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onstructing a Celtic Knot

nitial Comments

While reading Iain's book, I spent several weeks drawing various knots, trying to get a feel for the method. I seemed to be spending a lot of that time in the initial construction phases, building the diagonal grid on top of the square grid. So much so that I started using graph paper, and even created some special graph paper for it. So I started looking for patterns, to find a way to simplify the construction.

This method was designed with the thought of writing a computer program to generate the knots. Therefore, I tried to come up with simple, deterministic rules, rather than rules which would require an artistic eye or complex judgement calls. In the details below, a construction is described for a simplified single cord design, rather than the more pleasing single cord or the visually complex double cord . However, I think that this technique could be extended to those (and other) styles of Celtic knotwork.

Also please note that this is not a method for constructing a work of Great Art; it is merely a mechanical approximation. The "final" knot lines from this method are close to where they should be, but sometimes need to be moved slightly, or smoothed out, for purely aesthetic reasons. This method is a first approximation only, and, as such, will be most pleasing when used to build large knots (large in number of crossings) where the overall pattern is more obvious than the execution.

onstructing a Knot

The colors used in this sample construction are described in the key to the right. Blueish lines are construction lines which will be erased at the end. Reddish lines are the actual knot, and will be (with small exceptions) permanent.

Step 1: Grid

Start with a grid with an even number of squares in both directions. Place dots at alternating vertices, making sure to miss the corners. To put it more technically, construct a (2m)x(2n) grid, and place dots at each (x,y) where x+y is odd.

The dots indicate where the "splittings" can be placed in the next two steps.

Step 2: Outside Borders

A splitting is a line through which the knot is not allowed to pass. These lines are drawn slightly shorter than two grid units long, and are centered on the dots drawn in the previous step.

Place splittings on all the dots along the outside border of the grid. These lines aren't actually splitting the knot, but the knot acts just the same when approaching an outside or an inside border, so they're useful during the knot drawing steps.

Step 3: Inside Borders

Now the inner splittings should be chosen. These splittings determine the eventual form of the knot, and should be chosen with care. Symmetric patterns are usually more visually pleasing, but I've chosen fairly odd splittings to demonstrate all the various curve forms. It may take a great deal of experimentation to get a feel for how the knot will look for a given set of splittings.

There are several guidelines to follow when deciding on internal splittings:

All splittings are either horizontal or vertical.
Only one splitting may be placed at each dot.
If three splittings form a 'U' around a non-dot, there will be a "tailoff" (small loop) in the knot. These can add a certain flavor to a knot, but were discouraged by some knot makers.
If a section of the grid is closed off (surrounded by splittings), an internal hole formed, and can be left blank. If it is filled in by a knot there will be two completely disconnected (not even interwoven) knots.
Note that if no internal splittings are placed, the knot will be a simple gridwork.

Step 4: Straight Segments

This is the first actual drawing step; the first three only provided useful construction lines. At this stage, all remaining dots represent places where the knot will intersect itself.

Play "connect-the-dots" with adjacent dots (here, adjacent means diagonally adjacent; the sum of the absolute values of the differences in their coordinates is one).

Don't connect the dots completely; stop just before reaching each dot. Remember that these dots are the crossings, and only one of the knot segments is drawn at each crossing (the other one goes under). Crossings are dealt with in a later step.

Step 5: Short Curves

Going diagonally outwards from each dot, if the dot is approaching a splitting, draw a short curve out from just past the dot to the edge of the grid square. The curve should go straight towards the dot, and should be parallel to the splitting where it meets the grid edge.

To be more precise, the curve is an eighth of a circle of radius (the grid's unit length times the square root of two), centered at a nearby dot. If two short curves meet, they can be drawn at the same time (an entire fourth of a circle).

Once again, note that the curve should not quite reach the dot.

Step 6: Corners

Wherever a horizontal splitting and a vertical splitting meet in a corner, the knot will also have a sharp corner. When filling in these corners, draw at the same level as the short curves are at, so they meet smoothly. Since short curve ends are (square root of two) units away from a grid point, the lines of the corner piece should be (one minus the square root of two) units from the splittings.

Step 7: Long Line Pieces

Wherever there are thin stretches bounded by splittings all going in the same direction, the knot will be basically flat. These should be filled in with straight line segments.

