About socks and computers

What do socks and computers have to do with each other?
Well, I’d like to show you a pair of socks and an email I’ve received.

I never managed to knit socks or mittens, I just never got used to the fiddling with 5 needles, their movement annoys me, my thread gets caught between the needles… But my mum seems to be the best sock knitter in the world. I only wear socks knitted by her. She’s a quick knitter anyhow, and she does socks so smoothly and quickly that you can’t see what she’s doing – they just seem to grow and grow and be finished in no time at all.

As I always thought my patterns would be nice in socks, I asked her to do a pair for me, just to see. I sent her a few pattern charts, and she did. First she said she had to concentrate a lot, she mixed up the rows, but meanwhile she has done many pairs and loves them. She’s going to sell them at their Christmas fair for charity, and she says she can now watch TV, whilst knitting the patterned socks. Here are two pictures of the pair she sent me.

Here I've turned one sock inside out to show the other side's pattern.

Many thanks to my mum! Myself hasn’t managed finishing a project in a while, since there are always so many new patterns waiting to be tested.

Remember, I’ve said here that a computer program that could simulate these patterns would be handy, but I was doubtful a computer could do this? Afterwards I found the article “Simulating Knitted Cloth at the Yarn Level” by Jonathan M. Kaldor, Doug L. James and Steve Marschner of Cornell University, who are actually working on this. The article explains what the problems are in simulating knitted fabrics, and how they successfully simulated stockinet, garter stitch and rib fabrics. Mind you, I do not understand the complex calculations that are necessary for this.

I’ve contacted them and asked whether computer simulation of the patterns would be possible. Well, I was still doubtful. “I suppose I'm not wrong that it would be a huge challenge to simulate these structures on computer?” I asked in my email.

I was very pleased to receive an answer back from Jonathan Kaldor, in which he said:

“Regarding simulating the behavior of more complex knit structures and the feasibility of doing so on a computer: I am more optimistic that it is a tractable problem. What our paper demonstrated was that a.) its possible to simulate yarn abstractions directly and be able to scale up to large pieces of fabric, and, more importantly from the perspective of your question, b.) quite a bit of the behavior of knit fabrics follows from just the pattern of stitches and how the yarn is interlaced. As an example of (b), one of our experiments involved holding the simulated yarn parameters constant and only changing the pattern of knit and purls, resulting in the distinctive garter / stockinette / rib knit appearance in our simulated results. There's still more to do to account for all of the possible sources of variance between two knit samples, including several of the ones you mentioned in your post, of course. However, I think the computer graphics / textile community will eventually be able to predict with reasonable accuracy what geometric/color pattern you would expect to see in the final product given one of your stitch and color patterns as input. We're not quite there yet, of course, but hopefully we'll have some more interesting results in that direction soon.

So, it will be possible in the future! Such software would definitely be helpful!

Jonathan Kaldor and his colleagues in their article describe how they have also simulated the behaviour of a sock - well, a leg warmer it was. This is described as follows:

"Figure 10 shows a 44 x96 knitted leg warmer being pulled over a
foot. Because we simulate the yarn contacts directly, we are able
to resolve the complicated stretching pattern as it slides over the
heel. Due to the size of the model, there are over 100 billion pairs
of quadrature points that potentially need to be evaluated for the
collision integral at each step. Using our bounding box hierarchy,
however, we are able to quickly find the 3.7 million pairs on average
that are in contact, using only 12 million bounding box traversals
and 12 million sphere-sphere evaluations on average." (p 8)

Isn’t it amazing that something so simple as knitting seems to be a challenge for computer technology, but that in the end, when the complicated work to develop the software is done, it can in turn be helpful for knitters?

A Stitch in Time

Yesterday we had a lovely sunny autumn day at last, after summer hadn’t arrived this year. It was like waiting for Godot. Like a piece in time is missing. Was it not just late spring, also long awaited, when the hawthorn blossomed, blessed with the few dry and sunny weeks of this year, as were the aquilegias? When the Lady’s mantles just emerged. When we had strawberries from the garden with ice cream.

