Moderne, Part 2

Mindless and meditative holiday knitting, as I play with my little man, write some code, cook, clean home, and do some home-moving packing...Yeah, its growing nicely, from what it was last week. Excited and close to adding in the fourth colour, the dark green!

Do you know what this type of knitting reminds me of, and gives me a feel of? Remember those thick markers, thick brushes, and thick paints in childhood art classes or school time art? There was some strange kind of joy and pleasure in slowly and gradually filling in a blank sheet of paper with solid, opaque colours, and watching an abstract play of colours simply emerge. I would lose myself in the thick quality of the paint, and how it felt on the sheets of paper (this was very a very different feel from say thin water colours on the same sheet of paper). That is what it feels like while knitting something like this: like I am holding a thick marker or brush in my hand, and slowly and surely filling up the blank sheet of air with opaque colour. 

Permutating Friends of 3 Scarf Pattern

Every once in a while, you "unvent" something, in Elizabeth Zimmerman's words. To me it means new ways of doing old things, but also new ways to explain old things, and seeing relationships between diverse things that may on the face of it have nothing to do with each other.

I was recently playing Friends of 10 with my 5 year old son. The game introduces kids to the total number of permutations or ways in which you can put two positive numbers together to make a bigger number. So, for example, there are 11 ways (not counting commutativity, in math terms, since 1+ 9 is the same as 9+1 in our number system), by which you can make the number 10:

• 0 + 10
• 1 + 9
• 2 + 8
• 3 + 7
• 4 + 6
• 5 + 5
• 6 + 4
• 7 + 3
• 8 + 2
• 9 + 1
• 10 + 0

The most interesting thing is that counting this way, there are always an odd number of ways in which you can produce an even number. So, for example, there are 11 ways (count the bullets above) to make the number 10. And, in beautiful contrast, there are always an even number of ways in which you can produce an odd number. So, for example, there are 2 ways to produce the number 1: (0+1), (1+0). 

So, what does this have to do with a pattern? Well, here goes. I was crocheting as I played with him, and I kind discovered this pattern. Then, afterwards, I searched on the net, and found several similar variants, of what is called the "waves" pattern. But, re-discovering it from the first principles, starting from a math game, really tickled me. 

Permutating Friends of 3 Scarf Pattern

We will do friends of 3, and let a slip stitch (ss) stand for 0, single crochet (sc) for 1, double crochet (dc) for 2, and treble crochet (tr) for 3. So, now, lets look at the 4 combinations of making 3: 

• 0+3
• 1+2
• 2+1
• 3+0

Are you getting the idea? It's so exciting, isn't it? 

Cast on a multiple of 7+1 stitches. For the scarf cast on a number of stitches long enough to cover the length of the scarf, and depending on the needle size.  

Now, a simple two row repeat plus a foundation row, based on our friends of 3 permutations above: 

• R1: Foundation row: ss into second chain from hook, sc, dc, tr, dc, sc, ss, *ss, sc, dc, tr, dc, sc, ss*, repeat the 7 st pattern from * to *. Turn work. 
• R2: Chain 4 (stands for the first tr), now, working only in the back loops of the previous row, dc, sc, ss, sc, dc, tr, *tr, dc, sc, ss, sc, dc, tr*, repeat the 7 st pattern from * to *. Turn work. 
• R3: Chain 1, working only in the front loops of the previous row, ss into first chain from hook, sc, dc, tr, dc, sc, ss, *ss, sc, dc, tr, dc, sc, ss*, repeat the 7 st pattern from * to *. Turn work. 

Repeat rows 2 and 3 for pattern. Make the width of the scarf as thick as you want. Cast off and finish. 

In the first row we go singing: 0-1-2-3-2-1-0

Ravelry link to project

And in the second row we go singing: 3-2-1-0-1-2-3

Ravelry link to project

Ravelry link to project

And every stitch on the two rows together makes friends of 3, so the height effectively remains constant over the two rows, and we, nevertheless, get the waves. Plus, working into the back and front loops gives a raised pronounced look that defines the waves. How exciting! 

Ravelry link to project

By the way, this is just plain old kindergarten math leading to the explanation of a crochet pattern from first principles. There is a whole section in combinatorics and higher mathematics that looks at what is called partitions: computing the numbers of ways you can put together k numbers to add up to a number n. So, technically, we were looking at a 2-way partition. Can we look at multi-way partitions for designing patterns? Always, the simple builds bit by bit to build to the complex, and this never fails to inspire me and put the wonder back into me! Hope you enjoy the pattern!   

Hello world!

On any normal day, the title of this blog is one of the most heard sentences in our house. My husband and son have moved from getting mildly irritated to now smiling and saying it before I say it these days. The main reason for starting this blog, however, is that I keep designing, knitting, and crocheting, gifting, wearing, wearing out, and never ever document the ideas. And I thought I should, even if purely for the purpose of self-learning and reflection, and to share with other woolly friends. Here are some woolly yarny thoughts to share about knitting and crocheting. I am "soms" on Ravelry.

In my "other" life, I teach design and computation at the Design Lab, University of Sydney, research complex systems and, play with complex networks. I have never placed any emphasis over distinctions between science, mathematics, design, and art: in my world, they flow seamlessly into each other. It is therefore likely that odd bits of research thoughts and ideas may flow into this blog, please bear with me.