Celtic knots: adapting Infinity Loops to complex forms--Double Bowen Cross

Two samples, shown sideways

The knitted Celtic Knot Bowen cross was the subject of the last post. Today, the Double Bowen cross Infinity Loop takes center stage.  

If this is your first exposure to this series, Infinity Loops are a way to knit self-contained figures, like Celtic knots, then transform the knitting so there is no distortion in the cable arms or in the background fabric. After transformation, the figure lies smoothly. This is not true of ordinary knitted knots, which are generally distorted in the arms and the background. The introduction and first of the series is here. The second of the series (introducing shortcuts) is here.

Double Bowen cross,
shown as knitted
(upright)

DOUBLE BOWEN CROSS

Today's post is about analyzing complex forms like this one, to figure out transformation strategy. Does it make sense to use shortcuts or is it easier to transform the long way (half the figure)? If the long way, then we'll need to figure out how to transform long runs, including under a cable cross.

 As usual in this series, the pattern comes first, then the description of the transformation. Read through to the end before casting on, though, because choosing to use shortcuts requires as-you-go action. If transforming the long way, however, you first knit through the pattern without interruption and all the excitement comes afterwards.

Materials:

• scrap wool, worsted weight (5 sts/in) recommended
• knitting needles in size to suit wool
• crochet or latch hook to suit wool (latch hook works better imho)
• handful of bobby pins
• three 4-stitch scrap-yarn placeholders 
• tapestry needle for grafting (large eye, blunt tip)
• coil-less safety pin or other small stitch holder (long way transformation only)
• dental floss or strong sewing thread (not yarn) (shortcut transformation only)
• several 2-stitch scrap yarn placeholders (shortcut transformation only)
• optional: crewel needle (large eye, sharp point) for quick-grafting head-to-head cables (shortcut transformation only)

Charted Pattern.

Click here to see chart in a large free-floating window which can be printed. Choose portrait orientation. Scaling may be required. 

Above, printable chart with stitch directions at bottom. Below, written pattern. Both allow a margin of 4 purl stitches either side of the actual figure itself, neither includes OPTIONAL side borders. 

Written pattern.

The written pattern tracks the chart, adding one handy bit of info: stitch count. The third column in the written pattern shows the stitch count (st ct) and how you got there. For example, row 1 starts with 23 stitches, and then four stitches get added so the row ends with 27 stitches on the needle. For another example, row 37 begins with 35 stitches, but then eight stitches are removed in the course of knitting that row, leaving 27 stitches remaining. You could count this off the chart, but it is made explicit here. NOTE that the stitch count does not include any optional side borders you may choose to add. 

Geek note about stitch count: As discussed in greater detail in previous posts, with Infinity Loops, the number of background stitches never changes. All the increases are strictly for the cable arms, and do not change the fabric width. So, for garment shaping purposes (neck or armhole decreases, for example) ignore the stitch increases for the cables, and use only the background stitch count for figuring percentages.

