Ridges

What do you do when you pick up a yarn that is absolutely beautiful in terms of the yarn quality, and absolutely difficult in terms of the colour palette, and you picked it up just because you were getting 800 metres of pure lace goodness for $3? (I sometimes wonder, does anyone else do this?) 

This one (3 balls of it for $9) were bought last year Christmas sales, and has been sitting there, I did not know what to make of it. It has a bright shade of blue, followed by a bright shade of neon green, followed by a dark sienna type shade and for some strange reason is called Apple Mix! On the good side, its wonderful to feel and you can tell it is good wool, and a pleasure to knit with. 2 ply. 

So, after much thought, raveling and unraveling, I am happy to be producing something that REALLY suits the crazy colour scheme - its looking wonderfully textured and ripply, as THICK RIDGES, feels all mountainy-greeny-skyish and most importantly, wearable as a super casual T-shirt - jeans kind of scarf. I am happy to have rescued it :) 

Stitch Pattern Notes: No lace (colours too wild), knit only, no purls, yarn held double throughout. Aim: Produce nice thick but soft fabric, to show off the colours but also to mix them sequentially. Ripple increases and decreases on the right side, All knit on the wrong side. Increases: yarn over, knit, yarn over. Decreases: slip two stitches, knit one, pass two slipped stitches over. On the wrong side, to prevent lacy-ness: knit through the back loops of the yarn overs. Put as many stitches as you want for the "slopes" between alternate increases and decreases, I have put 6 here.  

Elf Leaf Scarf

Designed a super simple pattern, inspired when reading The Hobbit with my son :) The Elf Leaf Scarf. 

Pattern

I used 2 50 gram Splendour Yarn balls from Lincraft (Australia) with 4 mm needles. But, the pattern is easy to make in any yarn, since you can use the "principle" and vary the number of base stitches, more stitches for thinner yarn, lesser for thicker yarn. The "principle" is to alternate between an increase part and a decrease part, while maintaining the central leaf vein. The increases and decreases all happen on the side of the piece and the vein is maintained in the centre. Super simple, really. 

Make 2 pieces exactly the same, then join by the Kitchener Stitch. 

Knit = K

Purl = P 

Slip, Slip, Knit: ssk

Knit 2 together: k2tog

Pass Slipped Stich Over: psso

Yarn over: yo

Slip a stich: sl

For all rows, slip the first stitch purlwise. 

Edge: 

Cast on 41 stitches. Preparatory Rows (PR):  

PR1: K19, sl 1,  k2tog, psso (you have reduced by two stitches), K19.

PR2: Knit. 

Repeat preparatory rows 1 and 2 till you have 17 stitches left. That is, from 41 stitches, you are down to 17 stitches, or the "thinnest" portion of the scarf.  

Body: 

Increase

Start on right side with 17 stitches. Increase rows (IR):   

IR1: K8, yo, K1, yo, K8. (19 stitches) 

IR2 and all even rows on wrong side: K5, p to last 5 stitches, K5. 

IR3: K9, yo, K1, yo, K9. (21 stitches)

IR5: K10, yo, K1, yo, K10. (23 stitches)

Continue in this way till you have 41 stitches (or back to the original number cast on).     

Decrease

Start on right side with 41 stitches. Decrease rows (DR): 

DR1: K5, ssk, ssk, K11, yo, K1, yo, K11, k2tog, k2tog, K5. (39 stitches)

DR2 and all even rows on wrong side: K5, p to last 5 stitches, K5. 

DR3: K5, ssk, ssk, K10, yo, K1, yo, K10, k2tog, k2tog, K5. (37 stitches)

DR5: K5, ssk, ssk, K9, yo, K1, yo, K9, k2tog, k2tog, K5. (35 stitches)

Continue in this way till you have 17 stitches (or back to the thinnest portion of the scarf). Last row in this section will be K5, ssk, ssk, yo, K1, yo, k2tog, k2tog, K5. 

Keep working the Increase and Decrease portions till you have reached a length equal to half the desired length of the scarf, and end after working an increase portion. On a 4mm pair, I did 4 full repeats (increase + decrease) and then an increase (that is, 4 and a half repeats). Make 2 pieces exactly the same, and join the 41 stitches (or the number cast on) with the Kitchener Stitch. 

Wash, Block, Wear, Gift!

Baby surprise jacket, cap, and simple blankie

My mum is here, visiting for a couple of months. And when mum or mum-in-law are visiting, somehow, my knitting and crocheting activity peaks up. Has to be one of the best friendly things in the world, just sitting in the sun with a hot cup of tea and coffee and making new things. 

