Sunday, December 16, 2012

Gift for a gamer

One of the reasons I enjoy knitting as much as I do is that I really enjoy giving hand-made things to people I like.  It makes me happy.

I work on the Xbox team with a fantastic group of very smart, funny, geeky people. I like and admire them, and I really enjoy working with them, which means I feel instinctively compelled to knit things for them.  (Other knitters will understand this compulsion.)  But they are not necessarily good recipients for my standard repertoire of socks, hats, and gloves. So I have to take my cue from our context what sort of token of esteem would be right. 

I started yarn-bombing my co-workers' headphones last year.  It was totally fun, and I think it went over pretty well with them. But our group leader proved to be a challenge as he does not wear headphones at work.  What do do, what to do...

Just the other day, because Christmas is approaching and I have been playing with knitting spheres, this image suddenly popped into my head:

So, here you go boss. You inspire me to attack all sorts of complex problems and to have fun while doing so.  The best kind of boss there is.

Friday, November 23, 2012

The Math Behind Metamorph

On November 13, I published the pattern Metamorph.  This pattern was a long time in the making, and involved taking a journey deeper into the world of Topology than I had ever previously attempted.  This blog post is my attempt to document that journey.  Apologies in advance to individuals fluent in the language of Mathematics -- I only play a mathematician on YouTube.

The tale goes like this...

About 3 years ago while I was messing around with little form studies, I thought it would be cool to have a knitted form that looked like a torus (or donut) but had a whirlpool in the middle.  I knitted a tube, folded it, offset one edge, and grafted.  Here's what I got. 

Not exactly what I'd pictured, but interesting enough. I documented my experiment and considered it done.

Now I should mention: if there's something in my hands, I will probably play with it absent-mindedly.  So the next thing I knew, I looked down and saw this...

Given that this I’d just done a series of explorations dissecting the moebius form and thought I understood this form pretty well, this little object just about turned me on my head.

At its core, Metamorph is simply a torus. But when you offset one edge before sealing, this creates periodic harmonic orbits around the longitude, which introduces torsion -- or energy -- into the form. 

Image credit:

Image credit:

Mathematical models like the ones above show the periodic orbits.  With a knitted form, the energy created by these orbits manifests as folds in the fabric. 

After a little manipulation, the form will naturally relax into whatever shape requires the least amount of energy to maintain. In this case, this is the least-energy shape: 

Two conditions determine the least-energy shape:

(1) the amount you offset one edge before sealing, and
(2) the ratio of width:height. (Note that "width" here refers to the width of the knitted tube when laid flat, which is 1/2 the total circumference.) 
When the width:height ratio is 1:1, AND the amount of offset prior to sealing is 45 degrees, then after some gentle manipulation of the fabric, you will get a form with a single fold going all the way through the meridian. Or, a 90-degree offset will yield a form with two folds. So, Metamorph is divided into 8 equal segments because this affords a very simple mapping of n-button offset = n folds.

Well and good. But what if my width:height ratio isn't 1:1? Ah, I'm so glad you asked.  The conditions that correspond to 1 or 2 folds are continuous functions:

If height is less than 1/2 the width, or more than 2x the width, the form gets a little unruly.  The graph shows a comfortable range of sizes.
Let's say you're following the Metamorph pattern and you suddenly run out of yarn.  Your width is 12", but your height is only 10".  If you divide your form into 8 equal segments as directed in the pattern, you will not get neat-and-tidy folds when you button your form together.  BUT, you can still get a form with nicely-defined folds IF you find your position on the graph above and alter your degree of offset accordingly. 

1.  Figure out the width:height ratio, given width = 1.
12:10 --> 1:0.83

2.  Pick a spot on the x-axis that looks like it corresponds to (1:0.83) and move up to see about where you land on the continuous functions, then left to the y-axis to see how many degrees of offset correspond to the point on each line. In this case it looks like somewhere around 36 degrees for a single fold, or 1/10 of the total circumference. 72 degrees will get you 2 folds.

So you can still have a mapping of n-button offset = n folds if you divide your tube into 10 segments instead of 8. 

Or you could also go the other way: say you have 12 buttons and you want to use them all on your Metamorph.  Divide 360 by 12 and you get 30; this time the matching width:height ratio for n-button offset = n folds would be about 1:0.67.  Or you could double it up: with a ratio of 1:1.33, then if you divide your form into 12 equal segments, a 2-button (60-degree) offset will give you 1 fold and a 4-button offset will give you 2 folds. 

Is your head hurting yet?  Mine is.

Now, adventurous souls may be wondering: what will my form look like if I go outside those lines?  With the 12-button, 1:1.33 example, what if you offset by some odd number of buttons?  Again -- I'm so glad you asked! 