row ↓	Note: instructions for cable stitches are on chart	st ct ↓
bottom	co 23 (plus whatever side border stitches you choose--sample adds 3 garter sts each side). Work in garter stitch to make a bottom border to desired height. Switch to reverse st st and work a few rows, keeping borders (if any) in pattern. End on a knit row, turn work so purl side is facing you.	23
1	p11, place first two loops of placeholder onto L needle and work 1 K st into each, p1, place last two loops of placeholder onto L needle and work 1 K st into each, p11.	23+4 = 27
2 (38)	in this and every even row, K the k’s and P the p’s.  In this particular row, k 11, p2, k1, p 2, k11	27
3 (39)	p10, R-p-T, p1, L-p-T, p10	27
4 (40)	k10, p2, k3, p2, k10	27
5 (41)	p9, R-p-T, p3, L-p-T, p9	27
6 (42)	k9, p2, k5, p2, k9	27
7  (43)	p9, k2, p5, k2, p9 (k the k’s, p the p’s)	27
8 (44)	k9, p2, k5, p2, k9	27
9 (45)	p9, L-p-T, p3, R-p-T, p9	27
10 (46)	k10, p2, k3, p2, k10	27
11 (47)	p10, L-p-T, p1, R-p-T, p10	27
12 (48)	k11, p2, k1, p 2,k 11	27
‡ 13	p6, place first two loops of placeholder onto L needle and work 1 K st into each, p1, place last two loops of placeholder onto L needle and work 1 K st into each, p4, work a LDC-5 on next 5 sts, p4, place first two loops of placeholder onto L needle and work 1 K st into each, p1, place last two loops of placeholder onto L needle and work 1 K st into each, p6	27+8 = 35
14 (26)	k6, *p2, k1, p2, k4, repeat from * one time more p2, k1, p2, k6	35
15 (27)	p5 ,* R-p-T, p1, L-p-T, p2, repeat from * one time more, R-p-T, p1, L-pT, p5	35
16 (28)	k5, *p2, k3, p2, k2, repeat from * one time more, p2, k3, p2, k5	35
17 (29)	p4,* R-p-T, p3, L-p-T, repeat from * two times more, p4	35
18 (30)	k4, p2, *k5, p4, repeat from * one time more, k5, p2, k4	35
‡19  (‡ 31)	p4, k2,* p5, RFC-4 repeat from * one time more, p5, k2, p4,	35
20 (32)	k4, p2, *k5, p4, repeat from * one time more, k5, p2, k4	35
21 (33)	p4, *L-p-T, p3, R-p-T, repeat from * two times more, p4	35
22( 34)	k5, *p2, k3, p2, k2, repeat from * one time more, p2, k3, p2, k5	35
23 (35)	p5, *L-p-T, p1, R-p-T, p2, repeat from * one time more, L-p-T, p1, R-p-T, p5	35
24 (36)	k6, *p2, k1, p2, k4, repeat from * one time more p2, k1, p2, k6	35
‡ 25	p6, *LFC-5, p4, repeat from* one time more, LFC-5, p6	35
OPTIONAL: repeat rows 14-25 TO ELONGATE figure (see chart). This is an OPTIONAL repeat which inserts a middle set of side loops into the pattern. (Note that none of the samples show this option.)
26-36	Same as 14-24 This is the NON-OPTIONAL repeat which makes the top set of side loops	35
‡ 37	p6, slip next 2 knit sts to bobby pin, p1, slip next 2 sts to bobby pin, p4, LFC-5, p4, slip next 2 knit sts to bobby pin, p1, slip next 2 sts to bobby pin, p6	35-8 =   27
38-48	same as 2-12. This is another NON-OPTIONAL repeat which makes the top loop	27
49	p11, slip next 2 knit sts to bobby pin, p1, slip next 2 sts to bobby pin, p11	27-4 = 23
top	continue for an additional few rows in reverse st st, then add any top border you choose.	23

‡ If you want to do the shortcut tricks, rows 13, 19, 25, 31 and 37 are of interest. This is easier to see on the charted pattern (where they are also marked). See also the shortcut map, below.

About the "repeats." 

--The NON-OPTIONAL repeat of rows 14-24 is the same as knitting rows 26-36. This is because both the BOTTOM SET and the TOP SET of side loops on the double Bowen Cross are knit identically for these particular rows. 

--The OPTIONAL repeat of rows 14-25 ELONGATES the figure meaning you may choose to repeat row 14-25 in order to insert an EXTRA MIDDLE SET of side loops BEFORE working the repeat of rows 14-24 for the TOP SET of side loops. None of the samples were worked with this option.

--There is also a NON-OPTIONAL repeat of rows 38-48 which are identical to rows 2-12, meaning the TOP LOOP and the BOTTOM LOOP are the knit the same over these particular rows. 

Bottom line. Three different repeats: one optional, two not. 

_________________________________________

Begin at the beginning: map

Click here to enlarge

The first thing when you set out to make an Infinity Loop Celtic knot is to sketch a map of which way the stitches run, based on a picture of the finished motif. See, you know that to knit a Celtic knot, the cable arms must split tail-to-tail at the bottom (red dots) and meet head-to-head at the top (green dots), You also know that the stitches go upwards, building the cable in horizontal slices, row by row. The picture must also show which crosses are over, and which under. So that's really all the info you need for the sketch.  Above left, the Double Bowen stitch direction map. 

