Mathematical Knitting

March 3, 2013 at 8:33 pm | Posted in Fiber Art, Knitting | 1 Comment

The folks over at Botanica Mathematica have started an art project that’s right up my alley: illustrating mathematical concepts through needlework. I found them through Ravelry, where there’s a group to coordinate things.

One of the first projects: a knitted binary tree. Having spent too much time during my computer science degree dealing with the things, of course I had to play!

Binary Tree

Technically this is a perfect binary tree, since all the levels are completely filled. Of course there could be other versions, where not all branches are present. This would also be nearer to a natural growing tree, since nature tends to be messy. The important part so it stays a binary tree is that at each intersection, the branch splits in two.

Naturally other types of binary trees are knittable as well, but if you want the smallest branches to have always four stitches, calculating how many stitches to cast on and how to split can get a bit more interesting. To illustrate, I drew a few examples:

Types of binary trees

To the left is the perfect tree, this is the one described in the original instruction. The tree in the middle has three levels on the left side and four on the right. The tree on the right is even more sparse. You can easily calculate the number of stitches starting from the top: The last branch always gets the number “4”. When two branches meet, the branch below gets the sum of the stitches of the branches meeting. Repeat till you’re at the trunk, and you know how many stitches to cast on.

Those concepts are really fun to play with, I’m very tempted to do another one! As if I didn’t have enough projects on the go as is.

Knitted Lace Edging from the Encyclopedia of Needlework

October 6, 2012 at 3:19 pm | Posted in Knitting | 3 Comments
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I’ve been on the lookout for a nice lace edging knit sideways to use for a shawl. My first approach was to look through historical needlework books, and I found something nice in my old standby, the Encyclopedia of Needlework:

The instructions, as common in those old books, are pretty wordy, though:

Cast on 11 stitches.

1st needle—1 chain, knit 1 from behind, over, knit 1, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, knit 1, 1 chain.

The 2nd, 4th, 6th, 8th, 10th, 12th, 14th, and 16th needle, purled.

3rd needle—1 chain, knit 1 from behind, over, knit 3, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, 1 chain.

5th needle—1 chain, knit 1 from behind, over, knit 5, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, knit 1, 1 chain.

7th needle—1 chain, knit 1 from behind, over, knit 7, over, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, 1 chain.

9th needle—1 chain, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, knit 3, knit 2 together, over, knit 2 together, over, knit 2, 1 chain.

11th needle—1 chain, slip 1, knit 1, pull slipped stitch over, over, slip 1, knit 1, pull slipped stitch over, knit 1, knit 2 together, over, knit 2 together, over, knit 2 together, over, knit 1, 1 chain.

13th needle—1 chain, slip 1, knit 1, pull slipped stitch over, over, knit 3 together, over, knit 2 together, over, knit 2 together, over, knit 2, 1 chain.

15th needle—1 chain, slip 1, knit 1, pull slipped stitch over, knit 1, knit 2 together, over, knit 2 together, over, knit 1, 1 chain.

Repeat from the first needle.

So, first order of the day: draw a proper chart.

Looks easy enough, and so I made a sample using this chart:

Yup, fits pretty well with what’s on the picture above. There was one thing that in my opinion made things less than optimal, which was the ssk starting rows 9 to 15. So I moved that one in one stitch, and started those rows with a slip stitch as well. Here’s the adjusted chart:

I’m currently using this chart and a mirrored version to create a lacy shawl, but that’s for another day to write about, when there’s actually something to see.

Playing with Tiles à la Escher

April 28, 2012 at 5:17 pm | Posted in Knitting | 3 Comments
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Sometime last fall a call for test knitters for On the Shore came up in the German testing group on Ravelry. It’s a  blanket pattern inspired by art work by M. C. Escher, which I love. After seeing the pictures, I knew I had to sign up. Jana graciously accepted me as a tester, although I have no idea what she’d have said if she had known in advance how long this would take me. Knowing there was no way that I’d manage to finish the blanket in anything under 5 years or so, I opted to knit one of the accompanying pillow covers. While this was a smaller and more manageable project than a whole blanket, pillow covers have their own challenges, and it’s about one of those I want to talk today.

But first, so you know what I’m talking about, here’s my finished pillow:

In order to be able to put the filling into the finished cover, you need an opening and a way to close it. The pattern calls for use of a zipper, which after somee thinking about I agreed with as the most elegant solution. The zipper is supposed to run along the side through the middle of two of the turtles. The pattern avoids having to knit half turtles by knitting two additional turtles and folding those back on themselves to have a clean line in the middle for the zipper. I didn’t like this solution, because I’d end up with three layers of fabric (two layers of knitting and the zipper) in those places.