What you get is something like this:

This is a snapshot of a 1:1 form with a fold that goes only part of the way through the meridian.  I don't remember exactly what I did, but based on how far down the fold goes (looks like about halfway to me), my guess is I gave it a shift of about 22.5 degrees, or half of what it would have taken to get a single fold across the meridian, based on the graph above. 

I owe a huge debt of gratitude to sarah-marie belcastro, Joshua Samsor, and Yonatan Munk for helping me get this deep into the wonderland of Topology. 

Other fun places that I discovered along this journey:
Wikipedia's page on the torus
Strange Loop by Morgen Dammerung
Plug-ins for modeling the twisted torus
The Twisted Torus and Knots by Jenny Buontempo
Sketches of Topology

Now, to find my way back up this rabbit-hole... :)


Tuesday, November 13, 2012

Metamorph... the "other moebius"

To download Metamorph, please visit the Ravelry pattern page.

Anyone who reads this blog knows my affinity for the moebius form.  I'm particularly fascinated with how it takes multiple forms as you cut it apart and put it back together...

"Is there a topologist in the house?" October 2009 


So, take a look at the cowl below. It looks like it's the same form as the one on the above right... or is it?  

What will happen when you unbutton the buttons?  You just might be surprised...

Unlike the moebius above, the basic form of this cowl comes apart into just a simple tube. 

Don't believe me?  Watch this video on YouTube to see the live-action version. 

I have a new pattern on Ravelry exploring this topic, which you can download here.



Friday, August 24, 2012

"Keyhole" Buttonhole

The Keyhole Buttonhole

This technique was developed for a very specific instance; it is to be worked over 2 purl stitches that are flanked on either side by columns of knit stitches.  However, it would work just as well on stockinette.  The example uses (p2, k1) rib.

Keyhole is a hybrid of a two-row horizontal buttonhole and a yarnover (or “sheep’s eye”) buttonhole.  It doesn’t actually bind off any stitches, but rather uses paired decreases on the bottom row, and m1 increases on the top row.

Here is a YouTube video showing you how to do the Keyhole buttonhole.

Here are written instructions for the Keyhole buttonhole.

Work up to 1 st before the hole will begin, then:
Round 1
Ssk, YO, k2tog.
Work most of the way around, until you reach the place where you began – 1 st before the hole.
Round 2
k1, m3 in YO strand, k1.  (This creates an extra stitch on top, which just makes the buttonhole a little larger.)
Work most of the way around, until you reach the place where you began – 1 st before the hole.
Round 3
K1, p2, k2tog.
Continue working in pattern.

"Eye of Ra" Buttonhole

The Eye of Ra Buttonhole

I have to give credit where credit is due here: I would not be posting this if it were not for TechKnitter, whose always-impeccable illustrations and technical knitting mind have always been a great inspiration to me and many others.  My Eye of Ra buttonhole is very similar to her Tulips buttonhole, but uses different methods of reinforcement at either end, and requires no tools other than 1 pair of knitting needles.  Other than that, Eye of Ra is very similar to Tulips, as well as other reinforced horizontal one-row buttonholes in the knitting sphere.

If you're familiar with Lucy Neatby's crochet provisional cast on, you may recognize the adaptation of this method here for use with two knitting needles, rather than a crochet hook.  That said, feel free to use a crochet hook if you prefer.

Here's a YouTube video showing you how to do Eye of Ra.

Below are written instructions telling you how to do it.

The example used here is a 3-st buttonhole worked in stockinette, but this buttonhole can be worked on any stitch pattern over any number of sts.

1. Reinforce opening edge:
  1. Wrap st (reverse YO; sl1, pass rev YO over st and off R needle, sl st back from R - L).
  2. Sl1 R > L, then k this st.

2. Bind off 3 sts:
  1. sl2, pass 2nd st over 1st st and off R needle
  2. [sl1, pass 2nd st over 1st st and off R needle] 2x.

3. Work top of buttonhole:
Sl1 R - L and turn work.  This section is worked from WS.
  1. Insert R needle tip into the back leg of the 1st st on L needle from back to front; slip off to R needle .
  2. Bring working yarn between needles and to the back.
  3. Wrap yarn around both needles and pull loop through st on R needle.  Gently snug, not too tight 
  4. Repeat step 3 three more times, for a total of 4 cast on sts (number of bound-off sts +1). 
  5. Slip st on R needle up onto L needle without twisting. 
  6. Turn work.

4. Reinforce closing edge (RS)
Yarn should be in front at this point. 
  1. Sl1 R - L, then bring yarn to the back -- over the work and under the needles.
  2. k2tog
K to end.