The gray arrows show the upward direction of the stitches after knitting but before transformation. The red- and green-dot discontinuities are the target we want to eliminate via transforming stitch direction. Once transformed, the stitches (or all the ones we can see anyway) will all be laying in the same direction (no head-to-head or tail-to-tail meet-ups evident). Plus, there will be no background distortion either.

Transformation alternatives

With stitch direction map in hand, the next step is to figure out the transformation alternatives. The alternative easiest to conceptualize is generally the "long way," where half the figure gets transformed--as in the simple rings which started this series. However, we have at our disposal various shortcuts, as shown in the immediately previous post. So that's the other alternative, and we'll look at that first.

Shortcuts

As with the simple Bowen Cross post shortcuts on a smallish form like today's don't always make sense. This is because shortcuts exist to let you skip transforming diagonal-line elements (and, incidentally, crosses in those elements). In scrunched up figures, there aren't that many linear elements, proportionally speaking. However, if this double Bowen Cross were more stretched out so the loops were a lesser proportion of the figure than here, then shortcuts would make a lot of sense. This complex form today presents so you can figure out for yourself how to map shortcuts to determine whether they are going to make sense for your motif.

The shortcuts were laid out in (possibly exhaustive) detail in the Bowen Cross Celtic Knot post. But, if you don't want to have to flip back and forth between posts, there are links to the shortcuts in printable format below. 

These shortcuts are:

• Transforming tail-to-tail meetings at the bottom of a loop via a placeholder, which has the effect of moving the discontinuity along the beneath cable arm, to hide it under the over-crossing cable arm at the cable cross itself.  (Printable Google doc link to the placeholder trick.) 
• Using a dental floss to temporarily hold the under-crossing stitches of the beneath cable arm. When the other half of that beneath arm is transformed, the two halves meet head-to-head at the cross, under the over-crossing cable arm. Then, the head-to-head stitches of the beneath cable arm are stitched or grafted together. During transformation the floss acts as a barrier preventing the stitches from running out too far and holds them until they are ready to graft. (Printable Google doc to the floss maneuver.)

To figure out for yourself which kind of shortcut where, the original stitch direction map (above) needs more detail. The stitches to be transformed have to be sketched in as you have to figure out which cross-overs are to hide the discontinuities. In this matter, consult Occam's razor: the nearest cross with the least transformation is the one to use. 

On the Double Bowen cross, if we were to use shortcuts to move and hide every head-to-head or tail-to-tail meeting, the situation would be as illustrated in the below sketch map of the "all shortcut version." With shortcuts, there would be fewer stitches to transform, specifically, no transformation of diagonal traveling cables. (White on the map below shows stitches which remain as they were knitted.) The trade-off for not having to transform the diagonal arms is three head-to-head grafts resulting from the floss trick (purple stars on the diagram), and three placeholder tricks (tail to tail meet-ups--gray pentagons). The number of right-and left-arm dominant transformations would be equal. The yellow stars (three ordinary head-to-tail grafts at loop bottoms) remain constant whether using shortcuts or not.

On this sketch map, the transformations to the nearest cross are shown in orange. Once transformed, the stitches in the orange sectors would run the opposite directions to how they were knitted. The type of meetings (head-to-head, or tail-to-tail) brought on by the transformations are shown with blue arrows. Again, Occam's razor tells us to transform the shortest distance possible, with the type of meeting being a mere consequence.  

Once the map is sketched out and the decision taken as to which loops to transform, and in which direction, the next step is to  match the map to the charted or written directions. You are looking to figure out just exactly which rows contain the crosses designated on the sketch map. In this post, I have made it easy for you: the chart highlights which crosses are of interest in light green, and the written directions have a double-plus signal (‡) for rows of interest.

(1) On the double knot pattern (as on the single Bowen knot) row 13 hosts the LFC-5 cross which closed off the lower loop, so that's where the placeholder trick would be worked. On the shortcut map, this tail-to-tail meeting is marked with a gray hexagon.

(2) The next row of interest would be row 19, featuring two RFC-4's. Under the rightmost, we can engineer a tail-to-tail transformation, hiding it under the arm of a rightward traveling cable at the RFC-4 crossing. On the shortcut map, this (like all tail-to-tail meetings) is also marked with a gray pentagon. Specifically, we will work a left arm transformation of the lower right side loop, shown by the orange half-loop.  