So a good friend's baby shower brought out this joint effort. It is the very first time I have made the EZ's Baby Surprise Jacket. Actually, I did not make it, I "instructed" my mum, reading out the EZ instructions, and mum made it. And she did the cap. 

Like so many of her generation, my mum does not knit from written instructions - and while I marvel at the amount of knitting knowledge my mum, grandma, and mum-in-law simply carry in their heads and execute it at the right time, they instead marvel at all those wonders that exist in the knitting world, that they never knew about because they never "read" knitting. Like this Baby Surprise Jacket for instance - my mum was just completely bowled over by the construction of it, and she was anticipating the outcome like a little child while she was making it, and chuckling like a little child by the end of it! 

The blanket - well that's another story. Sometime last year, I had these two balls of Paton's Baby yarn, a very baby yellow, with no complete project coming out of it. So, mum-in-law (who was visiting then), sat and did these yellow squares, and we hoped that someday it would turn into something. And so, last week, I got some white, and turned it into a baby blanket, all ready for the new baby to arrive. Work is super busy right now, so this has to be the quickest bit of crochet I have ever done, trying to find odd bits of time to joining a square here and a square there (there was a time deadline, the baby shower invite). And yes, I did follow EZ's instructions and had it hanging around the kitchen, and even with my Mac on the train! (I can sometimes produce code and woolly things together, funny the two processes actually help each other). 

So, this gift had the fortune of having three knitters on it, me, my mum, and my mum-in-law, a true family project, a super welcome for a super new baby. 

Textured Ripples Blanket

Its been an amazingly long time away from writing - and a lot has happened. Work and life have taken over. But, here I am, very early morning, everyone else sleeping, with a warm cup of tea, and I remembered my blog again. 

I want to share a pattern today. Once I took my 6 year old little man to the wonderful Attic24 blog, and showed him photos of the wonderful work there. That blog, for me, as well as for countless others, is a constant source of inspiration (what an understatement, but I have to say it!). 

As little designers will always have the strong reactions of utmost clarity, so did he. He pronounced his decision: "I want a blankie with these many colours, however, I do not want the soft ripples. I want a blankie with many many colours, and I want the waves to be BIG and POINTY and VERY WAVY". 

I set to work. Here is what came out. And my little man has been warm and happy and snuggly and overjoyed with it, which made me very happy. 

I wanted to add some texture to the two sides, so that the edges of the blanket are even more big and pointy and wavy than the middle, to give it a nice definition. So, the edges look like this.

From one side: 

And from the other side: 

And the middle looks like this. 

So here is the pattern for BIG, POINTY, WAVY blankets. 

Pattern: Done over a multiple of 17 stitches. 

You can cast on any multiple of 17, as long as you cover a desired length of the blanket. Note that this blanket is made length-wise, not width-wise, but of course, this was a personal choice. I thought the ripples looked fantastic running along lengthwise. I cast on about 15 repeats, on a 6 mm crochet hook, so (15 X 7 = 105) chains. 

US terms

ch: chain

sc: single crochet

hdc: half double crochet

dc: double crochet 

Ch 105, or any multiple of 17 (with a larger hook). 

Textured edge pattern:

Use a hook 1 mm thicker than the main project. That is, if you are using a hook size of 5 mm for the main body of the project, use 7 mm for the edge. The reason is that we will be using single and half double crochet for the edge, so the same hook size may give a smaller, more "compressed" edge, and the blanket won't turn out a perfect "rectangle" but a sort of rectangle distorted inwards at the edges. 

Set up row: 

Chain 3 (at the end of the 105 chains), hdc into 4th chain from hook, 6 hdc into the next 6 ch (climb up the wave), 3 hdc all into the next ch, 7 hdc into the next 7 ch (climb down the wave), skip 2 ch, *(7 hdc into the next 7 ch, 3 hdc all into the next ch, 7 hdc into the next 7 ch, skip 2 ch)*, repeat from * to *, end with 7 hdc into the next 7 ch (climb down the wave).

First row:

Change color and turn work. We will now be working out of the back loops of every hdc of previous row. This is what will give the textured pattern. 

Ch1, working into the back loops of the hdcs of the previous rows only, sc into 2nd ch from hook, 6 sc into the next 6 hdc (climb up the wave), 3 sc all into the next hdc, 7 sc into the next 7 hdc (climb down the wave), skip 2 hdc, *(7 sc into the next 7 hdc, 3 sc all into the next hdc, 7 sc into the next 7 hdc, skip 2 hdc)*, repeat from * to *, end with 7 sc into the next 7 hdc (climb down the wave).

