Wednesday, October 22, 2014

Diagrams for Knots - Examplified by Two Loop Spanish Mat

The Spanish Mat or whatever it is called in English is a knot, which can be used for doormats in larger format or for hot pads in smaller format.

It differs notably from the Turkish knot which is more gridlike and only bends on the outside of the knot. For the Spanish Mat you start with on to five loops which remain such. And only loop or central loop crossing must contain at the end two strands crossing along one diagonal and one along the other one, and as the strand does that it also bends on the outside.

Let us say you start out with two loops, these point upward, the strand crosses itself in the same direction below. Then you make the central loop crossing so the strands at its lower end cross the other way. THEN you fill in the knot from the outside, so that in the end the central loop crossing has one diagonal one strand through, opposite diagonal two strands through. And this is where it gets complicated to describe in words without making a diagram. So, instead of getting on, why don't I tell you about the diagram making? You draw after my instructions, and then make the knot according to the drawing.

To start the drawing you assume the two loops have already crosses, so what you draw will be one left loop and one right loop with one almondshaped space in the middle. Draw them in one ductus of the pen.

Then concentrate on that central space. Draw two parallel lines low left to up right and one line crossing both within the loop (it can be bent so it's vertical in the middle, like a backward oblong s) upper left to lower right.

Then continue the lines to the outside of the two loops, under their upper crossing obviously and over their lower two crossings. Then connect the points where lines from centre get out and include the points where the loops get out below, if you see what I mean. If you don't see what I mean, think it through.

To the left the sole line through centre is prolonged so at the outside it connects to the lower parallel line from centre. The upper parallel line can be conneced to the start of the rope - the point where you started to put your pen. Or they can be marked off both as loose ends, since they are beginning and end of knot, but they can be connected and usually should, as with any flat knot of decorative kind.

To the right the lower parallel line from centre bends down to meet where the two original loops ended. Also to the right, the upper parallel line from centre bends down to meet the sole line from centre.

Both left and right, the connections imply a new place of crossing strands outside the original two loops.

Now you will fill in ALL the crossings of strands, whichever is above or below. When I draw, I mark the below strand by pretending two ends of strands get around the parallel lines of upper strand. Every strands everywhere in the know alternates above and below, above and below at the crossings, note well: when the knot is ready.

And after this, you can either try to hold the one diagram above where you are handling the rope, or you can make a series of diagrams showing the different stages.

Start from complete knot (and imitate the same series of diagrams in reverse order).

Next diagram the upper parallel line is no longer there - since it is the end of the knot, this strand is now taken away. Where any other strand went under it, draw instead a connected strand. The latter end of the knot should now be on the right side, and the middle loop crossing should have only one strand per diagonal. Take your time to make the crossings detail of the diagram right and corresponding to where exactly same crossings (check they are the same!) shall be in the last diagram (or are already in the first one you drew). If you have done it correctly, the second to last diagram should have a kind of pathway for the last strand, consisting of strands the cross twice below or twice above around where the last strand will cross above or below it.

I will enumerate these double crossings from upper right to lower left, I will suppose you got all crossing same way as I did, if you got them reverse way, reverse the directions (make double belows into double aboves), and what I had at the lowest parts of the diagram was loops crossing themselves the up-left - down-right lines above the low-left - up-right ones:
  • First, a double below belonging to the right loop at its upper end, between the right hand secondary loop from "previous" (not yet drawn) and upper bend of right loop.
  • Then, a double above, belonging to upper left loop, between upper right loop and the secondary line from previous.
  • Third, a double below, belonging to the diagonal through loop crossing that goes up-left to low-right, from the left part of the right loop to the crossing line.
  • Fourth, a double above, belonging to the left part of the right loop, from the diagonal up-left - down-right to the lower (in this diagram sole) diagonal of the low-left - up-right ones.
  • Fifth, a double below, belonging to the left part of the left loop between two parts of the left hand secondary loop from previous, and
  • Sixth, a double above, belonging to left hand secondary loop from previous between the low point above left part of left loop where previous ended to above where the additions of this started, also crossing left part of left original loop.

Then you take away the diagonal up-left to down right, you get another diagram, which is easier to describe from its starting point where the right hand loop ended at lower right, I presume you took loops ending at up-left - down-right above low-left - up-right on the lower side. As you take the end to upper right part of right loop, again you cross above, then two below under the crossing of the loops, then one above over lower left part of left loop. After that, you have the diagram in chords.

After that - now realising second to last diagram in chord - the end gets above upper left part of left loop, under up-mid left part of right loop, again under the previously made diagonal, above low-mid right part of left loop, below low right part of right loop, above original secondary loop.

AND from there you get the end upwards to get through the gateways of double aboves and double belows already described.

Now, getting beyond diagrams, the end of the knot should start again at the beginning beside the original beginning, and now it is just below-above-below-above all the way, sometimes crossing chords still single, sometimes crossing chords already doubled. At the end of the doubling, one can leave it there or triple, same method.

If one needs to even things out, by narrowing, and to get sufficient chord for the full tripling (or doubling) one does so by pushing and pulling so you get more and more of a loop until you get to the free end. Finally, the ends where doubling starts and ends are hidden under one of the other strands, like the one where the left hand loop gets down over itself. And they are firmly attached - sewing, gluing, etc.

Hans Georg Lundahl
Bpi, Georges Pompidou
St Mary Salomé

PS: I regarded a picture from Sweden of the knot. There is a variety which is popular, where the middle is traversed by three parallel horizontals instead of by two diagonals crossed by one opposite diagonal. I drew the diagram.

As the most popular variety starts with three loops, that is how I drew it.

Upmost and nethermost parallel horizontal belong to a loop added to original ones (thus, on my diagram as often enough, a fourth loop) and woven all way through, above-below etc. but obviously both strands of it above same and below same, till it passes the leftmost loop above the beginning end of the knot.

Then the midmost horizontal strand is added by taking the end of the strand and passing it between the strands of the horizontal loop, weaving now above where the surrounding strands are below the loop strands, and below where the surrounding strands are above it, until it passes through the leftmost bight of the loop.

This gives a hint of an alternative way - and an easier one - of making the variety I take to be more original. After original loops, the end only gets woven in towards the middle, then one makes a loop by crossing and gets that loop woven further left, then one gets the end of the srand woven right, take a bight, turn it left through the gates above described.

Added Day of St Raphaël, 24-X-2014/HGL

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