This is a little different than illustrated on the single Bowen cross and the PDF, because these are four-stitch crosses (no center purl) and because they are right crosses. Nonetheless, the principle of standing the stitches in chosen column on their heads using a placeholder is the same as described, just with no center purl spacer. 

The next row of interest would be row 25. This is the midpoint of the figure, and features two LFC-5's. 

• (3) The rightmost cable cross on row 25 hosts a head-to-head meeting using the dental floss trick (purple star on shortcut map). 
• (4) The leftmost cable cross on row 25 hosts a tail-to-tail meeting via the placeholder trick (gray hexagon on shortcut map).  

(5) Next up is row 31. Like row 19, it features two RFC-4's. The upper arm of the leftmost provides a hiding spot for a shortcut- a head-to-head meeting (floss trick-purple star on shortcut map). Like row 19, the shortcut is worked on 4 stitches--no purl spacer.  

(6) The final shortcut takes place at the base of the top loop, row 37 which hosts the topmost LFC-5. The upper arm will hide the lower arm meeting head-to-head via improvised graft. Like the rightmost loop on row 25 (3) and the leftmost loop on 31 (5), this too will be worked with the help of the dental floss trick (purple star on shortcut map).

These as-you go shortcuts do slow down the knitting. On rows 13, 19, 25, 31 and 37, you have to stop and fool around with placeholders or dental floss. However, once you get the hang of them, they go faster. Time is lost in monkeying around is (potentially, anyway!) made up in the quicker transformations. However, this approach takes more attention to knit, because the shortcuts are knit as-you-go.

Finishing: After the transformations (strandifying and changing direction) you must dupli-graft at the yellow stars and head-to-head graft at the purple stars. Recollect that the head-to-head graft can be as simple as drawing a length of yarn through all four stitches before cutting loose the dental floss, then burying the ends in the fabric. 

Long way transformation

To transform the figure the long way (no shortcuts) you'd follow the pattern straight through. There would be significantly more transformation: the same six partial loops as the shortcuts PLUS three additional diagonal-line traveling cables (and their crosses! more, below). As a trade-off, there'd be no fooling around Occam's razor, nor with floss or placeholders. And you'd eliminate those clandestine meetings between opposite-direction cable arms in the darkness under a bridge on the fabric back, the gray hexagons and the purple stars. Not that these are bad things, you understand. Even perfectly lovely cables swing that way sometimes.

One thing you would not avoid by choosing the long way transformation is drawing a map--you still have to do that, and here's why. As you see, transforming the long way has two options. Both end up with the same number of stitches transformed, but one version is significantly easier because you can actually see what you're doing more of the time. Just as with repairing a miscrossed cable by laddering it out then re-latching it back up, transforming a cross-OVER is easier than a cross-UNDER.

Click here to enlarge

Once again, it's the map to the rescue. The transformation map you would draw for a long-way transformation shows that on this particular figure, right-arm dominant transformation would result in fewer "under" cross transformations (three), while left-arm dominant transformation would have twice the number (six). This is not true of every complex Celtic knot: you always have to draw up a map to figure whether left- or right-arm dominant transformation has the fewer "under" crosses. 

Transforming an "under"

Shortcuts have one major advantage over doing things the long way: with shortcuts, there are no transformations of a cross in a cable arm, because (again) the diagonal cable arms remain as knitted, meaning crosses and all. So, if you choose to work the long way, there will come a time when you do have to transform around the cross on a cable arm. 

These crosses come in two flavors: "overs" and "unders." Transforming "overs" is simply no different than regular transformation. The stitches doing the cross-over are no different than any other stitches in the column, and are transformed the same way, it being immaterial whether another cable arm is passing under those particular stitches. 

This is not true of "unders," which are a bit more complicated. Here is how to transform an "under" in 5 illustrated steps.

1. Transform the outer column in the usual way, all the way down to the cable cross. The bottom loop of the outer column being transformed is colored blue, the stitch below it, red. The red stitch is the one which actually crosses behind the cable. I put it on a coiless safety pin and pulled it forward, just so you could see it peeking out from under the upper cable arm. In the ordinary course of things, the red stitch would NOT be visible. It would simply be waiting on the back of the fabric; not pulled forward, not put on a safety pin. 

