within the limit. The constraint is usually stated as a rule about a drawing; it is really a statement about how much of the catalogue exists, and the catalogue shrinks as the repeat grows.$ Weaves

Designing to a float limit

Every jacquard designer works to a rule of the form nothing longer than four. It reads as a constraint on a drawing. It is really a statement about how much of the catalogue exists, and the catalogue shrinks as the repeat grows.

Which move to use on 16 ends. For each satin move the order admits, the distance from an interlacing to its nearest neighbour, measured on the torus the repeat lives on. A move whose interlacings crowd gives the eye something to find; the one that scatters furthest is the one to weave.

Weaves

Which satins are worth weaving

Manuals give the moves a satin admits as a list, as though the survivors were interchangeable. They are not. Measure how far apart the interlacings sit and the traditional counter turns out to be the best move at the orders a weaver mostly uses — and to fail first at thirteen, where the square root names four and five scatters further.

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