Now all is wilting, drying, dying back - earlier this year, it seems, than usual - having been smashed so frequently by rain and wind. Strawberry time was good and happy. Mohrle was still here, our blind black cat. She loved to lick the empty ice cream bowls. She also loved egg yolk, when we had boiled eggs – served to her in the tops of the eggshells. She left us nearly three weeks ago, forever, after she had been a loved and loving companion for 13 years. She had only become blind about 1 ½ years ago and coped well.

Where I sat yesterday to write this post was her last favourite place in our mutual world. She used to have favourite places for periods of time. In the last few months every morning she insisted to go out to spend most of the day on the garden table, under the parasol we had bought in Lidl, initially to protect her from the sun at strawberry time. It turned out to be her umbrella sheltering her from the rain later. Now she is in her final resting place. She is missed. I will forever think of her when we’ll have eggs or ice cream, and especially at strawberry time.

Not when I’ll see the rhododendron flowering that grows down along the road, because Mohrle didn’t go that far anymore when she was blind. But rhododendron had the same good time as the strawberries and the hawthorn this year, other than the roses. Quite every year a wet period sets in when the roses would come into full bloom, and quite commonly that wet period lasts, and not their flowers. They hardly ever reach their full potential of beauty here.

I remember walking down with my neighbour at rhododendron time, and as nearly every year, she told me how fond the late old lady who had lived in our house, was of it. I said to her: If we think about it… We see nature’s seasonal signs and patterns, if we are lucky, only 70/80 times in our live… Maybe we should be more aware of this to value nature, and life indeed.

Seventy pattern repeats, that’s not much if you come to think of it.

I guess this post turns out to be about time and patterns. I’ve noticed that I can’t go on to always upload several colour sequences of one structure. It is technically time consuming, and it doesn’t go smoothly with real time, because in real time I’m always already at other structures.

I wish to thank some nice people in the “geek craft” group on ravelry, who have done some maths for me. I had asked for the total possible amount of different combinations of Ks, Ps, Xs and Os that go into a 4x4 grid, where every row or column contains at least 1 P or K. Their complicated calculations resulted in this number: 221238784. They agreed that only 1/16 of that is relevant for knitting because the grid = chart is repeated in knitting, and that makes 15 of 16 charts redundant. (ABCD repeated horizontally or vertically gives the same result as BCDA, CDAB, DCAB) That still leaves 13827424 combinations, possible different structures. And that’s only for the 4x4 grid. They said they don’t attempt larger grids, as the numbers would be “intimidating”. The various possible colour sequences are not considered in this.

So, there is a lot to explore, and I want to try different structures and do a range of colour sequences only sometimes. That means I’ll put up only a single pattern a day in the future, instead of giving nine colour sequences for one structure. It may also be less confusing for readers. I’ve shown how colour sequences do change the resulting pattern, and there is room for readers to experiment. The proverb fits quite neatly here: A stitch in time makes nine.

In a year’s time, if I really manage to upload a stitch a day there will be one for every day. That would give the possibility to use them as “birthday patterns” in birthday presents, for example.

I’ll start with a stitch a day tomorrow. It’s the birthday of a special person. Today I have these patterns for you. They are very easy to knit, but quite charming for that, I think. The resulting fabric is rather elastic, especially vertically. (The order is 1A, 1B, 2A,2B)

Wool and Cotton

Up to now I mainly did my patterns in wool, or wool mixes. I wouldn’t prefer to use the mixes in projects, but for knitting the swatches I admit I rely on cheaper yarns.
I’ve done some in cotton as well now, and wish to mention the different effects you get. Compare the swatches in the picture above. The two to the left were knitted with a wool mix, the right one is pure cotton.