Geek note: If you were working the dental floss trick, this red stitch would be the one the floss would have been inserted into as a barrier against latching down too far. Since we're working a long-way transformation, there's no reason to barricade the arm. We are going all! the! way! down! heck! yeah! 

2. Not illustrated. The head of the blue stitch is pulled to the back using the hook. Then, the fabric is flipped. Next, the red stitch is strandified, then re-formed into a stitch by being pulled through the blue loop. (Of course, in this particular case, the red stitch was taken off its safety pin to strandify it, but usually, the red stitch would just be sitting there waiting on the back, with no safety pin through it)

3. This is a view of the fabric back after step 2. Due to the red stitch having been strandified and re-formed into a stitch, the red strand has been pulled through the blue and is now the lead stitch in its column. The red stitch is now to be put on a coil-less safety pin or a bobby pin as a holder in real life. In other words, in this step, the pin isn't just for demonstration purposes unlike in step 1. In this step, you actually DO want to put the red stitch on a safety pin or other holder. As you'll see in the step 5, having the red stitch on a holder will help maneuver the stitch from the back to the front as part of the "undercrossing" being transformed. The green hole shown at picture 4 is not visible in this view, because the red stitch is flopped over it. 

4. This is a view of the fabric front. The stitch which was below the red stitch is colored purple. It is the first stitch past the cable crossing in the same column, the first stitch of its loop which sees daylight. It was waiting on the fabric front, and has now been put on a bobby pin for safekeeping. In this photo, I have stretched the fabric so you can now see the hole (green arrow). This hole is above the purple stitch, and was hidden by the red stitch in illustration 3.  Therefore, above the hole, at the back of the fabric where you cannot see it in this picture, the red stitch waits on its holder, as shown in picture 3.

5. Using the pin as a handle, the red stitch has been pulled through the hole marked with the green arrow. This fills the hole so it no longer exists. 

The next step would be to slip the red stitch from its safety pin holder back onto the crochet or latch hook, then remove the purple stitch from the bobby pin, then strandify and transform the purple stitch. After this, the remainder of the column would be transformed down to the bottom of the cable arm. The inner column will be transformed the same way when its turn comes to do the "undercross." 

Here you see a comparison of the cable cross before and after transformation of both the outer and inner columns. The gray V's show that transformation reverses the stitch direction (which is what eliminates the green- and red-dot discontinuities). The blue and purple stitches remain in the same position, just turned on their heads. The red stitches (which have also been stood on their heads) are not visible: they are on the fabric back. The green hole no longer exists, having been plugged when the red stitches (invisible on the fabric back) re-connected with the purple during transformation. 

Transforming an "under" resembles correcting a miscrossed cable by letting out a ladder and latching it up again, but without turning the "under" into an over, and with the added feature of strandifying and turning the stitches upside-down as they are transformed. 

Finishing 

Finishing involves "dupli-grafting" all the loose cable ends together, head-to-tail, shown on the "long-way" charts as yellow stars. 

Decision time

The shortcuts with placeholder and floss save you from having to transform the diagonal-line elements in a Celtic knot. The more or longer the linear elements, the more the shortcuts save you from more transforming. In this particular case, if you use the shortcuts, all the diagonal line elements will remain as originally knit (i.e.: will not need to be transformed). On the downside, less transformation comes at the cost of more grafting and more general fooling around. On the upside, shortcut transformations prevent your ever having to work an "under" (or, for that matter, an "over"). 

The bottom line is that, in transforming complex knots, the balance lies between fooling around with placeholders and dental floss to work shortcuts, or choosing to transform diagonal-line traveling cables (with at least some "unders") which otherwise would not need to be transformed. Sketching a map is your invaluable guide.

I must say that when I first invented the shortcuts, they seemed so complicated that I doubted I would want to use them if it could be avoided. But, with enough practice, the shortcuts do eventually become faster to work. And, after you've transformed enough linear elements that really could have been left alone, and when you realize that with shortcuts, there are never any "unders" to transform, why, you do become more friendly to them! 