Once again, the position of the segment should be such that it lines up with the short curves and the corners (not centered!). However, since long segments will never occur except next to short curves or corners, this should pose no problem.

Step 8: Centers

This step could actually have come before any of the drawing steps. However, it makes the diagrams appear more complicated. Do this step whenever it feels right.

Wherever there is a dot, fill in the center as follows:

On odd rows, connect the lower right piece to the upper left piece.
On even rows, connect the lower left piece to the upper right piece.

For a slightly different knot, swap the rules around. It makes little difference as long as consistency is maintained.

This is the step that would be the most difficult if the knot were drawn freehand. One would have to follow the knot around, alternating between going "over" and "under". That's the beauty of the mechanical construction; what once seemed magical and tricky becomes amazingly simple.

Step 9: Long Curves (optional)

This is the most complex step in all the constructions I've seen. Usually it is listed as optional, since doesn't affect the form of the knot, but merely makes it look much nicer.

A short curve followed by a long line segment looks a little odd, since it goes from very curved to completely flat quite suddenly. The two grid squares they occupy can be replaced by a single long, smooth curve.

This curve is also part of a circle (two long curves meet to form a smooth quarter of a circle) with a center several grid units away. But be warned that if it is drawn as a circle, the rest of the long line segment (and perhaps a corner) will have to be moved up slightly.

The true master knot constructor will see the long curves coming and draw them instead of the short curve/long line segment pair, rather than going back at the end and redrawing.

Step 10: Erase Construction Lines

Erase all construction lines.

Now the knot is complete!

Take the knot out and impress your friends with your amazing skill.

inal Comments

The drawing steps (four through nine) can come in any order. Drawing the centers first (step eight) can make it much easier to connect the pieces (and to keep from drawing the "under" pieces too close to the dots).

There is no reason why the initial grid has to be square, or even rectangular. As long as the width of any section of the grid shape is an even number of grid units, it will enclose an area that a knot can be drawn in.

In the strictest sense, every attempt should be made to make the Celtic knot be all one long piece (rather than several distinct, interwoven knots). However, it is difficult to see from the splittings whether or not the knot will all be in one piece. I usually make a quick sketch of the knot, count the number of components, and add or remove splittings to make it all one components before drawing the final knot -- hopefully without greatly altering whatever symmetries the knot was supposed to have.

2 Ways to Draw Celtic Knotwork
A side-by-side tutorial comparing two different methods!

I've been drawing Celtic Knotwork for years and I have developed several techniques and my own methods. These tutorials demonstrate those methods. The first (left side of the page) is similar in some ways to the methods of George Bain, his son Iain Bain and many of the artists that preceded them. The biggest difference between my method and the traditional methods is that I use computer graphics programs, but the instructions below are applicable to pencil and paper as well. The second method illustrated here uses the Celtic Knot Font. This font is based on the same forms that can be created using the first method, but the knotwork has been cut apart into separate reusable pieces. I then converted those pieces into characters in a font. The pieces are linked to keys on your computer keyboard, giving you the ability to TYPE KNOTS!

I realize that some folks may consider this comparison of methods to be biased because I profit from the sales of the font that is necessary for the second method. WELL THEY WOULD BE RIGHT! I AM BIASED! Even though I created it, I still use it a lot and consider it to be a very valuable tool. It makes the job of creating Celtic knotwork MUCH easier, allows for more flexibility in the patterns, and size, and the coolest thing about it is that the Celtic Knot font often surprises me by making patterns that I never would have thought of using traditional methods. It is actually lots of FUN!

The first method illustrated here is the method that I used to create the font. I still use this method, as the font cannot create every knot imaginable (I am working on that!). But even when I am designing a custom hand drawn knot for a project I still start with the Celtic Knot font to get an idea of what sort of pattern I want in the finished knotwork and then re-trace or stylize whatever I created with the font. Please read this tutorial with an open mind and pay attention to how much time and effort this font can save. Everyone's time has SOME value, and if you can save a couple of hours designing one piece of knotwork then the Celtic Knot font will save you money every time you use it..

