Oddly enough, knitting and geekiness are like chocolate and peanut butter -- what at first seems like an odd combination is very complimentary. The mathematics that underlies knitting probably helps...Mathematics
All blog entries in Geeky Knitting
thomasina's guide to Geeky Knitting
Geology and Paleontology
pseudotachylite (earning my undying gratitude at finally finding geologic knitting) suggested a tectonics scarf (now, 65 Ma, 190 Ma, 220 Ma, 280 Ma, and 350 Ma. The tectonics scarf was designed and knit by fisheggs at geoknitting, who has generously made the tectonics charts available to the geoscience / knitting community. I am starting my own journey to design and knit a tectonics shawl.
Also from fisheggs: a "Terry Dactyle" doll. Alan Dart created five dinosaur patterns. (I know, I know, only three are actually dinosaurs) for Sirdar, which are now out of print: Sirdar 4326 Troy Ceratops; Sirdar 4327 Tyrone O'Saurus; Sirdar 4328 Stella Saurus; Sirdar 4329 Terry Dactyle; Sirdar 4330 Wally Mammoth. These show up on eBay from time to time.
Microscale: Genetics and Microbiology
One of my personal favorites is the DNA scarf pattern, designed by June Oshiro while she was a graduate student at Rutgers; it is now hosted on her own server, Twosheep.com. This is also very popular amongst knitters, as googling "DNA scarf" or google imaging on "DNA scarf" bring up a multitude of scarves knit on this pattern. I've knit it several times, won first place at the state fair (which I credit fully to the designer), and have a post on yarn substitutions that I have tried.
botanicallyhip has suggested the following: Geek Chic from the Fall 2003 back issue of Interweave Knits. It contains different interpretations of the DNA scarf by the staff members (the red 3D one was apparently designed by Ann Budd), as well as a translation of the DNA cables to pillow form, and a cute DNA cabled purse. There is also a short article on geeky knitting.
Knitcast, the podcast about knitting, had their first interview with two knitting biologists who were inspired by their work. There are biology photos from the podcast, and hopefully there will be followup photos of the knitting, also. Permalink to the .mp3 podcast download post.
She Dances in Dragon, a redhead, decided to knit the variations in the MRC1 gene that result in her phenotype. She used the standard notation (G black, C blue, T red, A green), and has made her charts available: Redhead Genome Project chart; DNA chart, part 1; DNA chart, part 2.
Macroscale: Anatomy and Ecology
The Fall 2004 online issue of knitty has a bubble-gum pink uterus stuffed doll! There is a disclaimer that it is not entirely anatomically accurate, but it surely looks good enough to pass to me.
I highly recommend Mathematical Aphrodisiac. A story by Alex Galt (originally published in True Tales of American Life edited by Paul Aster) with math, knitting, and romance... what more could one want?
sarah-marie's mathematical knitting pages has a good collection of annotated links to mathematical knitting and textiles in general.
From sarah-marie, the AMS Special Session on Mathematics and Mathematics Education in Fiber Arts has some interesting abstracts relating to knitting and other fibers. She has a photographic walkthrough of the session, with detailed annotations on the individual photographs. She also provides a list of academic journal articles, mostly on weaving.
Math4Knitters is a podcast that is mostly focussed on utilizing math in knitting, in a practical sense, but the underlying appreciation of math also comes through. Highlights (so far) include an interview with Meg Swanson (Episode 8), and a guest spot on the podcast Cast-On on fibonacci sequences (Episode 23).
This is made into a math problem for students, but it shows that people in Antarctica knit, too. Cool -- we are taking over the world!
I really like the moebius scarves and klein bottle hats; there are multiple patterns online for these. I particularly like Priscilla at Fuzzy Galore's Moebius Capelet, which solves the problem I had with the scarves, which is that they are too droopy.
Continuing on the moebius front, there is a lacy moebius scarf, that can also be used as a head fitting, designed by Mary J. Saunders.
And someone (namely Isaksen and Petrofsky) designed a whole new moebius stitch, to have symmetry on both the horizontal and vertical axes. (Note: the estimable sara-marie disagrees with their conclusion that their stitch is the only way to properly make a knitted moebius strip).
My favorite Klein Bottle Hat is at sarah-marie's mathematical knitting pages; there are lots of other interesting mathematical shapes (warning, sarah-marie's patterns are written for left-handed knitters).
Since there is so much free moebius online, you might wonder why you would ever pay for a book based primarily on moebius shapes. However, I love the patterns that Cat Bordhi has come up with: in Treasury of Magical Knitting, she starts with scarves and continues on with hats and felted boots incorporating moebius twists. The second book, Second Treasury of Magical Knitting, has felted baskets and even a cat bed. (Oh, I so want to do that cat bed!). The price on the books is rather steep, though ($27 each for a thin paperback), which is the only thing stopping me from adding to my knitting book collection.
