Cross Stitch Pattern Maker

A photograph holds millions of colored dots. A cross stitch chart of the same scene might hold ten thousand squares in twenty colors, and somebody will fill every one of those squares by hand. That is the whole difficulty of charting. The work is not to keep as much of the picture as possible. It is to decide what can go.

The stitch itself could hardly be simpler. Therese de Dillmont’s Encyclopedia of Needlework, an old manual now in the public domain, calls it the foundation of every other stitch and works it in two lines: a row of diagonals one way, then a row back the other way to complete each cross. Everything else about counted cross stitch follows from the cloth. The fabric is a grid, the needle goes only through its holes, and so the design must be a grid too.

Four centuries of copying squares

The same school places the earliest evidence of cross stitch in burial finds from the Qadisha Valley in Lebanon, silk on an even cotton weave, dated to the thirteenth century. What survives in number comes later and has a name of its own. A sampler, as the Wikipedia article on the form records, takes its name from the Latin exemplum, an example: while printed patterns were few, an embroiderer who met a new pattern stitched a small sample of it onto a cloth to copy from again.

The earliest dated English sampler to survive is kept in a museum in London. Jane Bostocke stitched her name and the date 1598 into it, in silk and metal thread on linen, with pictures at the top and border and all-over patterns below. The same article gives its inscription, which also records the birth of a child, Alice Lee, in November 1596. Wikipedia notes elsewhere that the buttonhole stitch appears on it. It is a record and a reference sheet at once.

Over the next two centuries the sampler changed jobs. Sampler making moved into schools in the late seventeenth and early eighteenth centuries, and alphabets and verses joined the patterns. Through the eighteenth and nineteenth centuries samplers were mainly school exercises, worked almost entirely in cross stitch.

The letters had a use at home. Marcus Huish, in a history of samplers published in 1913, traced them to housekeeping: as households came to own numbers of each article of clothing and of table and bed linen, identification by marking and numbering became necessary, and alphabets and numerals joined the sampler as aids to marking the linen. The Wikipedia article on cross stitch adds that initials were stitched on household items to identify their owner. A girl who could stitch her letters could mark her linen.

The chart as we know it arrived with a craze. Berlin wool work, the Textile Research Centre in Leiden records, was embroidery on canvas worked from charts, in cross stitch or tent stitch, and its patterns were first published in Berlin in the early nineteenth century. The first were printed in black and white on grid paper and then colored by hand. The Smithsonian keeps one, a lily designed by Hertz and Wegener in Berlin, and its catalogue record describes the work: a master design on point paper, a copperplate engraved with a faint symbol in each square for the color, and colorists who painted the printed squares one by one with a tiny square-tipped brush.

Counted patterns on charted paper, much like a modern cross stitch pattern, let an amateur follow a design one square at a time, and the Wikipedia article on Berlin wool work adds that most were sold as single sheets, which kept them within reach of middle-class households.

So the modern pattern is an old idea. One square, one stitch, one color. Only the way the squares get filled in has changed.

What 14 count means

Fabric for counted work is sold by its count. A West Virginia University Extension guide for young stitchers puts it in one line: 14 count fabric has 14 squares in 1 inch, and as the count gets larger the stitches get smaller. So 14 count means stitches at 14 per inch. Wikipedia gives the range of counts in use as 11 to 40, so 14 sits at the coarse, easy end.

From that one number comes the size of everything. Finished size is the stitch count divided by the stitches per inch. The same West Virginia guide gives an example a reader can check in their head: a design 56 squares wide comes out 4 inches wide on 14 count. Move it to 18 count and it shrinks; move it to 11 and it grows. The chart does not change at all.

Linen and other fine even weaves add one twist. They are usually stitched over two threads, each cross spanning two threads in both directions. Stitching over two on 28 count linen gives 14 stitches per inch, the same as 14 count Aida. The count on the label is therefore not always the number to divide by. Halve it first when the pattern says over two.

Here is a worked example. Take a chart of 140 by 100 stitches on 14 count. Divide: 140 by 14 is 10.0 inches, and 100 by 14 is 7.14 inches, so the stitched area is 10.0 x 7.14 in, or 25.4 by 18.1 cm. You cannot cut the cloth to that size, because a hoop needs something to grip and a framer needs something to fold. With three inches of spare cloth on every side, a margin chosen here as a working default and not a rule from any authority, the piece to cut is 16.0 by 13.1 inches.