4
qse
fsssv
zsc
r

The old method

These instructions can be followed with pencil and paper or using any computer based drawing or drafting program. I have used Corel Draw, Adobe Illustrator, and AutoDesk AutoCad for various projects, but my favorite is Corel Draw. In the tutorial below I show the method that I use in Corel Draw; however, I have deliberately left out program-specific instructions. I did this to make the instructions more broadly applicable to work with as many drawing and CAD programs as possible.

This method, like most, begins with drawing the grid. Of course you could use graph paper, but that would limit the size of your finished pattern to the sizes of graph paper that you happen to have available. What size should you make the grid? Well that depends on what size you want your final pattern to be. If you are making a pattern for leatherwork, for instance, you would want to draw the pattern to be the size of the final project; say - wallet size. How many squares should you make? That is a tougher question. The number of squares depends on the pattern that you are going to make. The problem is that we often don't know what sort of pattern we want at this stage. So what do we do? Guess? Pick out a pattern that someone else created and copy it? We just have to pick a number of squares that fits into our final size and forge ahead hoping that the resulting pattern will look good and that we aren't wasting our efforts. This grid is 4 squares tall and 6 squares wide.

The second step is to draw in the diagonals. These lines will be the path followed by most of the knotwork. The diagonal lines must be drawn starting from the middle of the sides of the grid squares. In other words, don't draw the diagonals from the points of the grid squares or you'll end up with loose ends sticking out at all four corners.

Next draw in the connecting curves that will become the edges of the knotwork. I make these curves tangent to the diagonals. In other words they connect smoothly to the diagonal lines.

This is the step that most people have the most trouble with: deciding where to "Break the Grid". The thing that makes Celtic knotwork unique from the plaiting (or weaving) seen in many other cultures is the introduction of "BREAKS" into the weave. I've always found it to be rather fascinating: that Celtic knotwork is defined more by where the pattern ISN'T than where the pattern IS. It is a design form made of empty spaces within an otherwise solid object.

So, where do we put these spaces to make an aesthetically pleasing design? A person with extraordinary visualization skills could probably imagine what a knot will look like, but for the average person it is a "try-it-and-see" sort of operation. Here we find the biggest single problem with ALL of the traditional Celtic knotwork construction methods: you have to know what your knot is going to look like BEFORE you design it!

Here is how I do it:: I CHEAT! I use the Celtic Knot Font featured in the parallel tutorial to try out designs. I put together a bunch of pieces and experiment with them 'til I find a pattern that looks cool! I just plug in new pieces, delete the combinations that I don't like and try some more combinations of parts. You, however, don't have the Celtic Knot Font (yet!) so you have 2 choices:

1). Copy what I did here (or someone else's designs from a book).

2). Make some breaks by trial and error and see what happens. If you are lucky it will look good. If you aren't lucky you will waste a bunch of time drawing an ugly knot and have to erase it all and start over, or get disgusted and quit (or you could go here and order the Font). See, I warned you that I was biased....

But back to the tutorial. The red lines on our grid show where I am going to make my breaks.

Follow the diagonals until you come to a red line. When you get to a red line, add a curve so that your line continues into the other line that is broken at the same place. Adding these curves completes the path of the knotwork. Darken this line so that we can see the path clearly for the next step.

OK, now that you spent all of that time drawing the grid, the diagonals and the breaks, erase all of it except the knotwork path that we darkened in the last step. Here is what it should look like.

For this step a computer graphics program comes in real handy. We need to make a new outline all around the entire knotwork path. In Corel Draw you can combine all of the lines into one object and use the contour tool to make a line all around the knotwork path. In AutoCad you can use the offset function to make a line that is parallel to (but offset from) your existing lines. If you use Adobe illustrator you can create a custom pen type with 2 lines and stroke the knotwork path with your new pen. If you are doing this with a pencil you'll have to eyeball it. Draw a line all the way around the knotwork path and inside all of the little holes in the pattern. The new line should be offset from the original path by 1/2 of the desired width of the finished knotwork cord.

When you are done with doubling the line, erase the original knotwork path so that all that is left is the outline.

We're almost there! Hang in there just a little while longer and we will have a knot! And don't pay any attention to those smug folks that started the parallel tutorial at the same time that you started this one and finished making the same knot over an hour ago. You can be proud that you did it the HARD WAY!

