Laying out the numbers on a rectangular grid: method 4

This is the next part of my rewrite of my instructions for turning words into knitting charts (or charts for other crafts). Once the letters have been turned into numbers, they need to be charted on a grid. I already posted three ways of making rectangular grids with the numbers; this is the fourth way.

This is the method I tend to use most often for my lace stitch patterns, though it varies from word to word.

Where methods 1-3 for laying out numbers on a grid are all pretty similar—like graphing numbers using X,Y axes—method 4 is quite different. I think of it as being more like writing, though the direction I work in for placing the marks on the chart is the same as if I were knitting. This direction doesn’t really matter, though I prefer to be consistent in the beginning stages at least.

There are a couple of metaphors for how this method works.

The one that came to mind when I created it is that the the marks on the grid are like the spaces between written words: they help us know where one word stops and the next begins. There is this difference: instead of marking words on the grid, I’m marking the spaces between numbers. Each number is represented by a line of white squares equal to that number, with a black square following to show where the count ends.

My friend Katherine came up with the second metaphor, obvious in retrospect: the black squares are like the stitch markers in knitting. Count a certain number of stitches and then place a stitch marker, or count a certain number of white squares and then place a black one.

For the example layouts below, I’m going to use the telephone keypad numbers for peace: 73223. I’m doing this because it drastically reduces the number of possible options and makes all the charts smaller.

One of the advantages of this method is that it allows making multiple rectangles with different proportions and gives many more choices for the final appearance of the chart.

If you’re comfortable with arithmetic, you can calculate ahead of time how many squares will be needed. First count how many digits are to be charted, and then add that number to the sum of all the digits. There are 5 digits in 73223, so add 5+7+3+2+2+3 to get 22.

If you’re not comfortable with arithmetic, it’s not really important; it can be worked out along the way. I like doing both as a way of checking my work.

First make a grid that is 10 columns wide by a bunch of rows tall. Just make a guess about what seems reasonable. You can add more if needed while you’re charting, whether you’re using software or graph paper.

Peace method 4 10 columns 1I start in the bottom right corner as if knitting. Count 7 white squares, mark the next. The next digit is 3, but I can’t fit that in the two squares remaining on the first row. No matter: I count those 2 squares, then count the 3rd square on the next row, again working from right to left. Then I mark the next square. Then count 2 squares and mark the next, and so on, jumping to more rows as needed. The last marked square is in the third row, so I can cut off all the rows with no marks in them:

Peace method 4 10 columns 2There are some extra squares left over after the last black one, but that doesn’t matter for the code. Since there is no further mark after them, the knowledgeable knitting code chart reader will know not to count those squares.

Now I can easily count the minimum number of squares I need for the remaining charts: I’ve used 2 full rows of 10 squares each, which makes 20, and then I’ve used 2 more squares from the third row. 20 + 2 = 22 squares.

(Or you can make any further charts the width you want, leave room for a bunch of rows, and then cut off the unused rows as before.)

There are no zeroes in the set of digits I’m using, but if there were, the principle would remain the same: count 0 squares, then mark the next. Yes, this can mean two black squares in a row. For some encodings, it can mean three black squares in a row. (I’m cautious about using those for lace.)

The second version of the Method 4 chart for 73223 is 9 squares wide. The next larger multiple of 9 that will fit 22 squares is 27, or 9 x 3. My next rectangle will be 9 columns wide by 3 rows high:

Peace method 4 9 columnsAn 8 column rectangle again requires 3 rows:

Peace method 4 8 columnsHowever, a 7 column rectangle requires 4:

Peace method 4 7 columnsAs does a 6 column rectangle:

Peace method 4 6 columnsIf you’d like a square chart, a 5 column rectangle needs 5 rows:

Peace method 4 5 columnsA 4 column rectangle needs 6 rows:

Peace method 4 4 columnsA 3 column one, 8 rows.

Peace method 4 3 columnsAnd out of order, an 11 column one just needs 2 rows.

Peace method 4 11 columnsI’m including this one because it shows what things look like when the last mark ends up in the final square of the rectangle.

I usually lay out all the rows in Method 4 from right to left, as if I were knitting in the round. There is an alternate version that could be used as if knitting flat, where alternate rows are laid out from left to right. In Sequence Knitting, stitch patterns that alternate direction like this are called serpentine (because they wind back and forth). Some old manuscripts were written this way (with the letters facing the other way!); this writing style is called boustrophedon. Feel free to try it out, though I give no examples here.

There are two general options at this point: first, work with the grid as it is, and second, play with the possible symmetries.

Please let me know if any of this is unclear or if you happen to notice any errors. Thank you!

One thought on “Laying out the numbers on a rectangular grid: method 4”

Leave a Reply

Please log in using one of these methods to post your comment: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.