Probability, Chaos and Fractals
From Priscilla at Fuzzy Galore there is the Probability Sweater, which involves randomization through rolling a die.
Randomization is also important in using up a yarn stash: a sweater knitted from yarn scraps randomly pulled from the stash often turns out more pleasing to the eye than any but the most carefully crafted yarn combinations.
Okay, this is not knitting, but there is a beautiful crocheted Lorenz manifold; this is based on the strange attractor in chaos theory. Dr Hinke Osinga and Professor Bernd Krauskopf, of Bristol University's engineering mathematics department, used 25,511 crochet stitches to represent the Lorenz equations: more in the BBC article.
Just for inspiration, Eleanor Kent is a textile artist who knits fractal designs and mathematical formulae.
Sequences and Geometry
Those of you looking for cushions, there are tons of mathematically inspired ones at Woolly Thoughts. Check out the other designs, too -- I especially like the Double Vision scarf and the Square Deal afgan. Many of the projects can be crocheted, if that is more to your taste.
Elizabeth Zimmerman, one of the founding mothers of modern knitting, developed a lot of her patterns on mathematically-based principles. Wendy Johnson has an example of the pi shawl from Zimmerman's Knitter's Almanac. Wendy of Wendy Knits! has developed a very popular, free felted cat bed based on the increases and shaping in the pi shawl.
Priscilla at Fuzzy Galore suggests incorporating the Fibonacci sequence to transition between two different colors, and shows an example pair of Fibonacci Socks. I was inspired to fix my SnB Windy City scarf with a Fibonacci sequence.
Also from Fuzzy Galore: using Ada Dietz polynomials in knitting patterns. Ada Dietz was a lesbian mathematician who incorporated solutions to multivariant polynomials into weaving patterns. These make a 2D pattern that can also be adapted to knitting.
Rachel Bishop designed the perfect shuffle scarf. A perfect shuffle will interleave the cards - do this enough times, and you will return to the original card configuration. Based on modular arithmetic, certain cards will group together in some shuffles, allowing multiple colors to be incorporated into the pattern.
The formal definition of a tessellation is a repeating set of tiles (a single geometric shape or a set of shapes) that can tile a plane to infinity. First off, for those wanting to design their own tiles: a how-to guide and gallery (including an extensive collection of Escher tessellations) from Tessellations.org. Tessellation generally either requires a lot of intarsia, or a lot of seaming. Occassionally two-stranded knitting can be made to work.
The Fish Blanket has been a popular subject on the Internets. The individually knit fish tiles also make up bands (unlike "classic" Escher tiling), but each tile is also distinct. Hytrevant Knits has an example of the original fish blanket, as designed by Paula Levy and published in Knitter's Magazine 51 (Summer 1998; OOP). April Brokenarrow has reverse engineered a similar pattern; example fish.
Once I started looking for knitted tessellations, it was like learning a new word - you see it everywhere. My Little Fishy is a child's raglan with three bands of two stranded knitted fish. Designed by Marie Grace Smith at The Garter Belt. This is stretching the definition a bit, since seeing distinct fish tiles making up a band is open to interpretation.
The Fall 2004 online issue of knitty has Pasha, a penguin who just might be the Linux penguin.
Followed by something that definitely is the Linux penguin: in a bout of double geekiness, Heidi Antila has designed a Linux illusion scarf, with Tux, the Linux penguin, on one side and the word 'Linux' on the other. The pattern is in Finnish, in the online Finnish knitting magazine Ulle. In true open source fashion, the designer is generously allowing translations (which are released under a creative commons license): currently English and French, with Spanish coming soon. (This was brought to my attention by adriennec on the knittyboard.)
Given the binary nature of knit / purl, many people seem to have encoded binary sequences into their knitting. My favorite example is encoding the Code Red virus into knitting.
The best explanation of how to encode phases into binary, and from there into knitting, is provided by Joe Klinkhoff, after a discussion on knitlist: HEX and BIN meet my Friends Knit & Purl. I found this link through Of Troy, on the knittyboard.
History inspires lots and lots of patterns. Celtic patterns are certainly popular. Some particular highlights (for me, at least):
I love a lot of Elsebeth Lavold's knitting. Her Viking Knits project is an incredible interpretation of Viking patterns and knotwork. I like the first book, Viking Patterns for Knitting, the best; it is more technical and design-oriented. I also like her historical pattern-focused books, The Viking Knits Collection (Viking patterns) and The Embraceable You Collection (re-interpreting armor designs as knitware, from many different cultures -- including Klingon!).
I am thinking about knitting a shawl incorporating the Labyrinth on the floor of the Chartres cathedral, possibly as a shadow shawl, for my mother, who really should have been a historian.
The Incan practice of encoding meaning with binary knotwork -- khipu -- certainly provides food for thought.
I haven't seen this idea put into practice - but encoding braille into knits and purls seems like a natural fit. I might do this for a Christmas present.