The transformed double Bowen cross

Further info for adapting Celtic Knot patterns to Infinity Loops

To adapt a Celtic knot pattern to the infinity loop method, here's more info you might need. 

All the infinity loops in this series, already published and to come (rings, Bowen cross, Double Bowen cross, hearts/lobed forms, spirals) are worked on two-stitch wide cable arms, and all the loops are started off with a purl spacer. That makes five stitches per loop: 

• four stitches at loop base to be created onto scrap-yarn placeholders, then grafted away at loop-top 
• one stitch--the purl spacer--requisitioned from the background fabric at loop base, then returned to the background fabric at loop-top. 

When adapting 2-stitch wide cable arm patterns written elsewhere, you don't have to add for the purl spacer, because it is returned to the background fabric at the end of the motif. However, if you're adapting a pattern written to start on 4 stitches, you do have to re-center the figure on the central purl spacer--5 stitches. 

 Another thing to figure is to subtract for stitches used as the base for a loop or ring (usually a single stitch giving rise to a 3-in-1 or 5-in-1 increase, but watch if two stitches aren't used as the increase base).  An m1 (make one) need not be accounted for however, because the scrap-yarn placeholder takes its place. 

If your pattern features interaction of cable arms arising from different bases, like two Bowen Crosses interacting, for example, then, in order for the cable arms from disparate motifs to meet up correctly, you'd actually have to chart the entire pattern. This is because the differing stitch count between Infinity Loops and the way most Celtic knots are started might have the arms from one motif missing a meetup with those from another by a stitch or two. 

Three-stitch wide cable arms  I haven't shown these because, as they go around tight curves, the inner column of three gets tightly squeezed, while the outer column gets more stretched. If three-stitch wide cable arms are a must-have, adjust for these different radiuses (radii?) by knitting (and subsequently, transforming) a stitch or two fewer in the inner column, along the tightest part of the curve. In other words, slip a stitch when knitting on the inside of a tight curve, adjust the tension accordingly, and then remind yourself not to pick up the slipped strand by accident when transforming. I leave this sort of differential experimentation in your capable hands. 

Side loops As mentioned in the last post, a certain kind of side loops need no shortcuts; not head-to-head, not tail-to-tail. This makes this sort of side loop pattern easy to convert from ordinary Celtic knot pattern-writing to knitting them Infinity Loop style. Specifically, as illustrated below, where the side loops have only ONE crossing (rather than two, as in the Double Bowen Cross), then shortcuts do not apply.

• The lack of shortcuts is because stitches of the diagonals in one-cross side loops are naturally continuous to the adjoining left or right side of the loop on which they enter and leave. It is only the stitches in the OTHER arm of the loop (colored orange, above) which lie opposite-wise and need transformation. 
• A free-standing arm is easy to transform at top and dupli-graft at bottom, just like with the simple rings, with no shortcuts needed. 
• Therefore, with one-cross side loops, only a small amount of transformation is required: one arm of the loop, either right or left dominant, as per the diagram. This is just as with the simple rings, and the diagonals remain as knitted.  

For a real life example of a one-cross side-loop pattern, have a look at this sweater. (And, you know...that's a free pattern!) 

• If those outer loops were started on on a scrap yarn holder instead of on M1's, and 
• if the increase in the middle stitch was ignored and that stitch instead turned into the purl spacer, and 
• if the arm was then transformed on the outer half of each side loop, and then dupli-grafted shut, 

then the rest of this lovely sweater could be knit just as written, and you would have eliminated the distortion in loops or background stitches. 

BONUS IDEA for using SWATCHES--eyeglasses case

After knitting two identical samples (the darker one with shortcuts, the lighter one with transitions the long way) I slip-stitched them together on three edges, and on the fourth, put a zipper in with my no-sew zipper trick. Before inserting the lining, I sewed it onto the zipper tape. Result: a Double Bowen Knot eyeglasses case. (Details  on Ravelry.)

Next time, hearts and other lobed forms. Til then, good knitting

--TK

Questions? Feedback? Talk to me about this post on TECHknitting Ravelry forum.

This is part three in a series. The other parts (so far)

Infinity loops--Intro. A new trick to improve Celtic knots & continuous cables, Part 1

Celtic knots, improved: Bowen cross and introducing shortcuts. Infinity Loops part 2