All that is left is to figure out the "Over / Under Thing". You can start anywhere on the path of the knot and make 2 little lines at each intersection. Be sure to alternate one way and then the other, over and under, until all of the intersections are done or until you run into an area where you find that you went OVER-OVER, or UNDER-UNDER. In which case you erase lines until you've eliminated the ones that are wrong and do it over. Look at the next illustration and you can see what I mean. Of course if you had used the Celtic Knot Font you wouldn't have to worry about the "Over / Under Thing" because that has been done for you already.

So, there you have it, a completed Celtic knot! It looks pretty good. Of course I'm a professional graphic artist who has done this sort of thing for a living for over a decade, so your results may vary. Because I am fairly proficient at this, it only took me about 2 hours to make this knot for this tutorial.

Now that you have read this tutorial, read the next one to the right to learn another method.

The Celtic Knot Font Method

This tutorial shows how to create Celtic knotwork by a revolutionary new method. The secret is an ornamental font! It does not make letters like an ordinary font; it makes pieces of Celtic knotwork. The basic pieces that you need to create a Celtic knot are located conveniently in one corner of you computer keyboard:

The corners of this square of keys (OK, it's a parallelogram) make the corners of a knot. The sides of this square make the sides of a knot, and the middle makes a middle piece. Like this:

We can make the TONS of knots using just those 9 keys (the Celtic Knot font has almost 200 different pieces). Just by typing more of the side and middle pieces

qwwwwe
assssd
assssd
zxxxxc

we can make this:

There is no layout phase, no grids or diagonals to draw - just type those keys and you have this artwork! Many people stop here and think that they are finished. This really isn't Celtic knotwork yet. Read my rambling speech in the parallel tutorial for some of my philosophy about the breaks in knotwork. Without the breaks this isn't knotwork yet. So let's add some breaks, but first, scroll down because we are already way ahead of the folks in the parallel tutorial.

Keep going....

Yes we really are that far ahead of them....

OK, we need to figure out where to put the breaks. If you have read the other side you already know that I used the Celtic Knot Font to design the knotwork used for these tutorials. How did I do that? After I made the pattern above, I simply substituted pieces to see what looked good. I started in the middle of the top row and replaced 2 of the "w" pieces with "j" and "k"

How did know where those pieces fit? Well, aside from the fact that I made this thing and I know how ALL of the pieces fit, I could look at the keyboard chart that is included with every copy of the Celtic Knot font.

Click on this image to see a larger version.

Notice how similar parts are grouped together? Let's take a closer look.

See how the "j" and "k" fit together to create horizontal lines? We can use them to replace the two middle pieces on the top row. I tried it and it looked good, so I did the same thing on the bottom using the "m" and "," keys. Similarly, the "7" and "u" and the "8" and "i" work together to form vertical lines. I used them to form the sides where I wanted straight lines in the knotwork. Notice that these are all pieces that work well on edges.

Next, I decided to try adding some breaks in the middle, so I tried the "5" and "t" Like this:

So to make breaks, you just replace "Unbroken Pieces" with the equivalent "Broken Pieces". Here are the pieces that I need to replace (shown in gray) to get the same design as shown in the parallel tutorial.

After we make those substitutions WE ARE DONE! We can sit here smugly, knowing that we are finished while those folks doing the other tutorial are still laying out their grid! Here is what our completed knot looks like:

OK, I admit that I have an edge, by being extremely familiar with the font; but I can go through ALL of these steps in under 2 MINUTES without hardly trying! REALLY! Of course your results may vary! :) But even if you are really slow, you can design a Celtic knot in under 10 MINUTES instead of the 2 or more HOURS that were necessary for the old method. That gives you 1 hour and 50 minutes more time to work on the project that you wanted this knotwork for! Furthermore, your knots will look just as good as these; skill and artistic ability are no longer an issue! And if you are an artist, you'll have a lot more time for the really fun part, embellishing your knots in amazing ways now that the prepwork is done!

Click here to get your Celtic Knot Font!

If you used the method on the left and you want to change your knotwork, then you will have to start over . If you used the Celtic Knot Font method you can modify what you have.

