Textile Structure
how cloth is put together
How this site is made

The figure library

Every picture here is generated from code at build time. This page lists the generators, each rendered at its defaults.

No figure on this site is a drawing that was made once and saved. Each one is a function: it takes parameters and returns SVG, so the same generator produces the p4 plate and the p6m plate without either being redrawn.

That is the reason the collection can keep growing without the illustrations drifting apart. A generator is written once, checked once, and every essay that calls it inherits the same line weights, the same colour roles, and the same behaviour in dark mode. There are 20 of them so far.

bias

How far the bias goes, and where it stopsExtension along the bias against shear angle, with the angle at which the threads jam marked for three settings. The curve is geometry and so is the wall — a more closely set cloth reaches it sooner.0%10%20%30%40%0°15°30°45°60°cover 40%locks at 66°, +38%cover 60%locks at 53°, +34%cover 80%locks at 37°, +26%extension along the biasshear anglethe yarns never stretch; the net changes shape

colour-weave

Colour and weave — 2/2 twillOne interlacement, threaded in two colour orders. What a reader sees is the colour of whichever thread is on the face, so the visible pattern can be something the draft gives no hint of.only the order the coloured threads are put in changesthe weave2/2 twillfour dark, four light▪▪▪▪▫▫▫▫two dark, two light▪▪▫▫the face colour computed, not designed2/2 twill

cover

The same thread count, twiceTwo cloths with identical thread counts and different yarn. The count is the same number in both; the fraction of the surface the threads actually occupy is not, and that fraction is what thread count is usually taken to mean.100 ends and 100 picks per inch in bothfine yarncover 78%coarser yarncover 97%cover from diameter and spacing, circular sections

crimp-interchange

Pull it lengthways and it narrowsThe same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.as wovenwarp crimp 8.0% · weft 4.0%pulled 3% along the warpwarp crimp 4.9% · weft 7.1%warp thread 108.0 and weft 104.0 — unchanged in bothboth thread lengths checked, not assumed3% pull

cross-section

A warp end in section — plainOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spansplainwarp crimp 22.3%8 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility3 face changes

curl

Why one curls and the other does notA knitted loop is not symmetric front to back. Worked every course the same way, the asymmetries add along the edges and the fabric rolls; worked alternately, consecutive courses point opposite ways and cancel.the dots mark which way each course facesstockinette — every course the same0 face changes · curlsgarter — alternate courses reversed5 face changes · lies flatface changes counted, not the curl itself

draft

The 2/2 twillThe 2/2 twill on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.2/2 twilllongest float 216 interlacings per repeat1 separable clothrepeat 4 × 4generated, then counted4×4

draft-symmetry

A draft is a two-coloured patternFor each weave, the symmetries that leave warp-up as warp-up and those that exchange the two. Only a balanced weave has any of the second kind, because exchanging warp and weft is only a symmetry when there is as much of one on the face as the other.weaveleave the faces aloneexchange themplain1616basket16162/2 twill16163/1 twill16none5-end satin20noneevery candidate operation tried against the repeat

drape

A cloth laid over a sphereEvery thread segment is exactly one pitch and none has stretched. What has changed is the angle at each crossing, and the amount is decided by the surface — a developable one costs nothing and a curved one costs more the further the cloth goes.a sphereworst shear 22.2°cells closelocks at 57°nothing jamsthe fishnet construction, every segment checkeddoubly curved

float-map

Where the floats are in the 5-end satinEvery longest run of warp on the face, marked. A float is smooth because nothing interrupts it, which is the same reason it snags: there is a length of thread lying on the surface with nothing holding it down.5-end satinwarp floats of 4weft floats of 120 markedruns measured round the repeatfloat 4

hangs-together

Whether the cloth is one clothTwo drafts. Both interlace everywhere, both have short floats, and both look like perfectly ordinary weaves. One is a single fabric and the other is two fabrics lying on each other, and the bars beside each strand say which layer it belongs to.the bars mark which separable cloth each thread belongs toan ordinary 2/2 twillone clothevery end and pick interlacestwo separable clothsconnectivity of the above-and-below relation, computed

interlacing

What an interlacing costsEach weave's interlacing count beside the closest it can be set in the same yarn. The two run opposite ways, because a thread that changes face often has to bend often and a bend takes room.weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch

loop

The knitted loopOne thread, bent into a course of loops, each of them drawn through the loop below. Nothing here is straight, which is why a knit extends in every direction while a woven cloth extends only on the bias.a course runs acrossa wale runs down5 wales × 4 coursesevery loop passes through the one below itweft knit

loose-end

A thread that is not woven inOne warp end stays on the face across the whole repeat, so nothing holds it down. On point paper it is a solid column and nothing more; in cloth it is a thread that can be pulled straight out.1 strand never interlace2 separable clothsthe marked end lies loosea column with no gap is a thread with nothing over it

run

One break, two outcomesThe same single break in a knit and in a weave. In the knit nothing holds the loop above the break, so the failure climbs the wale; in the weave every other thread is still held by the threads crossing it, and one thread comes loose.a knit — the break runs up the wale3 loops freeda weave — the break stays put1 thread freedcounted from the structure, not from experience

satin

8-end satin, move 3A 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.8-end satin, move 3warp floats of 7moves available: 3, 532 interlacings per repeatone weft point per pick, scattered8 ends

satin-table

Which satins existFor 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.ordermoves that give a satinhow many3 endsnone — every step shares a factor with the order04 endsnone — every step shares a factor with the order05 ends2 326 endsnone — every step shares a factor with the order07 ends2 3 4 548 ends3 529 ends2 4 5 7410 ends3 7211 ends2 3 4 5 6 7 8 9812 ends5 7213 ends2 3 4 5 6 7 8 9 10 111014 ends3 5 9 114enumerated from the coprimality condition, not recalled3–14

separable-census

How often a draft falls apartEvery four-by-four draft in which each end and each pick interlaces at least once, sorted by its longest float, with the fraction that describe more than one cloth. The counts are produced by running the enumeration rather than by recalling it.22,874 drafts tested · 144 separateof the 90 balanced ones, 0 separatelongest float 10 of 20.0%longest float 20 of 880.0%longest float 3144 of 227840.6%enumerated while the figure was drawn4 × 4

shear

A trellis sheared 30°The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.shear 30°bias +22.5%across -29.3%area 87%locks at 60°every segment checked against its own lengthno thread stretches

weaves

The weaves everything else is built fromPlain, twill and satin on point paper. Reading across, the floats lengthen and the interlacings fall — and every property a weaver cares about follows from that one trade.plainfloat 1 · 8 interlacingsfirmness 1.002/2 twillfloat 2 · 16 interlacingsfirmness 0.505-end satinfloat 4 · 20 interlacingsfirmness 0.40a filled square means the warp is on the facecounted from the matrices, not from the pictures