So, what did I do instead? I decided to actually split those turtles in half. To make the assembly easier, I started with the whole pattern at the tail, and split the pattern after row 15. I doubled up the middle stitch of the pattern, so it became the new selvedge on both the right and left sides. Otherwise the pattern was worked exactly as on the chart. Increases were made between the selvedge stitch and the rest, for decreases I included the selvedge stitch out of necessity. I ended up with two split turtles that would come to lay head to head in the final assembly. To stabilize things, the birds and fishes bordering those two turtles were added befor dealing with the zipper. I figured it would be easier to insert the zipper before assembling the whole pillow, so I blocked just the part with the split turtles before dealing with the zipper to make sure the pillow wouldn’t grow when blocking, since the zipper is rigid and won’t grow at all.

I tried to get a straight edge for sewing, but wasn’t entirely successful, due of the structure of increases and decreases that make up the pattern for the turtle:

To make life easier for sewing, I grabbed a crochet hook and worked a row of chain stitches right next to the edge:

Here’s a view of both sides:

The effect is subtle, but provides the needed stability. I then proceeded to add the actual zipper. For applications like this, I like to buy endless zippers that I can cut to size myself easily. I don’t have pictures of the process of sewing in the zipper, but there are basically three steps:

  1. Use pins to position the zipper where you want it to be. Make sure the left and right side are symmetrical. I wasn’t entirely successful with this, since the two fishes in the middle don’t meet at exactly the same place. But it’s near enough.
  2. Using a strong sewing thread in a contrasting colour, I basted in the zipper by hand, removing the pins in the process. If you’re inserting a zipper into a knit item, it’s important to leave a little bit of space between the zip and the edge of the fabric, otherwise you’re in danger of catching your selvedge in the zipper or the zipper not being able to move properly.
  3. I then sewed the zipper in with the sewing machine. Since everything is held together by the basting thread, this is a no sweat operation. Just choose your stitch length quite a bit longer than you would do for normal fabric when working with hand knits. Afterwards, remove the basting thread, and you’re done.

This is how it looks like:

Only then I proceeded to sew the rest of the seams. I’m happy with the result, although that turtle is probably not the best pattern for such a delicate operation!

Cabled Cardigan—Finished!

August 28, 2010 at 4:22 pm | Posted in Knitting | Leave a comment

I’ve been working on my cabled cardigan for quite a while, and have finally managed to finish it, and I’m very happy with the result:

The pattern is worked from side to side, starting at the end of one arm and ending at the end of the other one. I lengthened the pattern quite a bit from the original pattern in Sabrina Magazine 08/2009, since I didn’t want the cardigan to end in the exact place where I don’t need any extra volume. Other than that, it is basically worked after the pattern. Of course I also used a different yarn with a different gauge, so I had to completely recalculate the pattern.

The challenge with this kind of construction is to get the pattern to be symmetric at the right and left sides. I had to calculate exactly how many rows I’d need to knit just to know where in the 24-row pattern repeat I needed to start if I wanted to end up right in the middle of a repeat in the middle of the back. But luckily I’m one of those knitters who doesn’t mind that kind of challenge. I have many more problems with just starting to knit and figuring out the details somewhere along the way. Here’s the back view of  the cardigan:

I’m very happy with the result! Knitting the whole thing in one piece has its advantages and disadvantages. There’s less fiddly sewing involved, which I like, but at the end I was handling quite a heavy piece of work that I had to turn around at the end of every row.

The yarn I used is Toscano from ggh, which is a ribbon yarn. I really enjoyed knitting with this, the only problem I found were a few too many knots for my taste, leading to having to hide way too many ends.

All in all, I thoroughly enjoyed knitting this cardigan, and I’m pretty sure I’ll enjoy wearing it just as much in the Fall.

Finding the Right Tool for the Job

August 2, 2009 at 1:43 pm | Posted in Knitting | 1 Comment

Remember this?

Maltese Shawl from Victorian Lace Today

Yes, my Maltese Shawl from Victorian Lace Today is growing, albeit slowly. I really enjoy knitting the pattern, but finding the right needles to help me with that turned out to be an adventure. The first try was using my trusty Addi Click needles. While there’s usually no problem using the interchangeable needle tips from Addi, the joins are definitely not smooth, and working with this lace-weight yarn was simply impossible, since it kept snagging at the joins all the time. So after a couple of rows I switched to a fixed Addi needle of the same size (at the top):

Lace Needles

They’re nice, shiny, the yarn moves smoothly over the needle, but for this kind of lacework, the tips aren’t pointy enough. This pattern has lace stitches in every row, so you end up having to purl stitches together when one of the stitches is a yarn over. Trying to do that with blunt needles leads to lots of cursing and severe lack of motivation.