On the next row, work plain.  You may find some loose stitches next to the opening edge; if so, use your needle tip to gently distibute the slack backwards along the previous stitches in the round.

Note that although you added a total of 5 sts when casting on, two of them end up getting worked into each edge, leaving you back at your original stitch count.

Down the Button-Hole

I mostly knit socks, scarves, and other accessories that don't have closures, so I haven't had much use for a knowledge of buttonhole techniques... until now. I recently began designing garments with buttons, and it turns out the buttonhole rabbit hole is deeper than I realized! 

There are 3 basic categories of buttonholes:
  • Eyelet buttonhole, in which a yarnover creates a hole in the fabric; no sts are bound off or cast on;
  • Vertical buttonhole, in which separate strands of yarn work each side of the hole independently;
  • Horizontal buttonholes:
    • Two-row buttonhole, in which sts are bound off in one row and cast on in the next; and,
    • One-row buttonhole, in which sts are bound off an cast on in the same row.
TechKnitter, as usual, has provided an excellent and comprehensive exploration of all these buttonhole techniques.  If you want the nitty gritty, she's your source.  If you want the Consumer Report, read on.

Within each buttonhole category, there are limitless variations on a theme, and of course everyone claims that their way of doing it is the best.  Resist these claims -- different methods work, or don't work, for different knitters! 

As for the main three categories of buttonholes, here is my take:


  • Pros: super-easy to do!
  • Cons: leaves an un-reinforced, loose area of your fabric that is somewhat vulnerable to disfigurement with frequent handling.


  • Pros: ?
  • Cons: Personally I was not able to identify any redeeming qualities of this method.  It requires using a second, independent length of yarn, which means more ends to weave in, and possible color-matching issues.  The design places a lot of stress on the stitches at the top & bottom of the hole, warranting reinforcement with yet another length of yarn and access to additional tools.  Also, if you are not skilled at working a selvedge, the vertical edges will not look tidy.


  • Pros: These buttonholes can be made to be very tidy and strong without requiring extra tools or lengths of reinforcing yarn.
  • Cons: the edges of the hole will be weak and loose without reinforcement -- but there are several simple workarounds that mitigate this.
The Horizontal buttonholes were the most interesting to me, so this is where most of my exploration took place.  Here are some good resources for making horizontal buttonholes.

TechKntter on Horizontal buttonholes
In this post, TK delivers an illustrated deconstruction of why the un-reinforced simple two-row buttonhole is a poor choice.  She also includes instructions for her own horizontal reinforced one-row buttonhole, "Tulips" , complete with link to video by Eunny Jang.  Note that although this buttonhole is attractive and highly functional, the method of execution is very complicated (IMHO, unnecessarily so).

Reinforced one-row buttonhole using cable cast on for top stitches.  The end result of this buttonhole is similar to TK's Tulips, but the method of execution is much simpler. Uses different methods of reinforcing each side of the opening, and uses a different cast-on for the top stitches (TK uses a provisional chain cast on).  Here are links to the same exact buttonhole, in three formats:
1. Video tutorial -
2. Photo tutorial - NeoKnits
3. Illustrated tutorial - Knitting Daily

Homegrown variations

My exploration of this topic gave birth to a couple of my own variations that work best for me.  These are each explored in greater depth in their own posts.
Eye of Ra
I wasn't completely happy with any of the horizontal reinforced buttonholes I found because I wanted something that would look just as beautiful as TK's, with a similar structure, but would be easier to make.  "Eye of Ra" is thus named because the appearance of the top and bottom edges reminds me of an Egyptian heiroglyphic eye.

Here I wanted a buttonhole for a very specific context: one that would nestle neatly into a 2-stitch purl column flanked by columns of knit stitches.  Keyhole does not actually bind off any sts, but uses paired decreases in the first row, topped by M1 increases in the next row. 

Thursday, August 23, 2012

Anatomy of a Wrap

I wrap stitches a little differently than most knitters.

You might notice that the technique illustrated below is rather a hairsplitting one.  But I bring it to you because I use it in several different contexts, and its utility is not commonly known.  I figured it was about time I documented it. 

Here is the classic way to wrap a stitch:

1. With working yarn in back (shown here in pink), slip a stitch from L to R needle.

2. Bring the working yarn to the front, and around the slipped stitch.

3. Slip the stitch back from R to L needle and bring the yarn to the back again.
Voila, the stitch is wrapped.

Straightforward enough.  Here's how I do it.

1. Reverse yarnover.

2. Slip a stitch from L to R needle.

3. Pick up the YO with the tip of the L needle, and pull it up and over the slipped st and off the R needle.

4. Voila, the stitch is wrapped.

Did you see the key difference in the resulting wrapped stitches?