You can change the size of your knotwork by just changing the point size of the font:

You can copy a section and paste it over and over to make a long line of knotwork:

You can reuse sections and delete sections.
You can experiment and play with the knots, creating endless variations on a theme:

You can use the font DIRECTLY in Photoshop and utilize all sorts of spectacular effects:

Of course you could do that with a hand drawn knot, but by the time you are finished drawing the knotwork you're exhausted, drained and at your wit's end! With the Celtic Knot Font you are inspired and energized and ready to DECORATE THE WORLD WITH CELTIC KNOTWORK!

Making Celtic Knots (felt-tip pen)

This is an easy way to draw a Celtic knot. You don't have to rub anything out! This method uses colour and outlines. It is particularly suitable for free-form, flowing knots and entangled animals, as used in illuminated manuscripts. It is so simple that it can be used by young children. If drawing it on paper (in the 'real world'), then use a pale broad felt tip pen for the initial lines, and a dark thin felt tip for the outlines.

Draw some lines

Cross with some more lines

Outline one line, with a gap where the line goes underneath

Outline the other lines. Make sure the gaps are right!

Outline the rest of the lines

Join two of the lines

Join the rest, with the corners

This has left two ends. I've added a head and tail!

Here is an action replay of that!

If you have an even number of lines in both directions, as in the example above, there is only one way to have the knot as a single string, and you will get two loose ends. You can get other effects by joining the ends in different ways, but these lead to different numbers of strings. I've coloured them differently to high-light this, but you can colour them all the same and many people wouldn't notice!

If you want a knot with just one string and no loose ends, you must start with an odd number of lines in both directions. You don't need to restrict yourself to a square. You can also tilt the shape into a diamond. Here you must start with a square.
You can also join the ends to make other combinations, with more strings.

Once you've mastered the technique, you can try more complicated shapes. You can vary the length of the lines to produce a diamond, and then join them in the usual way. The shape on the left uses several strings. The tilted shape on the right only has one string. You might think it similar to the rectangular knots above, but note the diagonal strings. knot

You can make any shape you want. Draw out the lines in the paler colour, making sure that they cross approximately at right angles, and that you've left a little room between them. Then draw the outlines, making sure that the lines go over and under. You can have circles, if you want! This technique is so simple to do that children under 10 years old can use it to produce their own designs. Just encourage them to draw the crossing lines first, then the outlines, then join the ends, or finish them with twirls or blobs or heads and tails. The octopus on the right is an original design by a child. You didn't know that an octopus could cross its arms, did you?

knot

You do not need to restrict yourself to a simple grid pattern (see left). Draw the crossing lines as you will, then follow one line, outlining as you go.

I am not sure whether the painters of illuminated manuscripts used this technique. I don't see why not. They didn't have felt tip pens, of course, but they could paint in the colour, and let it dry. Then they could do the outlines in a dark paint with a fine brush. This technique couldn't be used in stone, such as the Celtic crosses in the Isle of Man and elsewhere.

Making Celtic Knots (double strands)

When looking at Celtic knots on the Manx crosses in the Isle of Man, I found that some of them were double stranded. I enjoyed copying the patterns and assumed that these double patterns would be harder. To my surprise I found them much easier to draw. In fact I wondered if the original craftsmen had discovered this too!

You start by drawing the centre line (between the two strands). Draw a weaving pattern with a single line, with BIG gaps in the right places. Then you can draw in the strands on either side of the central line. You then neaten up the lines where they cross, and finish off any edges. You can do this without any measurement, or guide lines, or rubbing anything out.

Draw lines with staggered gaps

Draw the lines the other way to make a weaving pattern

Draw lines either side to mark the two stands

Do this for all strands

Extend the lines to meet each other

Join the ends as you wish

Here is an action replay of that!

In this method, colour isn't necessary, although of course you can colour them in as you wish. When carving patterns on stone crosses, you wouldn't use colour, so perhaps this is why this design of multiple strands appear on stone crosses. It's an attractive design, and the illuminated manuscripts sometimes use it, or use a line of dots down the centre of the single strand.

knot

If you made a very loose pattern to begin with, with very big gaps, you can make a four-stranded design with two strands either side of the central line. On the left, there is a four-stranded knot which is tilted (click here for how to do this). To get three strands, however, you would need to start with a central strand, and add one either side.

knot

One advantage of a Celtic knot with more than one strand is that you can make a very close knot, without any gap between the strings. If you only have one strand, a close knot produces squares in the middle of the knot, with no clue as to their direction (see left). The double strands overcome this problem (see right). I still think that a small gap improves the look of the design! The older designs on the Celtic crosses tend to have little or no gap, but the more flowing designs in illuminated manuscripts often have wide gaps, or different width lines.