Whilst both show irregularities in the small parts of the patterns, this is much more noticeable in the cotton swatches. I suppose this has to do with the fact that cotton is much less elastic than wool. To me it seems that the interaction with neighbouring stitches and rows does not go as far as it does with wool. I also find that with cotton the yarn itself shows more and doesn’t blend in that well with the pattern as wool does. Roxana Bartlett in her book Slip-Stitch Knitting says that cotton yarns have no halo to soften shapes.

So in choosing yarn for these patterns this has to be kept in mind. Wool is probably easier for a start. The geometry of the pattern is more apparent with it. The irregularities coming with cotton on the other hand give the fabric a more lively appearance. If we think of the elements that constitute patterns in nature, we notice how each individual element is different from the others.

In knitting it all depends on what one intends to achieve.

A bit about the exploration process

I discovered the patterns in the swatch below today. I thought I put it up whilst I’m at it. I have only done 4 colour sequences so far, but I am amazed by the fairly different texture and patterns the structure yields on the two sides of the fabric.

When I knit the swatches I never know what the results will be beforehand. It can’t be foreseen. A computer programme that could create the patterns from the charts would be handy, but I consider it impossible. How could a computer simulate the behaviour of the threads, the interaction of the stitches, and colours, the tensions in these fabrics? By the way, if someone knows of any scientific/theoretical description or explanation of the knitted fabric structure for common stitch patterns or even stocking stitch I’d be grateful to get a link to it.

I tend to describe for myself what I’ve developed meanwhile as a kind of grammar. I have the four elements K, P, X and O (or A, B, C, D privately) and put them on paper in basic arrangements. A few restrictions come from the knitting technique itself; such as you can’t slip all stitches in a row, nor slip a stitch vertically all the time.
These basic arrangements could be called morphemes. These then undergo further transformations, much based on symmetries really. There are many possible transformations, and what I get sometimes opens up the possibility of new transformations on earlier ones. And added to this for each resulting structure are the various possible colour sequences. Sounds a bit technical, I know. But is also for me a kind of an evolutionary process. Sometimes my mind boggles, and I have difficulty to remember earlier stages. Anyway, there are so many possibilities and I can only knit some of them.

The funny thing is, if the letters on paper would for example stand for four types of vegetables to be planted in that order in a flower bed, we would get an analogue order on the flower bed. But with the dimensions in knitting the resulting pattern is hard to be related to the letters in the chart. It’s also different to weaving, where you can arrive at a drawing of the pattern quite easily from most charts. In a way I don’t know the meaning of my charts until they are knitted.

Okay, here is today’s swatch, and the chart is below. One side has a distinctive horizontally ribbed texture. I’m not sure if the picture can show this properly.

Colour sequence 1 is at bottom of swatch, 2 and 3 are above respectively.

The other side is much more flat, but still has a lovely texture even in the one colour-version.



There is a little mistake in 3 here. See it?

The black area between 1 and 2 here is a result from changing the colour sequence.

Here is the chart

Thanks to yarnpiggy for her encouraging comments.
I've meanwhile done five more colour sequences on this structure, and wish to add them here:

Knitting, music, science and sports

Hand knitting is an amazing activity. The same is true for crocheting. For simplicity of writing lets understand it as included when I talk about knitting.

All over the world a tremendous amount of the most diverse objects have been and are created through these crafts by countless knitters and crocheters. Yet their tools are as simple as tools can be: a crochet hook, or between two and five knitting needles is all they need to turn yarn, the knitters’ material, into the greatest variety of beautiful, useful, funny objects, with greatest dexterity.

I can’t think of many more such virtuous actions of our hands, apart from playing a musical instrument, and - come to think of it - knitting indeed has much in common with this.
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The difference is that musical instruments in most cases are more sophisticated and more specified tools than knitting needles. And the results of these two activities do differ materially. Knitting creates lasting objects we can touch and see. Music is an event in time that only exists when it is played - lets not take into account music that is recorded here: that is something different.

Both abilities are learned through exercising them, and virtuosity grows on, and together with, curiosity, perseverance and patience. Making mistakes, and overcoming them, is incredibly productive and constructive in this process.