Fewer pixels, then fewer colors

Turning a picture into such a chart takes two reductions. The first is in resolution. Each stitch must stand for a whole block of the picture, and the fair way to choose its color is to average everything the block covers. Averaging has a trap. The numbers stored in an image file are not amounts of light; sRGB encodes them along a curve, set out in the CSS Color specification as a short linear toe followed by a power of 2.4. Average the stored numbers and a field of black and white dots comes out too dark. Convert to light first, average, convert back, and it comes out the gray the eye sees from across the room.

The second reduction is in color, and it is the harder one. A blurred photograph still contains thousands of slightly different colors, and nobody wants to buy thousands of threads. The standard approach is clustering. In the k-means method the goal is to minimize the sum of the squared distances of the items from the centers of their clusters. Here the items are stitches, the centers are thread colors, and the distance is how different two colors look.

How different two colors look is itself a measured thing. Distances are taken in CIELAB, a color space built so that equal steps look roughly equal, and the later CIEDE2000 formula refines the measure further. The paper by Gaurav Sharma, Wencheng Wu and Edul Dalal on implementing the formula came with supplementary test data for checking an implementation, which is how one knows the arithmetic is right. A useful side effect is a warning: when two colors in a palette sit only a unit or two apart, they are one thread too many.

Clustering has limits worth stating. Finding the best clustering is a hard problem in the technical sense, even for two clusters, and the usual method settles quickly on a local optimum: a good answer, with no promise that it is the best. A chart maker returns a good palette, not the best possible one. It also knows nothing about what the picture shows. It will spend three colors on a blotchy wall and one on a face unless a person steps in, merges colors and repaints.

Why confetti ruins a good chart

There is a famous trick for faking colors you do not have. Error diffusion dithering, published by Floyd and Steinberg in 1976, pushes each pixel’s rounding error onto its neighbors, so that a value halfway between two available colors comes out as a checkerboard of both. On a screen this looks like a smooth blend. On cloth it is a checkerboard you have to sew.

Scattered single stitches of this kind are what this page calls confetti. Each one means threading a color, anchoring it, making one cross and ending it, or carrying the thread across the back to the next lone square. A hundred stitches in a solid block go quickly along a row. A hundred lone stitches in a hundred places can fill an evening. A chart with fewer colors and no confetti is not a cruder picture so much as a kinder one, and from the distance at which embroidery is usually seen the difference in the image is small.

That is the argument for leaving dithering off unless the shading truly needs it, and for tidying afterwards: finding every stitch that has no neighbor of its own color and giving it the color most common around it. Tidying cannot know that a lone stitch was the glint in an eye. Look before you accept it.

Reading the chart, and buying for it

A finished chart follows conventions old enough to be nearly universal. One guide lays them out: each square is a single stitch; darker lines mark off blocks of ten by ten; numbers run along the top and the side; arrows at the top and side point to the center, and it is good practice to begin stitching there. Each thread has a symbol in the key. In color a square shows a color block and a symbol; in black and white the symbol works alone, which is why the symbols must be easy to tell apart. Backstitch appears as lines drawn over the grid.

Thread is harder to predict than cloth, but geometry gives a floor. On 14 count the holes are 1.81 mm apart. A full cross has two diagonals on the front, and when rows are worked out and back, the two-line method Dillmont describes, two straight runs behind. That comes to about 4.83 hole spacings, or 8.76 mm for each strand in the needle.

Now fill the 140 by 100 example completely, with two strands, and the crosses alone use about 245 m of single strand. Stranded thread comes with several strands lying together, so divide by the number in your skein: with six, that is about 41 m off the skein, or 49 m with a fifth added for starts and ends.

Treat that as an estimate and no more. It ignores the thickness of the cloth, the length lost at every start, and how far you travel across the back. Skein lengths vary too, so read yours off the label before dividing.

One thing a chart made this way does not print is a thread maker’s color number. Makers publish their own shade cards, this page copies none of them, and a number guessed from a screen color would be a guess presented as a fact. A screen is not daylight in any case. The honest method is the old one. Take the printed swatch to the thread, hold them together by a window, and write down the number of the skein that matches. That is, after all, what a sampler was for.