Asymmetry or Symmetry?

(This is part of a series of posts on different ways of hiding meaning in your knitting.)

Table of Contents: Embedding meaning in Your Knitting | Converting Words to Numbers | Making a grid | Possible layouts | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Further Resources

You might be perfectly satisfied with the grid you have without any further modification. If so, you'll want to skip to "Converting grids into stitch patterns".

The first step in deciding this is to lay out multiple repeats of your stitch pattern to see if you like it as an all over design (if that's what you're after, of course).

If I take the base 6 version of peace from "Making a Grid"



and repeat it three times in each direction, I can get a sense of how the repeats interact at the edges:



This has distinct possibilities as it is, but let's see what happens if I play with it some.

The first obvious variation is to mirror it. Here it is mirrored horizontally:



Or if you don't like the doubled squares at the edges, you can overlap them:



Here is the latter, in a three by three repeat:



Now mirror it in both directions:



and see how it looks repeated, this time three times horizontally by two vertically (because the symmetry makes it easier to see how the repeats interact).



If the grid has more white space than you like and you're not making a secret code, you can mirror the grid on itself so that it's doubled (shown in two colors to make the mirroring clearer):



If you have an even number of squares, you can again eliminate duplicate columns if you'd like:



And here is the allover layout of the latter:



These are probably enough ideas to be going on with, but if you'd like to try out some other variations (whether with the original asymmetrical grid or the mirrored), have a look at the pattern design resources in Further Resources.

Just for an example, one basic pattern repeat variation you'll find is the half drop, asymmetrical:



and symmetrical:



If you would rather comment on Ravelry, I've cross-posted there.


Next post: Converting grids into stitch patterns.

Making a grid

(This is part of a series of posts on different ways of hiding meaning in your knitting.)

Table of Contents: Embedding meaning in Your Knitting | Converting Words to Numbers | Making a grid | Asymmetry or Symmetry? | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Further Resources

There are several ways to turn a short sequence of numbers into a grid that can be turned into a stitch pattern chart. I'm going to demonstrate the ones I can think of. Once I've generated some grids, I'll explain how to convert them into knitting charts.

The word that I'm going to use for my examples is peace. Working my way across my table for encrypting letters as numbers, I get the following possibilities: 1605010305, 1705010305, 2005010305, 2205010305, 2405010305, and 8069656769. (You'll note that since most of the letters are smaller than 6, they're identical in most of the variations.) The Dewey Decimal number for peace is 303.66. Watch out for those zeroes!

Keep in mind the difference between inspiration and encoding: if you're going to make a secret code with a friend, you'll need to always use the same method of choosing numbers, never omit zeros, and always use the same layout method. If you're using meaning as a springboard for design that doesn't need to be decipherable, you can be more flexible.

One concept per line

If you have multiple meanings you want to incorporate, you can sometimes make a pattern that puts one meaning per row of the grid. Here, for example, is a grid of the Dewey Decimal numbers for peace (303.66) and knitting (746.432). Peace is the first row; knitting the second. I counted from right to left for both rows, and decided to count ten for the zero.



If I wanted to, I could make the knitting line slightly shorter than the peace line; this can be accommodated with increases and decreases. If the difference in repeat length had been drastic, I would try repeating the shorter set of numbers again. As it is, I just filled in with a couple of blank spaces.

Plotting the numbers on an X,Y grid

If you treat the number of the base you're using as one axis of the grid you're filling, and the number of digits you're encoding as the other, there's some more variations possible. I'm going to show peace in both base 10 (the one we usually deal with in everyday math) and in base 6.

The letters in peace converted into base 10 are 1605010305; converted into base 6, they're 2405010305. There's ten digits regardless.

I have chosen to leave in the zeroes. In the base ten grid, I'm putting them in the tenth square; in the base six grid, in the sixth.

Here is the base ten grid. I've started in the bottom right corner again (though really it's arbitrary). For this grid, I'm counting which digit it is from right to left, and then plotting the value of the digit vertically. So the first stitch is in the first row, the second in the sixth, the third in the tenth, and so on.



Here is the base six grid. I've started in the bottom right corner again (though really it's arbitrary). Zero is marked in the sixth column. For this grid, I'm counting which digit it is from bottom to top, and then plotting the value of the digit horizontally. So the first stitch is in the second column, the second in the fourth, the third in the sixth, and so on.

Adding it all up

A method of laying out a grid which can result in denser stitch patterns involves a little basic arithmetic (addition and division).

