Math and Knitting

I went to a graph theory conference in Detroit a few weeks ago, and while there was math happening, nothing really caught my fancy. I went to talks, I listened, I zoned, I free-associated. And this happened:

This is the Petersen graph. It's a well-known and much-used example and counterexample graph. It's complex enough to be interesting, but basic enough to be easy to play with and test things on. (Trying to find a way out of ending that sentence with a preposition. Failing.)



The graph above has had the vertices (the dots) labeled by me to go with the matrix below. An adjacency matrix is a representation of a graph in which the vertices correspond to both columns and rows, and the entries are the number of edges (lines) connecting adjacent vertices. The top matrix below is the adjacency matrix of the graph above. Below that is a chart. The entries in the matrix have been replaced with yarn overs.



The symbols along the diagonal are k3tog, the ones on the right edge are k2tog. o's are yarnovers, - is purl, and if unspecified, they're knit stitches. Since the diagonal of an adjacency matrix is a funny place, defined by whether or not you consider a vertex to be adjacent to itself (I said no in my matrix), I figured decreases would work along it. Since I didn't want to deal with triple decreases, I made them double, but since the graph is 3-regular (every vertex is adjacent to three others), I needed a third, hence the line of decreases on the right. The purl column was for definition, but I'm not sure how necessary it is.

I knit it up using the yarn and needles I had on me at the time (giant grey man socks that are still threatening me with their not-done-ness). Here's the swatch that resulted. The top is the pattern in the chart. Below is the same, except the k3tog's are instead slip 1, k2tog, psso.



It's a crappy blocking job, but I'm pretty sure a good one would still have issues with the diagonal skew - which seems like it would be predictable were I a more experienced lace knitter. In all, I'm not in love with it. I find it highly doubtful that I'll be working on Petersen socks anytime soon, but I found the idea interesting anyway. I have a hypercube matrix charted out that might have fewer issues, but then again, it might have more.

Blocked

Progress report:
I washed the Petersen swatch and pinned it to the carpet today. I hope to have pictures in the next few days. The grey sock is to the heel flap, the blue fuzzy sock has the heel turned, but the gusset is not yet picked up. The first sleeve of the sweater is almost where it started today when I realized I really didn't like the way the increases were, so frogged back to the start of the elbow and redid them. I've got myself a bit blocked about how the whole "paired increases" thing works. Need to start the second mitten if I want to finish the pair in the month, which I do. Also need to start writing up that cabled sock pattern.

Auburn is currently winning, but I'm not counting on that continuing. Am Hoping though. War Eagle.

Move along, nothing to see here.

It's been a while since we've had an FO here. I know, it's grating on me too. Darn pairs of everything. I have most of a mitten (no thumb) done and three second socks going. The sweater is getting to a point where Something needs to be done, but I'm not quite sure what (but I bet it involves a second sleeve), and between the two jobs I have now, knitting time has been scarcer.

Besides, I had a couple evenings of complete zombieness. It was cold. I have lost the furnace wars. Maybe next year, when I have more finished knitwear, I will last longer. Really it was kind of amazing the difference the three degrees between 65 and 68 made in my ability to be productive yesterday.

Okay. There's football on. LSU lost, which gives Auburn a chance at winning the SEC. But first they have to beat Arkansas, which they're doing right now in a really boring game.

I have gray sort-of lace swatch that grew from last weekend's math conference. I need to block it and see if it actually looks remotely like something worth having. Lace charts from graph adjacency matrices could work, right?

Ok. Moving along myself. Good weekend, everyone.

Fuzzy green snowflakes

I cast on my Norwegian Mittens for the Strikke-along last night. I never did get yarn for it, so I just pulled some stuff from the stash. Classic Elite Lush in lime green and black. Worsted weight on size 4 needles, it's actually not bad. Very soft, but the stitch pattern is going to look fuzzy, with it being an angora blend. The first cuff went very fast. You can see my crappy job of weaving the i-cord at the back.



I was getting through the cuff and trying to decide whether I wanted to do the snowflake design or the winter spruce. I was leaning toward the spruce, since I'd wound up with green yarn, but I really like the snowflakes better. Since it was about 1:30 in the morning, I'd had some wine, and my husband was subjecting me to his favorite episode of Married With Children ever, I was in a goofy place, and decided to go with green snowflakes and call them Nuclear Winter Mittens.

Chris then started telling me what snowflakes would actually be like in a nuclear winter (i.e., not green), but we eventually agreed that if we mispronounced nuclear, we could also have green snow. Therefore, these are my Nuke-ular Winter mittens.

***

Fall is coming. The light is changing, I can feel the world getting greyer, and I'm waiting for the fall colors. Fall up here is gorgeous, brilliant and spectacular in a way it's not back home, where every other tree doesn't turn. I'd be glad to have it, but I still feel like I missed summer somehow. I'm going further north this weekend, and I hope some good math will come of it. Meanwhile, I think it'll be good to just get away for a few days.

My Sock. MINE!

This is why I didn't cast on for the Strikke-along yesterday. First sock is finished. Worked the toe while watching what seemed to be Dead Baby night on Meerkat Manor. I'm going to let it sit mateless for a while because taking a bajillion pictures trying to get one that was almost worth posting made me cranky at it. (Plus now that I see it, it's a little busy, don't you think?) Besides, I need to make sure my notes make sense when creating the second sock. And I'm still flummoxed by the thought of writing this thing up. Charts? Row by row? I used my row counter till row 88, does that information need to be included? If I write my instructions using modular arithmetic, will that freak people out? The mirrored cable thing makes it complicated. Ergh.

I'm going to let this go for a minute and see if there's some way of encoding a finite field in a big cable. Have a good one.