Why do some sizes make more than one cord?

A plain plait is a cord bouncing diagonally off the four sides of the panel, like a ball on a billiard table. It comes back to where it started after travelling a distance set by the least common multiple of the width and height, and the panel holds the greatest common divisor of the two such cords side by side. So seven by five is one cord, six by four is two and nine by six is three. The Turk's-head knot follows the same arithmetic: one strand exactly when its two counts share no factor.

How do you know it is one continuous cord?

It is counted, twice, from the finished drawing. One count follows each cord from point to point until it closes; the other joins the short pieces between points wherever the drawing connects them and counts what is left. A one-cord design is only returned once the first count says one, and the page then makes the second count and says so beside the drawing if the two ever disagree.

Is the over-and-under always right?

Yes. Every cord is walked from start to finish and the crossings it passes are read off in order; they have to go over, under, over, under all the way round, and a cord that passed an odd number of crossings could not do that. Every design is checked this way before the page describes it as checked.

Can I use the designs for a craft or a product?

The designs are generated here from a plain grid, not copied from any manuscript or existing artwork, and you are free to use what you make. The plait-and-break method itself is the traditional construction and belongs to nobody.

Celtic Knot Generator

Celtic knotwork is a cord, or a few cords, woven back and forth across a panel so that it passes over and under in strict turn at every crossing. A plain plait is the starting point; the designs come from breaks, where the cord turns back instead of crossing. This draws a panel of the size you choose, places breaks at random under the symmetry you choose, and — unless you say otherwise — joins the result into one continuous cord, so a finger can follow it all the way round and come back to where it started. The page counts the cords from the finished drawing and says how many there are.

Width (squares)

Height (squares)

Symmetry

Breaks

Cords

Style

Seed (optional)

The same seed and settings draw the same knot again. It is for getting a design back, and is not cryptographic.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. The page addresses and dates a browser normally prints across the top and bottom are already kept off.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

A knotwork panel will appear here.

What this generator does

Draws knotwork the way it is set out by hand: a plait on a grid of crossings, with breaks where the cord turns back instead of crossing. What makes it different from the other pattern pages here is that the result is one object rather than a field of tiles. The Truchet and geometric pattern generators place a motif in each square, and a line that leaves one square only meets the next by design; here a cord is followed from crossing to crossing, the number of separate cords is counted, and over and under are assigned so that they alternate along every one of them.

How to use this tool

Choose the width and height in squares. A long thin panel, such as twelve by two, makes a border strip.
Choose a symmetry and how many breaks to place. No breaks gives a plain plait.
Choose one continuous cord, or let the breaks fall as they may and see each separate cord in its own colour.
Press Make a knot. Press it again for another design, or type a seed first to be able to make the same one later.
Choose Outline only to print it for colouring in; download it as an SVG file to scale it, cut it or stitch from it.

Understanding the controls

Width and height: Two to twelve squares each way. The size alone decides how many cords a plain plait has: the greatest common divisor of the two. Seven by five is one cord, six by four is two, twelve by twelve is twelve. Once breaks are added that rule no longer holds, which is why the page counts the cords afterwards rather than predicting them.
Symmetry: None, a mirror from left to right, mirrors both ways, or a half-turn. Symmetry is of the breaks, so the shape of the cord repeats; the over-and-under survives a half-turn but is reversed by a mirror, because a mirror image of a woven cord has every crossing the other way up. With a half-turn or both mirrors, a panel whose width and height are both even is always an even number of cords, so one cord is refused there rather than searched for.
Breaks: How likely each crossing, or each symmetric group of crossings, is to become a break: none, a few, some or many. More breaks give larger open loops and fewer crossings. With none and one cord asked for, the page adds the fewest breaks that join the plait into one cord — one fewer than the plait has cords.
Cords: One continuous cord, or however many the breaks make. With one cord, the page changes crossings after the draw until the cords have joined, and says how many it changed. The other setting leaves the draw alone and colours each cord separately, which is the way to see how a design is built.
Style: Coloured bands, or white bands with a dark outline for colouring in. The outline style is the one to print on a home printer.
Seed (optional): The same seed and settings give the same knot again, so a design can be reprinted or shared by the word that made it. A seed makes the design repeatable; it is not a secret, and a seeded design is not cryptographic.

Worked examples

Seven by five, mirrors both ways, some breaks, one cord — seed rainy-day: One cord through 42 crossings with 16 breaks. Seven and five share no factor, so the plain plait is already one cord; the breaks split it, and one symmetric change was enough to join it again. The cord passes 140 points before it closes.
Six by four, no breaks, cords as they fall — seed rainy-day: Two cords, each in its own colour, 38 crossings between them. The greatest common divisor of six and four is two, and that is the count — the two cords are the same length, 48 points each.
Twelve by eight, no breaks, one cord — seed rainy-day: The plain plait is four cords. Three breaks were added, the fewest possible since each break can join at most two cords, leaving one cord through 169 crossings.
Nine by six, mirror left to right, many breaks — seed rainy-day: Left to fall, the breaks make four cords: one long cord of 160 points and three small loops of 16 to 20. Asked for one cord with the same settings, the page made two changes after its draw and returned a single cord through 61 crossings.