Take the individual digits of the number you've come up with and add them together. Then see if you can divide it evenly; if not, we'll pretend it's the next number up. If the grid uses the exact number of squares, the last stitch marked will be in a corner; if you skip to the next number, the final corner will be empty.

For this section, I'm going to pretend I don't have any zeros. The digits from 1605010305 add up to 21, which is 3x7. The digits from 1705010305 add up to 22 (2x11); from 2005010305, 16 (4x4); from 2205010305, 18 (3x6); from 2405010305, 20 (2x10); from 8069656769, 62 (2x31. That would make a very long and skinny stitch pattern; we could pretend it's 63, which is 7x9). I'm not going to show grids for all of these; it would take too much space.



For the first grid, I worked my way back and forth as if knitting flat. For this one, I used the ASCII numbers. I started in the bottom right, counted 8, then counted 6, then 9 and so on. Each time I got to the end of a row, I turned around and continued the count on the next row. You will note that since my grid didn't have the exact number of squares that there's a blank square left over at the end.



In the second, I did all my counting from right to left. If I couldn't fit all the stitches on a row, I continued the count on the next.

Each of these grids has possibilities for being turned into a stitch pattern, and you can see them knit up in swatches.

If you would rather comment on Ravelry, I've cross-posted there.

Next blog installment:Ways of rearranging the grids to make more symmetrical patterns, if desired. The entry after that discusses making the grids into actual knitting stitches.

Further Resources

(This is part of a series of posts on different ways of hiding meaning in your knitting.)

Table of Contents: Embedding meaning in Your Knitting | Converting Words to Numbers | Making a grid | Asymmetry or Symmetry? | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Further Resources

Novels with secret codes in fiber arts

• Dickens, Charles. A Tale of Two Cities. (knitting; historical fiction)
• Jones, Diana Wynne. The Spellcoats (spinning & weaving; children's fantasy; part of a series)
• Wrede, Patricia and Caroline Stevermer. The Grand Tour or The Purloined Coronation Regalia. (knitting; YA alternate history/fantasy; part of a series)

Knitting codes

• Batten, Wayne. "Madame Defarge's Knitting Cipher". Wayne Batten's Web Pages for Montgomery Bell Academy. 23 July 2009. [http://home.montgomerybell.edu/~battenw/Defarge%27s%20code.htm]. Accessed 7 Feb 2011.

Encryption & Steganography

• Subject headings to look for at a library:
  • Ciphers.
  • Cryptography.
• "How to Create Secret Codes & Ciphers". WikiHow.com 7 Mar 2011. [http://www.wikihow.com/Create-Secret-Codes-and-Ciphers]. Accessed 8 Apr 2011.
• Hipschman, Ron. "The Secret Language". The Exploratorium. 1995. [http://www.exploratorium.edu/ronh/secret/secret.html]. Accessed 7 Apr 2011.

Pattern Repeat Design

• Subject heading to look for at a library:
  • Repetitive patterns (Decorative arts)
• Proctor, Richard. Principles of pattern design.
• "Symmetry and Pattern Design Resources". Artlandia. 2010. [http://www.artlandia.com/wonderland/#Textile-design] Accessed 23 Apr 2011.
• Waterman, V. Ann. Design Your Own Repeat Patterns: A Quick and Easy Approach.

Converting words or letters to numbers

(This is part of a series of posts on different ways of hiding meaning in your knitting.)

Table of Contents: Embedding meaning in Your Knitting | Converting Words to Numbers | Making a grid | Asymmetry or Symmetry? | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Further Resources

A first step in converting words to knitting (or other fiber arts) is to convert letters to numbers. An obvious way to do this is to assign a number to each letter. The simplest way to do this is to use decimal numbers, assigning A=1, L=12, and Z=26. This can produce nice results.

If you don't like the way the stitch patterns come out, you can translate the numbers into different base systems. I've provided a chart at the bottom of this post for numbers in base 10 down to base 6, as well as ASCII values. Other possibilities for conversion include binary, Morse code, or Braille.

Another option is to use the numbers on a telephone keypad, though this would be a one-way cipher; it would be tricky for someone looking at your stitch pattern to turn it back into the original letters, even if you wanted them to.

Using ASCII values for letters also works. (And in fact, if you look at the complete list of ASCII values online, you get upper and lower case and punctuation.) Finally, there are various encryption techniques that turn words into numbers.