Second row: 

Change color and turn work. We will now be working out of the back loops of every sc of previous row. This is what will give the texture (also). 

Ch2, working into the back loops of the scs of the previous rows only, hdc into 2nd ch from hook, 6 hdc into the next 6 sc (climb up the wave), 3 hdc all into the next sc, 7 hdc into the next 7 sc (climb down the wave), skip 2 sc, *(7 hdc into the next 7 sc, 3 hdc all into the next sc, 7 hdc into the next 7 sc, skip 2 sc)*, repeat from * to *, end with 7 hdc into the next 7 sc (climb down the wave).

Repeat this two rows for a very thick nice textured edge. I made about 22 of these rows (set up row, about 10 first rows and 10 second rows, one more repeat of the first row). The ripples will be very pointy. You can also try smaller or larger number as the base number, that is a number other than 17, keeping in mind the ripple design basic: equal number of stitches for climbing up and down the wave, and 3 on the top of the wave, and missing two at the bottom of the wave. What a marvellous symmetry!

Main body

Change hook to 6 mm (or 1 mm lower than hook used for edge). From now on, we will be working with dcs, and not into the back loops, but normally. 

First row: 

Change color and turn work. 

Ch3, dc into 2nd ch from hook, 6 dc into the next 6 sc (climb up the wave), 3 dc all into the next sc, 7 dc into the next 7 sc (climb down the wave), skip 2 sc, *(7 dc into the next 7 sc, 3 dc all into the next sc, 7 dc into the next 7 sc, skip 2 sc)*, repeat from * to *, end with 7 dc into the next 7 sc (climb down the wave).

Repeat this row as many times as needed to give you the width of the blanket. 

Textured edge again

When the main body is up to the desired width, change hook size to 7 mm (or 1 mm larger than the one used for the main body) repeat the textured edge pattern again, for the same number of repeats as the beginning. 

That's it! Enjoy and hope you have a lovely pointy ripply time!

Randomized Permutations and Partitions

A little while ago, I posted the Permutating Friends of 3 Scarf Pattern. I also joined the Woolly Thoughts group on Ravelry, and started talking to the great folks there. Woolly Thoughts is one of a kind: combining math and generative knitting, and it turned out that at some point, they too had thought about putting together knitting with permutations. And so, some crazy new thoughts emerged in my head.

I was basically pondering on the idea of scaling and visualizing permutations and partitions: how quickly things scale up in mathematics, (for example, see this link on MathStackExchange), and therefore, how quickly it becomes completely impossible to visualize these permutations and patterns exhaustively. So, if I left out the constraint on exhaustive visualization, the design challenge is to come up with a pattern that plays with any number of partitions of any given number. So, relaxing the requirements on exhaustive visualization where ALL possible k-partitions have to be visualized, could I simply use randomization as a generative idea? I also deliberately wanted to leave k and n as parameters, since that way using a single idea we can produce as many patterns as we would like, but at the same time ensuring that no two patterns are the same! 

So, I quickly put together some Matlab code: a function to generate randomized permutations of k-partitions of any given number n. Code is attached at the end of this post, please feel free to use it or modify it in any way, but please acknowledge this original source if you do. 

Here are some interesting results:

Say you want to generate randomized partitions of the number 30 into 2 colours. Cast on 30 stitches in colour 1 (blue), use the good old garter stitch, and simply follow the chart here (this came out of the Matlab program by setting n = 30, k = 1). The magic of this type of computation, of course, is that every time you run the program, it will show you a different pattern.

To follow the chart, every row shown needs to be knit twice in garter stitch. So, for example for the square below:

1. Row1: Beginning from the bottom right, k1 in colour 1 (blue), change working yarn, and k29 in colour 2 (red). 
2. Row 2: Turn, k29 in colour 2, k1 in colour 1.
3. Row 3: In the next row, there are 18 stitches of colour 1, 12 of colour 2. So, k18 in colour 1, carrying along the colour 2 yarn, then k12 in colour 2. 
4. Row 4: Turn, k12 with colour2, and k18 with colour 1. Sine in the subsequent row, the pattern is k10 with colour 1, and k20 in colour 2, carry colour 2 along loosely by knitting the first 4 stitches in colour 1, bringing yarn forward, twining colour 2 yarn around working yarn, taking working yarn back again, and continuing to do this, till you reach the colour 2 yarn to the correct stitch. 
5. Row 5: K10 with colour 1, k20 with colour 2. If you have brought yarn forward from the previous row, colour 2 yarn should be available to knit at the correct stitch. 
6. Row 6: K20 with colour 2, k10 with colour 1. 
7. Row 7: K18 with colour 1, when you come to colour 2 after 10 stitches (refer to previous row), carry along colour 2 yarn along back of work in the usual way of twining around the colour 2 yarn around main working yarn for 8 more stitches, then k12 with colour 2. 