Usually where the double strands cross, you get one pair of strands passing over the other (see left). However, it is possible to weave the pairs of strands together (see right). You wouldn't necessarily want to do this for all crossings, but you might use it for the central crossing.

knot

However, many of the manuscripts which use double strands treat each strand separately for all crossings. The advantage of this is that then the central line does not get interrupted (see red lines, right). So you can draw the whole pattern with a line which crosses itself. Then you can draw in the lines either side with gaps, making the interleaving.

If you try to draw a Celtic knot with a single strand, the first line you draw must become one edge of the strand. When you draw the other edge, the whole pattern tends to become lop-sided. It's much easier to draw the centre of the strand, then edges either sides. You could scratch the centre of the strand very lightly on the stone, or even mark it with charcoal or washable paint, and remove it afterwards, leaving the edges of a single strand. (The equivalent on paper or a computer would be to draw the central line in, possibly in a different colour, then rub out out when no longer needed as a guideline.) However, I suspect that one craftsman decided to leave the central line in, so making two strands, and starting a fashion!

Making Celtic Knots (dots method)

This is a method of drawing Celtic knots that I found in a book of Celtic and Anglo-Saxon painting. It called the knots 'interlace', and said "Interlace is not a motif that can be learned by simply looking at a model. One must know the 'trick', and from unfinished interlace borders we can tell how it was usually made up." This suggests that there was only one method, but looking at examples of Celtic knots, I suspect that several methods was used. This method would only work for close-weave knots in a simple border.

	Start by drawing dots in a diamond lattice pattern like this. You would normally draw this in black, but I'm making the dots red to contrast with the later lines.
	The dots should be diamond-shaped themselves. When you start drawing lines, draw them alongside the dotes rather than through the centre, otherwise this technique doesn't work.

The patterns below are from the Durham Gospel.

Simple plait with four strands

	Draw the top left diamond. Draw the top left and bottom right sides only. Keep inside the dots. This is the first strand.
	Draw a curved line at the top. This represents the strand bending round to go downwards.
	Draw the lower diamond the same, still keeping inside the dots. This will make the long line look wonky. This is the second strand.
	Draw the middle diamond. This time you draw the bottom left and top right sides. Keep within the dots! This is the third strand.
	Draw the top diamond and the top curve, as before. This continues the second strand.
	Draw a bottom curve and bottom diamond, to start the fourth curve.
	The middle diamond continues the first strand.
	The top diamond and the top curve diamond continues the fourth strand.
	Continue to complete the knot. I have changed the red dots to black so you can see the finished effect. There is a suggestion of a black background as well, to heighten the effect.

Twists with four strands

	This design starts the same as the last one.
	Continue the top curved line twice as far as last time. It's better to rub out the surplus dot altogether.
	Continue with the next two diamonds, the same as last time.
	Make a second shorter curve, below the top one.
	Make a long curve at the bottom, remembering to remove the surplus dot.
	Make a short curve above the bottom curve.
	Draw the second middle diamond.
	Draw the second middle diamond.
	Draw the two outer curves...
	... then the middle two diamonds.
	Here is the final result.

Entangled loops

	Draw a line straight down in the centre. This is the start of a new loop.
	Draw in a normal under and over from bottom left heading up and right, and curve it round.
	Make a short curve, bending round the top of the loop.
	Draw in another under and over next to the previous one, but this time bend it round with a long curve. removing the middle dot.
	Make a long curve at the bottom in the same way.
	Draw a line straight down in the centre. This is the end of the old loop.
	Repeat.
	The final pattern.

I don't think this can have been a design tool for Celtic knots, since it's quite easy to get lost (which is why I've broken it down into small steps). But if you designed a rough draft using a looser design technique (see below), then this method could be useful for transferring your pattern to the final copy. It would also be useful for bending patterns round curves, to fit inside letters, for example. It can be hard to predict the angles of the lines, but you could mark a pleasing regular pattern of staggered dots, then fit the pattern round it.

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