The last way I've thought of to convert meaning to numbers (and my favorite) is to use the Dewey Decimal System—one of the methods librarians use to assign call numbers to books so they can be shelved according to their primary topic. The best resource for this (because it goes into the most detail) is the set of books that lists all the Dewey numbers in it. To use this, you'll need to go to a library that uses Dewey for its call numbers; I recommend calling the library reference desk to find out if they have the books available for you to use.

A good backup system is to use WorldCat. Do a subject search for your meaning. If that doesn't produce results, do a keyword search, and then pick a likely looking subject heading. On the detailed record page, look for the Dewey Decimal number for the books that come up. The one that appears most often is probably the Dewey Decimal number for your topic.

Finally, if you enjoy the idea of encryption, there are a number of techniques for putting words in secret code, which you could then further encode as knitting. See Further Resources for some suggested links.

The Problem of Zero

Once you've generated numbers to use in your stitch patterns, you'll be using those numbers to count stitches or squares on a grid. Counting to zero can be tricky. One option is to add one to every digit, so that 0 is 1, 5 is 6, and 9 is 10. Another option is to turn zero into ten. A third option is to ignore all zeros. Note that this will make your code one way: decryption will be nearly impossible, even for someone who knows the code.

If you would rather comment on Ravelry, I've cross-posted there.

Letter Conversion Table

	10	9	8	7	6	ASCII
A	01	01	01	01	01	65
B	02	02	02	02	02	66
C	03	03	03	03	03	67
D	04	04	04	04	04	68
E	05	05	05	05	05	69
F	06	06	06	06	10	70
G	07	07	07	10	11	71
H	08	08	10	11	12	72
I	09	10	11	12	13	73
J	10	11	12	13	14	74
K	11	12	13	14	15	75
L	12	13	14	15	20	76
M	13	14	15	16	21	77
N	14	15	16	20	22	78
O	15	16	17	21	23	79
P	16	17	20	22	24	80
Q	17	18	21	23	25	81
R	18	20	22	24	30	82
S	19	21	23	25	31	83
T	20	22	24	26	32	84
U	21	23	25	30	33	85
V	22	24	26	31	34	86
W	23	25	27	32	35	87
X	24	26	30	33	40	88
Y	25	27	31	34	41	89
Z	26	28	32	35	42	90

Forthcoming post: Placing numbers on a grid so they can be turned into stitch patterns.

Embedding meaning in your knitting: Index

Table of Contents: Embedding Meaning in Your Knitting | Converting Words to Numbers | Making a grid | Asymmetry or Symmetry? | Converting grids into stitch patterns | Lace | Cables | Other Encodings | Summary of My Method | Further Resources

I've known about Madame Defarge and her knitting code from A Tale of Two Cities for a long time, and have read a number of novels which include the idea of encrypting things in fiber arts. This may be what subconsciously inspired me to encode meaning in my Secret Code of the Librarians shawl (still in progress) and then to write up this series of posts.

Sometimes we knit for a special occasion: a wedding, a birth, graduation from college. In those cases, the beauty of someone else's design can be wonderful, but it can also be fun to create something new for the occasion. Why not combine the birth dates of two people who are marrying in a special gift, or perhaps encode their names into it?

You might be knitting a gift for someone who is ill--why not knit your wishes for good health into the design? Or if, like me, you wish you were more patient, you could knit yourself a shawl with "patience" hidden in the stitches.

Choosing Words or Numbers

A first step in converting meaning to knitting is to find a way to express that meaning in numbers.

To reduce the number of steps involved, the easiest thing is to pick numbers that are meaningful: dates, phone numbers, and so on. Dates have the further advantage that they can be expressed in a variety of different ways. Take the third of May, 1990. 1990 could also be written as 90. Three could be either 3 or 03, five could be 5 or 05. The five could come first or the three could come first (depending on whether you use US date order or not). The different configurations of dates will change the way your stitch patterns can be arranged, providing better flexibility in their appearance.



(This code swatch was knit using the date I started college.)

You can also combine multiple dates in one stitch pattern: if making a stitch pattern for a wedding shawl, you could use the engagement date and the wedding date, or the birthdates of the people getting married.

Some of the methods I'll explain later lend themselves more to writing long sequences of words, but I particularly like choosing one or two words to convert to numbers and then to stitch patterns.

I have limited these posts to the craft of knitting, but I am certain that some of the techniques I mention could be translated into other crafts. I would love it if someone gave it a try.

If you would rather comment on Ravelry, I've cross-posted to my group there.

Next post: Converting words or letters to numbers

(This series of posts assumes you are familiar with reading knitting charts.)