Despite the promise of our header, I'm not sure we've ever had a puzzle! (Aside from our about page, that is). So here's a couple brain teasers for you.
1. What kind of fabric do you get when you knit a patchwork of diamonds in knits and purls? Ya know, like this (empty squares are knit, dotted squares are purled):
Well now, you might think "if you knit this, you would get a patchwork of diamonds" and you'd be right. What I'm really asking about is the texture of the fabric, and here's what made this puzzling to me: purl stitches that are next to knit stitches get pushed down (like in ribbing), but purl stitches that above or below knit stitches get pushed up (a la garter stitch). So what happens when you change between knitting and purling along a diagonal?
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2. How do you knit this fabric? It's like popcorn stitch on steroids, with high peaks and low sinks (dips? pits? Is there a better word for these local minima?)
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Well, as you may have guessed: the answer to 1 is 2! It seems that the purl stitches at the skinny points in the tiers of purl diamonds have upward forces on them from the above and below knit stitches, and no counteracting downward forces, so they become peaks. Meanwhile, the knit stitches at the skinny points in tiers of knit diamonds have only downward forces on them and become sinks.
I really like the waffley effect of this, and I'm hoping a light blocking doesn't smush it too much.
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ReplyDeleteI was thinking about this a couple years ago, but never got to the point of having actual examples... This setup exactly the sort of thing that comes up in statistical mechanics: you have a finite choice of states for each location in a grid. The thing that people usually think about is the large scale behavior that you get if you randomly choose the states under some probability distribution. The most interesting question I thought of along these lines is what's the typical curvature of the surface that you get as the gauge goes to infinity? Is there an interesting phase transition in the shape of the surface as you change the ratio of knits to purls?
ReplyDeleteI've been curious about the statistical mechanics of knitting too -- largely, wondering about the correlation distances between an "off" stitch and how far away you can see the effects. I like the idea of sending the gauge to infinity -- but worry about the issues of approximation that come up in thinking of knitted fabric as a surface ....
DeleteI'm glad you finally posted something puzzlish...I was feeling a bit guilty about that myself. There has also been a sad dearth of both puns and space unicorns.
ReplyDeleteI wonder, if you blocked this hard, would it flatten out and look like diamonds?