So, I needed another option. My LYS just got some Addi Lace needles (middle of picture) that are ostensibly designed for this kind of knitting, so I got myself one of those. The tips are nice and pointy, so the lace stitches immediately became much easier to work. But, the gold-coloured coating of those needles tarnishes really fast (there’s almost no reflection of the flash on the photo, and I haven’t knit more than maybe 10cm of the shawl with it), and when that happens, the stitches stop to slide easily on the needles. I had to work all the time to get the stitches to move to where I needed them. No wonder I started to ignore the project in favour of others.

I needed another option. I had heard the KnitPro (KnitPicks for any Americans) needles (bottom of picture) have good tips and a smooth surface, so I decided to give those a try. This is another system with exchangeable tips, but the joins are constructed differently so they’re smooth. And they’re pretty, too. You can see the tip geometry is almost identical to the Addi Lace needle. I tried them out, and yay, the fourth needle I tried for this project finally does the trick!

This was a really good lesson to remind me that using the appropriate tool for a job can make all the difference between fun and tedium. If something obviously doesn’t work, try something else! This is a good thing to keep in mind for hardware tools of all kinds as well as software. If something seems to be more difficult than it should be, check if you’re using the optimal tool for the job!

Addicted to Lace

June 14, 2009 at 4:22 pm | Posted in Knitting | Leave a comment

Now, that’s nothing new around here, isn’t it? 😉 After writing that glowing review for Victorian Lace Today a few weeks ago, of course I had to try my hand at one of the patterns. I’m going to make the Maltese Shawl, after finding the appropriate yarn, of course. Thanks to the perfect service from Jürgen Weidner, I soon was in the possession of this:

Malabrigo Baby Merino Lace in Bergamota 94

Three skeins of Malabrigo Baby Merino Lace in Bergamota. The first skein is already wound using my shiny new ballwinder, which I acquired at the same time. The yarn feels really yummy, and it’s a joy to knit up, as you can see here:

Maltese Shawl from Victorian Lace Today

I made a provisional cast-on over a spare cable of my Addi Clicks, and acquired a 4.5 mm Addi lace needle after a few rows, since I want to make my life with this as easy as possible, or I’ll never finish. The pointier tips of the lace needles are just what I need here. I have the feeling the gold-coloured finish of the lace needles is a bit less slippery than the normal Addis, but this could well be my imagination.

The picture was made after 3 pattern repeats from 88 comprising the main panel of the shawl, so I’m into this for the long haul. You can also see some big bulky metal rings in the picture. Those are my sorry excuses for stitch markers currently, since my open plastic ones were driving me to distraction with catching the yarn in all the wrong places. I’d like to have some closed rings a bit smaller, but for the moment those will do.

So, don’t expect to get updates of this venture very often, this is definitely not TV knitting, being “real” knitted lace, meaning every row is a pattern row, no dreaming while purling back across the wrong side allowed. But I think the look of the finished lace will be so worth it.

Book Review—Victorian Lace Today

May 24, 2009 at 7:01 pm | Posted in Book Review, Knitting | 1 Comment

There are tons of knitting books out there. Being someone who isn’t particularly interested in pattern books usually, I don’t get excited about a knitting book very often. But when I had a chance to have a look at Victorian Lace Today by Jane Sowerby at my LYS a few weeks ago, I was immediately hooked and just had to have it for myself. Thanks to the wonders of Amazon that happened pretty fast, and even at second and third look that book is just marvellous. It works on so many different levels for me, I’m sure I’ll use it as  a source of instruction as well as inspiration for a very long time.

While browsing randomly through the book at the LYS I came across an image of a page from an old knitting book that looked oddly familiar:

My Knitting Book page 12

Reading up on that page confirmed my suspicion: It’s the only illustrated page from Miss Lambert’s My Knitting Book (link to google books). And since I’m currently working to make this one available on Project Gutenberg through Distributed Proofreaders, naturally I’d seen this page before. And I can tell you, those old knitting patterns look very strange to today’s knitters, starting with the fact that charts were not yet invented and some of the terminology was completely different from today, going all the way to not having illustrations of the finished items and the pattern descriptions being rather sparse for today’s tastes.

And this is exactly what makes Jane Sowerby’s work so amazing: She tells the story of those early pattern writers and their books, showing what they did for knitting, where patterns were usually handed down orally before. And then she goes ahead and moves those patterns into the 21st century, presenting them in a way that’s attractive to today’s knitters. The author comments extensively on the trials involved in figuring some of those things out, and the results are beautiful.

And she doesn’t stop there: At the end of the book, in addition to explaining all the different stitches used in the book and showing methods of cast-on etc. suitable for lace knitting, she goes on to explain how to use the patterns given to design your own, complete with a work sheet to help you crunch the numbers.