Image A shows what results from the traditional way of wrapping stitches: your working yarn is coiled around your wrapped stitch like a spring, with the tail of the working yarn, shown here in light pink, emerging from the top of the coil.

Whereas, Image B shows what results from how I wrap a stitch: the working yarn emerges from underneath itself, like a loop cast on turned on its side.

It's a subtle difference, yes, but my method makes a neater result because the wrap can't creep up the sides of its stitch when the fabric is under stress. It is this little difference in structure that makes Jeny's Surprisingly Stretchy Bindoff so elastic, and gives my reinforced "Eye of Ra" buttonhole its tidy edge.

P.S. Almost forgot!  Above applies to how I wrap a knit stitch, because the yarn starts and ends in the back.  When wrapping a purl stitch, the yarn starts and ends in the front, so it works a little differently.  This is why, in JSSBO, you do a reverse yarnover for knit stitches and a regular yarnover for purl stitches.

Here's what happens.  Purl sts are shown in darker grey.

1. Yarnover the usual way, and bring yarn to front of work.

2.  Slip a stitch from L to R needle.

3. Pick up the YO with the tip of the L needle, and pull it up and over the slipped st and off the R needle.

4. Voila, the stitch is wrapped.

Here's how it looks close up:

Wednesday, June 27, 2012

Yarn Bombs

I work in an open workspace shared by about 10 people. Sometimes it gets rowdy, and we frequently find the need to don noise-reduction headphones in order to get any work done.

Unfortunately, my heaphones folded right at the crown of my head and the hinge pinched my hair.  It was impossible to take them off without ripping my hair out.  Solution: knit a cover for them so they don't pinch the hair (really this was just a transparent excuse to engage in some yarn bombing).

It wasn't long after I brought my first prototype to work that my fellow researchers wanted covers for their headphones.  So first, I tried a series of variations on the simple knitted cylinder...
These are the guys' headphones.
Left to right: John S., John D., Erik, Ramon
Made with primarily BMFA, Heritage, Koigu, Tosh

Ramon (my most-excellent boss) finding creative ways to model his pink 'phones

John likes blue.
BMFA (Haida), MadelineTosh (Fathom), Three Fates (I forget the colorway)

The other John refused to model for me, so Erik kindly modeled both his own and John's phones!

I wasn't aware of it at the time, but I ended up doing all the guys' headphones in sequence, and then turned to the women.  By the time I started doing the women's headphones I was a little sick of playing with diagonals, so first I tried a little color work...
Erin got a Space Invaders band (made with Louet Gems).
This one made the boys jealous!

Then started playing around with hardware.  I used O-rings to connect the sides of this one around the band.  It ended up having a much more subtle effect than I'd pictured...

... so the owner of said headphones was kind enough to supplement with her own grunge imitation.  You rock, Jenn!

Francie's headphones with the big pink ear cradles always made me think of overstuffed earmuffs, so I decided to bring my vision to life...
 Pink angora with rhinestone studs!

Elaine's Bose headphones clearly called for swanky coverings...
Tosh Sock (Poseidon) with square cobalt Japanese seed beads.

Although not evident from the picture, Rivelea's headphones had a distinctively gothic theme, and the inside of the ear cradles had a spiderweb graphic. I wanted the outside to reflect the inside.
The tricky part of doing these headphones was identifying the right material.  It turned out I needed something stiffer than yarn.  I trolled around the craft store and picked a variety of materials for trial and error.  DMC memory wire was the clear winner.  Plastic spiders just for fun.

When I wasn't really paying attention, someone snapped this one of me...
I think it captured the mood of the day rather well!

Friday, June 15, 2012

Sage advice for any situation

A wise person once said:

So if anybody kindly tells you that what you are doing is "wrong," don't take umbrage; they mean well.  Smile submissively, and listen, keeping your disagreement on an entirely mental level.  They may be right, and even if not, they may drop off pieces of information which will come in handy if you file them away carefully in your brain for future reference.

Sounds like it should come straight out of How to Win Friends and Influence People, doesn't it?  Well it just so happens that the person who uttered this wisdom was Elizabeth Zimmerman, in Knitting Without Tears. 

Right on, EZ.  Sorry I never had the priviledge of meeting you.

Tuesday, May 29, 2012

Pet Peeves

I don't understand why people complain about patterns being too complicated. If you don't enjoy knitting things that are complicated, then don't knit things that are complicated.

I also don't understand why people complain about patterns being boring. If you're bored by what you're knitting, then stop knitting it.

Life is short. Do what's fun. Isn't knitting supposed to be a "Leisure Art"?