mathematical knitting

knitting patterns have a certain mathematical quality to them. knitting is basically a binary system - knit & purl stitches. so it's possible to knit binary sequences, letters eg convert the letters to ascii hex, then binary - some people knit their names as signatures in their work.

people knit in fibonacci sequences and end up with patterns and colours / stripes that somehow seem natural, just as the fibonacci sequences showing up so much in nature.

so I'm keeping a list of some patterns and urls for sites on logical / mathematical knitting.

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there's also the crocheting - such as the hyperbolic plane crocheted recently by Daina Taimina as a way to describe it physically. I need to practice crocheting though, so will stick to knitting for a while

another crochet project is the hyperbolic crochet coral reef project using patterns based on the hyperbolic plane by Daina Taimina. her website also lists an excellent collection of mathematical links

also the crocheted Lorenz manifold based on the strange attractor in chaos theory.

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Knitted Mobius bands by dr. sarah-marie belcastro

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Ada Deitz polynomials - In 1946, Ada learned to weave and figured out how to use solutions to multivariant polynomials to design patterns. These were featured in magazines at the time.

eg: the solution to (a + b) ^2
(^2 = squared)

Ada Deitz's "Algebraic Expressions in Handwoven Textiles" booklet is available on this handweaving.net page (dak_alge.pdf link) or direct link

(I made a knitted polynomial camera bag based on Ada Deitz' patterns)

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Algebraic Expressions of Handwoven Textiles article by Lana Schneider

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thomasina's Guide to Geeky Knitting lists all sorts of mathematical and biological knitting, using the following categories :
Geology and Paleontology; Biology : Microscale: Genetics and Microbiology, Macroscale: Anatomy and Ecology; Mathematics : General, Topology, Probability, Chaos, and Fractals, Sequences and Geometry, Tessellation; Computer Science; History; Linguistics.

she also mentions String, and Knot, Theory of Inca Writing, an article on khipu, an Incan method of writing / encrypting / encoding information using cryptic knotted strings

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Eleanor Kent's knitted textile art

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Radical Knitting Circle - an activist based knitting group

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Critical Pixels quote
[quote]
Knitting is, in itself, a remarkably rich metaphor when considering issues of gender and power; hitch this up to a discussion of computer viruses and things really start to blossom. Kirsty, for example, took the binary code from an existing virus called Code Red and converted it into a piece of knitting (in red wool, of course). Rather than rendering the virus harmless, this act was actually a form of re-encoding; one could imagine it being carried invisibly (ie worn as a garment) until the wearer decided to decode it.

There's also a certain kind of circularity at play: the earliest programmable computers were based on the Jacquard Loom's innovative use of punchcards. The Loom itself marks a key moment in the industrialization of craft skills (cf knitting).
[/quote]

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Reference List: Mathematical Articles on Fiber Arts

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knitlist.com has an article on binary knitting

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fuzzy logic knits is another blog with links on mathematical knitting

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Home of Mathematical Knitting has links to other resources.

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knitting in mobius stitch & more instructions

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moebius scarf (different spelling of 'mobius')

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fibonacci sequence sock pattern on Fuzzy Galore's site

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Wooly Thoughts site has some great pattern books for mathematical patterns & cushion covers. I've got the Cushy Numbers pdf book and it has lots of great patterns to try. they also have a Wooly Thoughts group on Ravelry

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Elizabeth Zimmerman's books - whilst not being strictly mathematical knitting, did change the way patterns were made, and she showed many people how to knit and get the control of the patterns back to the people and away from the yarn companies.

[quote]
Her [Elizabeth Zimmerman's] "EPS" (Elizabeth's Percentage System) is still widely used by designers: it consists of a mathematical formula to determine how many stitches to cast on for a sweater, given that the sleeves and body are usually proportionate no matter what yarn or gauge is used. Other patterns and techniques for which she is well known are the so-called "Pi Shawl," a circular shawl that Zimmermann claimed was formed by regularly spaced increases based on Pi -- as she said in her book Knitter's Almanac, "the geometry of the circle hing[es] on the mysterious relationship of the circumference of a circle to its radius. A circle will double its circumference in infinitely themselves-doubling distances, or, in knitters' terms, the distance between the increase-rounds, in which you double the number of stitches, goes 3, 6, 12, 24 and so on." The shawl is not, however, based on Pi in any special way, but only on the property common to all two-dimensional shapes in Euclidean geometry that all dimensions increase by the same factor at the same rate; the circular shape is simply created by regularly spacing the increases). Zimmermann is also known for the "i-cord" (or "idiot cord"), and the "Baby Surprise Jacket," which is knitted completely flat and then folded, origami-style, to create a shaped jacket."
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Slippedstitch knitting blog by Alice Bell has an article on Knitting on the Web after she was featured in Wired magazine. 2020 science also wrote an article about her knitting and links to science.

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knitted genetics project :
About the project

Our aim, bizarre though it may seem, is to knit a piece that explores the link between the craft of knitting and science.

We see knitting and science as similar. They are both based on structure, both man-made and involve certain tools. Luckily for us too, both inevitably involve human error which can be visible, or masked by repair. We are all novice knitters, but what we lack in skills, we make up for in ambition.

We are basing our creation on a rough plan (which we’ll put up when it’s a bit less rough), but like science, its evolution will depend on its progress: what is created will depend on what has been created beforehand.

Different colours, materials, stitches and techniques will be used to represent different scientists, theories and fields throughout the history of genetics. We see our creation as beginning with a few single, tentative strands, then broadening gradually, more and more noticeably after each key event. Rediscovered theories such as Mendel’s will feed back into the knit after a period of absence. The discovery of the structure of DNA by Watson and Crick, and the later ‘cracking’ of the genetic code, are seen to be explosive events (we’re thinking bright coloured pom-poms)

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illusion knitting
Illusion knitting is a special a technique that provides you with a secret image when viewed at an angle. It may look complex but is about the simplest form of patterned colour-work going. At heart, its just alternating patches of garter and stockinet. If you can purl, you can illusion knit. DNA and illusion knitting could be made for one another. Looking across the scarf, the ladders of the striping pattern twist round those of the helix as purls and knits start to bunch together to display a regular shape (at least for those initiated on how to look).
-- from rosalind pattern page on ravelry

wendy's toe-up sock pattern
lovemeknot pattern on slipped stitch blog
rosalind scarf on slipped stitch blog
rosalind pattern on ravelry
Cheshire Cat 'Wonderland' socks
rosalind 2 - DNA for me pattern on ravelry
magic cast on for toe-up socks - figure 8 cast on using circular needles rather than DPN

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