Continue in this way, bearing in mind to look at the subsequent row and deciding to what stitch number you must carry along the other yarn. I will try and post a photograph of a completed square soon. 

Here is a 3 colour pattern of 30 stitches:

Here is a 4-colour pattern of 30 stitches:

And then, the obvious next step is that you can start putting them together to bring out afghan patterns or wall hangings. Here is one in which 9 different squares of 100 stitches on standard 4 mm needles can be put together, with 3 colours (all the 9 squares are unique): 

Here is one in which the same square is knitted 9 times, and put together one after the other:

And here is one in which the same square can be knitted 12 times, and you can rotate, invert, or do anything you like to produce interesting variations:

Here is where you can go crazy, set n = 300 (the number of stitches, say for a full afghan on 4 mm needles), set k = 9 (this means you are looking at 9 partitions of the number 300, and using 10 colours to represent them) and follow the number chart to produce this: 

At this point you must be thinking, as the numbers and sizes go larger, how do we follow the pattern as we knit? The program below produces a matrix of numbers called R, along with the visual representation. After you choose and fix a colour paletter, R tells you the count of stitches, row by row, that you knit for each successive colour. So, for a 3 colour pattern, if the first row of R = [4, 15], this means knit 4 stitches in colour A, then knit upto the 15th stitch with colour B, and the last remaining stitches in colour C. A bit tedious for some, but not a great deal for those who are used to following charts, or doing any kind of fair-isle, or lace knitting. 

What excites me most about this kind of designing, is that, just like many known biological or mathematical generative rule based systems, all the patterns look "similar" or belonging to the same "style" or "typology" of patterns, and yet, no two of them are exactly alike! Instead of the randomization idea, the other extreme would be use a regularization idea, and put together partitions in some deterministic organized and growing way, so that regular visual patterns can emerge.

If anyone decides to knit anything using these ideas, I would love to see links to your work! If you are unable to run programs and would like me to send you some R matrices and charts, set to some number specifications, please do let me know. If someone develops another version of the program, say in something universally available, like Python, that would be most exciting too! I think the code is working fine, but if there are errors, let me know too. Enjoy :)

Ravelry link to pattern.

PS: Special note for those new to garter stitch special properties: Each coloured row in any of the above patterns here to be produced by using two rows of garter knitting, that will produce 1 "ridge". Thus, each coloured row means two rows of knitting. Carry along the yarns as needed for the next row. 

function [A,R] = randomizedPartitionSquare(n,k)

%Function to generate randomized partition squares

% Author: Somwrita Sarkar

% Version: 1

% Date: 6 Jan 2014

% n is the number of stitches, that is the size of your knitted square

% k is the number of partitions. For example, if k = 1, then a number can

% be divided into 2 parts, for example, 5+5 = 10; if k = 2, one possible

% partition is 1 + 1 + 8 = 10; and so on. The number of colors needed to

% knit the square is equal to k+1. 

% Run the program as many number of times as the needed numbers of squares.

% Since each square pattern is going to be different, you can think of

% innovative ways to put them together. 

% Examples to run code:

% 

% Generate initial matrix / square

A = zeros(n,n);

% Now generate the square

for i = 1:n % for each row

    for j = 1:k

        r(j) = floor(rand*n); % generate partition vector

    end

    r = sort(r); % sort it in ascending order

    R(i,:) = r;

    p = 1; % set initial counter for number of columns

    c = 1; % set initial color counter, starting color 1

    for m = 1:k 

        A(i,p:r(m)) = c; % first partition set to color 1

        p = r(m)+1; % then add number of columns, i.e., for next loop, p goes to (r(1) + 1:r(2));

        c = c+1; % for next loop, next color, i.e., color 1 goes to color 2, etc. 

    end

end

figure

imagesc(A)

% % Initial code for a 3 partition

% for i = 1:n

% r1 = floor(rand*30); % partition 1

% r2 = floor(rand*30); % partition 2

% if r1 < r2

% A(i, 1:r1) = 1;

% A(i,(r1+1):r2) = 2;

% end

% if r1 > r2

% A(i, 1:r2) = 1;

% A(i,(r2+1):r1) = 2;

% end

% end

% figure

% imagesc(A)

end

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!