The layout of Guitar lace

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When I posted Guitar lace last week, I said that there was something unusual about the layout. I’m going to walk through what I meant by that. First, I’m going to explain what happened in the layout. Second, since I’m going into a lot of detail anyway, I’ll explain how I encoded the word.

The layout process

A rectangular grid which is four squares high and ten wide, with a random-seeming pattern of circles in twelve of the squares.
Figure 1: click to enlarge

Most of my encoded lace starts with a grid like figure 1. Each of the circles represents one of the numbers in Guitar turned into numbers. (See the end of this post for more information.) I was pleased to see so many single yarnovers on this starting chart, but there’s a hitch.

As described in text.
Figure 2: click to enlarge

I usually like to mirror my charts before I start adding decreases and swatching my rough drafts of the final lace. I copied and pasted Figure 1, mirrored it, and placed it right next to the original to make Figure 2.

I like the look of this, but suddenly there’s a lot of double yarnovers. Because so many of my stitch patterns are complex in various ways, I like to make them as simple as possible, ideally without double yarnovers. Fortunately, there’s a standard layout trick that might work in this situation.

As described in text.
Figure 3: Click chart to enlarge

In Figure 3, I decided to “drop” the copied & mirrored version of the chart halfway. This means that I saw that the chart is four rows high, and I slid that part downward by two rows. Note that I could have dropped the other side instead; it doesn’t matter which.

This technique is called glide reflection when discussing mathematical symmetry, and is a variant of what’s called a half-drop by many surface pattern designers. When doing a half-drop in knitting design (as opposed to some other fraction of a drop), this only works when there’s an even number of right side rows.

When I got to this stage, I thought it looked promising, so I went on.

As described in text.
Figure 4: click to enlarge

I need my lace chart to be a rectangle, not an odd zigzag, so in Figure 4, I’ve started to fix this. The part that’s sticking down below the main rectangle on the left is the same size as the empty space at the top, so I’ve cut off the part that’s sticking downward. Next, I will put it in the empty space at the top of that side.

As described in text.
Figure 5: click to enlarge

Figure 5 is the final yarnover layout. It is now a rectangular grid with a bunch of circles on it in a pattern. Each circle has a blank square to either side, which means there are no double yarnovers. I looked at it when I was planning the stitch pattern, and was pleased that it looked as if it would also work without any double decreases. (In fact, that was the case.)

But then I noticed something interesting!

Figure 6: click to enlarge

The two tiny diagonals on each side of Figure 6 are doing what I expected: the one on the left is in the bottom half of the chart; the one on the right is at the top; and finally, they lean in opposite directions because of having been mirrored.

But if you look at all the other yarnovers in each half, they are identical! This isn’t a usual result for this kind of layout, but I think it’s fascinating regardless. It turns out that the left side of my original Figure 1, before I’d done any copying and pasting, was already a mirrored half-drop/glide reflection of the right side. This wasn’t on purpose, but was an accidental result of how the code was laid out on the rectangle. Speaking of which, the next section shows how I made that rectangle to begin with.

Encoding the word Guitar

The first stages of encoding a word for me are to turn its letters into nine sets of numbers. The set I ended up with for this chart used base 8, and the numbers for guitar in base 8 are 07 25 11 24 01 22. I replaced 0 with a black square, 7 with seven white squares followed by a black square, 2 with two white squares followed by a single black square, and so on.

A picture of a line of emoji as follows: one black, seven white and one black, two white and one black, five white and one black, one white and one black, one white and one black, two white and one black, four white and one black, one black, one white and one black, two white and one black, two white and one black.
Figure 7: click to enlarge

Figure 7 shows the final result. This is fairly boring as a lace design, though it would work. You’d end up with vertical stripes of yarnovers and stockinette.

A rectangle made of black and grey squares that almost matches the arrangement from Figure one.
Figure 8: click to enlarge

I like to put in line breaks at various points to make different size rectangles with different arrangements of squares. The one in Figure 8 has the line breaks after ten squares. This looked almost possible, but the two main clusters on each side didn’t look right for lace to me, so I flipped the whole thing vertically.

Figure eight has been flipped vertically to make figure nine, which has the same arrangement as figure one.
Figure 9: Click to enlarge

After flipping Figure 8 vertically, I got Figure 9. Now it looks better for lace to me. And indeed, this is the arrangement I ended up using. I converted it to a chart with yarnovers as seen at the top of this post, made the layout manipulation shown there, and then I added in the yarnovers and 1/1 cables that made it into Guitar lace.