Common use cases

A colouring page that is a real knot, with every crossing going over and under in turn, rather than a tangle of lines
A border or panel to trace for woodwork, leatherwork, embroidery or a card, scaled from the SVG file without losing sharpness
Showing a class why a plain plait six squares by four is two separate cords while seven by four is one
A starting design to redraw by hand, with the breaks already placed and the cord already proved continuous

How this generator works

The panel is a grid of points where cords meet, one at the middle of each edge of the squares. At each point a cord either crosses straight over another or meets a break and turns back; along the outer edge it always turns back. Breaks are drawn at random, by the chance the Breaks setting gives, and placed in matching groups when a symmetry is chosen. The cords are then followed from point to point and counted. If one cord was asked for and there are more, the page looks for a crossing where two different cords pass and makes it a break, or a break where two different cords turn and makes it a crossing: either change always joins those two cords into one, so each such change removes exactly one. With a symmetry, whole symmetric groups are changed together; when no group change lowers the count, one group is changed at random and the search carries on, within a fixed number of tries. Over and under come from position alone: at every crossing the strand running one way is on top in even columns and the other way in odd ones, which makes each cord alternate. The finished drawing is then checked from scratch — the cords are counted again by a second method that joins the pieces between points rather than walking along them, every cord is walked to confirm it goes over and under in turn, and the breaks are compared with their images under each member of the symmetry.

Randomness and fairness

Chance decides which crossings become breaks, which way each break lies, and, when one cord is asked for, the order in which joins are tried. The cord count, the over-and-under and the check involve no further draw. The joining step changes the design after the draw, so the designs you see are not an even sample of every possible panel. Without a seed the draws come from your browser's cryptographic random source; a seed swaps in a repeatable source, for reproducibility rather than secrecy.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

Rectangular panels only. Round knots, corner pieces, animal interlace and knots that follow the outline of a letter are not drawn.
It does not write your name or a word in knotwork. A letter drawn as knotwork needs a letterform to follow, and those are designed one alphabet at a time.
Breaks lie along the grid only, which is the standard plait construction; the diagonal breaks some setters use for sharper corners are not offered.
Bands are a fixed width with rounded turns. The pointed, tapered corners of manuscript knotwork are a matter of hand drawing.
Twelve squares is the largest side. A bigger panel can be made by drawing two and joining them by hand, but the page will not check the join.

Common mistakes

Expecting a mirrored design to look identical in its mirror, crossings and all: The path of the cord is mirrored; the over-and-under cannot be, because a mirror turns every crossing the other way up. Choose a half-turn if you want the weave itself to repeat.
Asking for one cord with a half-turn on an even-by-even panel: It cannot be done: those panels always split into an even number of cords. Make the width or the height odd, or choose a left-to-right mirror.
Colouring a printed multi-cord design as if it were one cord: Switch Cords to as they fall before printing; each cord is then drawn in its own colour, so you can see where each one goes.

Practical tips

For a border, choose a long thin panel such as twelve by two. As a plain plait that is two cords; asked for one cord, the page joins them with a single break.
To redraw a design by hand, draw the plait first, then the breaks, then follow the cord and ink over and under alternately — the printed panel is the answer to check against.
Open the SVG file in any vector drawing program to change the colours or the band width; it scales to any size without blurring.

Privacy and your data

The knot is drawn and checked in your browser. The only thing you can type is a seed, which is not stored, not sent anywhere and not included in any usage count; the downloaded file is made on your device and holds only the drawing.

Frequently asked questions

Why do some sizes make more than one cord?: A plain plait is a cord bouncing diagonally off the four sides of the panel, like a ball on a billiard table. It comes back to where it started after travelling a distance set by the least common multiple of the width and height, and the panel holds the greatest common divisor of the two such cords side by side. So seven by five is one cord, six by four is two and nine by six is three. The Turk's-head knot follows the same arithmetic: one strand exactly when its two counts share no factor.
How do you know it is one continuous cord?: It is counted, twice, from the finished drawing. One count follows each cord from point to point until it closes; the other joins the short pieces between points wherever the drawing connects them and counts what is left. A one-cord design is only returned once the first count says one, and the page then makes the second count and says so beside the drawing if the two ever disagree.
Is the over-and-under always right?: Yes. Every cord is walked from start to finish and the crossings it passes are read off in order; they have to go over, under, over, under all the way round, and a cord that passed an odd number of crossings could not do that. Every design is checked this way before the page describes it as checked.
Can I use the designs for a craft or a product?: The designs are generated here from a plain grid, not copied from any manuscript or existing artwork, and you are free to use what you make. The plait-and-break method itself is the traditional construction and belongs to nobody.