Faced with so much inspiration, of course I had to go and play. The requested object was a skinny shawl from one ball of yarn, to be completed within a couple of weeks so my mum could wear it to my brother’s wedding. Completely different from the elaborate lace patterns in the book, right? Yes, on first sight, but the pattern for one of the simpler center panels proved to be just the ticket, and gave me an enjoyable first experience of “real” knitted lace (meaning there’s patterning both in the right and wrong side rows).

Narrow Scarf in Faggotting Stitch

Oh, and that’s not all of it: the book would make a great coffee table book as well. There’s lots of brillant photography not only of the knitted items but also of Victorian houses, parks and gardens. The information on where exactly all those photographs were taken is in the back of the book, so one could make a trip to Britain to see the beauty for real. Now I only need an opportunity for wearing one of those elaborate Victorian shawls, so I can make one.

Cabled Square Challenge

May 4, 2009 at 7:42 pm | Posted in Knitting | Leave a comment

There’s been a challenge to design a 30*30 cm square for a knitted blanket on Ravelry: Verzopft & Zugedeckt. The deadline was April 30, and even if you’re not on Ravelry, you can admire the results here. The requirement to participate was to design a 30*30 cm square that includes some cabling somewhere. Being in love with cables right now, of course I had to play. Can’t be that difficult, right? Sure, only if you insist on making your life more difficult than necessary.

Since the start in February, I’ve been playing around with lots of different possibilities to knit a square. I was trying to get a complicated construction to work, and nothing worked in practice as well as on a piece of paper. So I frogged my sample square, more than once. Not getting anything to work, I gave up and forgot about it for a time, being more than busy elsewhere in the meantime. But the challenge kept nagging me. I didn’t want to give up so easily, and a week before the deadline I finally remembered what I usually forget when I try to design something: that there’s nothing lost by keeping it simple. Designing is as much about leaving out the superfluous as it is about putting features in. So, over the weekend, I finally got to work on a much simpler pattern than all my previous ideas and came up with this one:

Cabled Square

I like the effect that the cables seem to be woven in at the top and bottom by horizontal stripes. This really came out like I imagined, which makes me happy. 🙂

It always amazes me how even designing something so small and simple ends up taking quite a lot of time. Collecting and discarding ideas, trying things out, working the design and writing up the instructions always takes way longer than I anticipate. A big thank you goes to all the designers out there who do all the work so I can do some mindless knitting without thinking whenever I feel like it. I appreciate their work all the more since I’m trying, little by little, to get into designing my own projects.

Fingerless Mitts—Adventures in Designing

March 29, 2009 at 6:20 pm | Posted in Knitting | Leave a comment

A friend of mine asked me for a simple pair of fingerless mitts, nothing too fancy. I wanted to have some fun knitting, so I needed someting with a pattern. Every pattern I looked at had too much patterning, though, so I decided to make up my own as I went along. Here’s the result:

Asymmetrical Cabled Mitts

The mittens have a small cable on the back of the hand that’s positioned asymmetrically towards the outside of the hand. The cable grows out of the 2×2 ribbing and is a bit asymmetrical. The effect isn’t as strong as I’d like, since I wanted to emphasize the asymmetry of the design by making the cable asymmetric as well. You can see it a bit better in this progress picture:

Fingerless Mitts in Progress

So, while I like the result, I’m taking notes for the next time. I’d like to make the asymmetry within the cable stronger, so it really looks intentional and not just a bit wonky. Having the cable pattern run through the ribbing might add some further interest to a fairly plain pattern. Maybe I’ll make another pair, I’d like to have some for myself!

Knitting Swatches

March 22, 2009 at 7:24 pm | Posted in Knitting | 1 Comment

Until now I’ve pretty much successfully avoided projects that needed to match a certain gauge to work, so I never knit any swatches before diving into the project proper. Now, while currently trying to finish up all those wintery projects so I’m prepared when spring finally comes around, I’m dreaming of summer knitting.

After some browsing of the magazines at my LYS I think I made a decision for a cardigan from the current Verena. The model I’m thinking about is the one on pages 6/7. Since this model isn’t available in my size and I want to use a different yarn, I needed to knit some swatches. I’m simply amazed how much difference needle size can make!

Swatches for Cabled Cardigan

The upper swatch is worke with a 3.5 mm needle, the lower one with a 4.0 mm. The lower one hits the target gauge precisely on number of stitches, although the row gauge is still off. But I think I can work around this. I like the way the yarn (Online Linie 214 Senta) knits up with the larger needles, so although I’m currently doing another swatch in a different yarn, I think I’ll go with this. I think I might hate myself for ever deciding to knit something with that many cables before finishing, though.

Now I just need to do the mathematics to make the model fit my size, which will be an adventure for sure. But nothing a few hours with a calculator can’t solve, I guess!

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