How I use my secret code methods in a non-rectangular space

This is the basic method I used to make the Galaxite stitch pattern, though I’m going to use a much shorter word to make things quicker to explain.

Sky in base 6 becomes 31 15 41. In my description of how I do my secret code charts, I’ve called the method I used for laying out the code in the diamonds, “adding it all up“, but it’s not really well described, I think. (I’m going to be rewriting that whole section of my site; when I got Sequence Knitting, I instantly realized that this particular method uses the spiral form of sequence knitting.)

If I pretend that each digit of the code represents a word, I can write out each of those “words” by counting out that many squares in the chart, and then marking the next square. (This helps account for encodings that contain zeros—sky is quite unusual in not having a single zero in it.)

I usually start in the bottom right corner of my charts, as if I’m knitting. If I mark out 3 1 1 5 4 1 on one row of a chart, starting on the right, here’s what I get:

sky 1 rowThree light squares, marked off by the black square in the fourth square. Then one light square, marked off by the black mark in the sixth square, and so on. Sky in base six takes up a total of 21 squares (the same as adding up all the digits and then adding on the number of digits used to encode the word: 3 + 1 + 1 + 5 + 4 + 1 + 6 = 21.)

That’s my sequence. Now I can lay out my sequence on rectangles of different proportions; they don’t have to be exactly 21 squares in area, though they can be.

Imagine that the white squares are knit and the black squares are purled (they could be anything, but that’s an easy substitution. Now, cast on seven stitches in the round and work the sequence above; it will fill three rounds perfectly, as shown below. Alternately, cast on six stitches; it won’t quite fill four rounds. This is where I depart from the regular form of sequence knitting, which would continue to fill the space (the code would stop working if I did that).

sky in other rectanglesIn the four row version, there are three extra spaces at the end of the fourth row. They don’t matter for the purposes of the code; there’s no black square following them, so we don’t have to count them.

Now, it turns out that the pieces don’t have to be cut into equal lengths. I first realized this with Beloved, which is also tiled diamonds, though I didn’t explain it in detail at the time.

I did introduce an added complication at that point; I wanted to outline the diamonds to help define the code more clearly since it’s not a rectangle. I’m not entirely sure this is necessary, or even helpful. Still, it’s how I’ve done things so far; what do you think?

The end squares of each row of diamond are marked in orange. I don’t place a black marker in those squares. They act as margins between the diamonds.

Here’s the blank diamond I started with.

whole diamondBecause I like symmetry, I cut the diamond in half before putting the sky sequence into it.

half diamondSo, keep in mind that I treated the orange squares as being off limits.

sky 1 row

Here’s the long row of sky, just as a reminder.

There are 2 squares available on row 1. The first two squares of sky are blank, so no black squares will go on row 1, and squares 1 and 2 are now accounted for.

rows 1 and 5There are 5 squares available on row 3 (I’ve hidden the alternate rows because those will be plain knitting), so the contents of squares 3 through 7 will go on row 3.

row 5There are 8 squares available on row 5, so the contents of squares 8 through 15 are placed there.

row 7There are 5 squares on row 7, so squares 16-20 go there.

half sky

And finally, there are 2 squares on row 9, so square number 21 goes there, with one square left over in the diamond. All of the sky sequence has been placed on this half diamond.

whole skyHere it is, mirrored, making the diamond to be tiled.

sky diamond orange squares

Here’s the diamond tiled in a crescent shawl, with the orange boundary squares still present.

sky diamond no orange squaresAnd with the orange squares removed.

To turn this into an actual stitch pattern, the knitter would need to work out what kind of stitch was represented by the black squares and then work the knitting accordingly. When I design lace, each black square is replaced by a yarnover, and then I figure out where to place the decreases and any decorative stitches.

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