For both activities simple notations have developed that make it possible to share a piece with others, so that it can be “played” by whoever chooses to, reproduced countless times. At the same time both crafts leave endless room for a maker’s or player’s own compositions and interpretations, and in both there is no right or wrong. It makes no sense to argue about knitting, nor music playing, to say for example: “You shouldn’t knit like you do”, or “you should knit this or that way”. He and she, who play a musical instrument or the knitting needles, have the freedom to make what they experience as mistakes, and to improve their technique accordingly if they feel they need to, so that their project accords with the vision they have. In knitting a single project, or in playing a single tune, our hands, hearts and brains work perfectly together. In learning and in improving our technique we develop various methods, and our aim to produce something beautiful, be it for ourselves or for others, is directed by our hearts.

Another characteristic common to these two activities is that they can be done spontaneously and everywhere – lets forget about electrical musical instruments here, they are of a category similar to knitting machines. I’ve done weaving for a considerable time, on a four-shaft floor loom. This is a large device; so working at it is defined to the room where it stands. And weaving requires a lot of pre-planning. When you’ve decided on a warp you can’t just switch to another project you would have in mind. But in knitting and playing a musical instrument changing to another tune, or make variations, is very easy.

Both activities are essentially harmless and peaceful, and can be soothing. Both are not characterised, or even defined by competition, as is the case with most sports. Yet sports are a subject in many schools, whereas even the basics of knitting, or of playing a musical instrument, are mainly learned outside of schools. That is probably a mistake. There is a lot of bemoaning in Ireland for example that only few students are interested in science. I don’t think that sports help this. To learn and develop one’s knitting skills, however, implies a lot what is needed in science. This blog http://knitzoid.blogspot.com/2006/04/knitting-as-science.html has a lovely little humorous post comparing knitting and science (The blog is not alive anymore, I hope the author doesn’t mind me quoting it here):

"Knitting as Science

You know,Dear Readers, it occurred to me that knitting is like science. Yeah, I know, everyone talks about knitting as being so creative. But coming from someone who is creative on a regular basis, I see the science in knitting. We all know there is a lot of math involved in both science and knitting. But there is more than just math. There are theories and calculations. There is balancing these equations like in chemistry. There is biology involved. Physics, algebra. For example, take the sweater I am knitting for my brother. First I had to come up with a theory. Will this yarn choice with this pattern idea work. And the biology, does my brother wear wool. What other yarn fiber will work with my theory. Maybe cotton is too heavy. Then I had to experiment. To get the ribbing to work, to make the cable design work. The calculations for the decreases and how many cable designs will fit nicely on the sweater. Then I decide if the theory worked or didn't. Do you begin to see the science? How many of our children will become scientists through knitting? Who knows? But it is an interesting theory. Happy knitting dearies! "

Sports, via their competitive character, lend themselves to consumerism, the number of consumers usually much greater than that of the competitors. Recorded music is also consumed a lot, whilst an audience to a musician’s life performance seems as natural to the activity itself as it is to spoken language or bird song. Knitting is not too exciting to be watched, possibly because it is a slow repetitive process. Knitting is most exciting when taken up by oneself. Knitting can also be done alongside with other activities, like listening and talking. Many knitters can consume even sports competitions on TV whilst knitting, or listen to music.

In my school time we used to knit during classes. It helped listening, and it also prevented us from getting bored and acting out stupid ideas to overcome boredom. The knitters in our class, which were nearly all females and one male, made a jumper together for our favourite teacher. Everyone brought in remnants and knitted a piece of the jumper in whatever way he/she decided. The result was a beautiful and colourful piece, presented to the astonished and pleased teacher after leaving cert. That was constructive, wasn’t it?

Back to the comparison to playing a musical instrument: Whilst it is not possible that knitters work simultaneously together at one piece in the same way as musicians do in an orchestra, because of the material differences between the two, it is possible to team knit.