Xtreme-knitting's Jennifer Rose Thurston created these three cute dinosaur patterns: Bronty, Trice, and Mr. Stegs: PDF pattern.
First, an update: Dr. Sarah-Marie Belcastro's Home of Mathematical Knitting has moved to her new website, Toroidal Snark. Her work is a mainstay in the Geeky Knitting links, so it will take awhile to re-link.
I would also like to introduce the podcast Math4Knitters. This is mostly focussed on utilizing math in knitting, in a practical sense, but the underlying appreciation of math also comes through. Highlights include an interview with Meg Swanson (Episode 8), and a guest spot on the podcast Cast-On on fibonacci sequences (Episode 23).
Yes, I've heard all of the criticisms: the twist is backwards, not the right offset between the two coils, not enough base pairs per twist... But really this trumps all objections - you recognize instantly what it is.
Why yes, I have seen the knitted digestive system that has been taking the 'net by storm. Probably, so has everyone else. But I'm updating the geeky knitting section, so this is going in too. I'm also starting to put in thumbnails - I don't want to step on any copyrighted toes, but small photos fall under fair use, and the illustrations really add to the link collection.
I've already blogged Heidi Antila's design of a knitted illusion scarf featuring Linux and Tux, originally published in the Finnish online knitting magazine Ulla. 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.
I have had a fractal pattern that has been stewing for awhile (so old it is not in the notebook that my SP gifted me, but rather on random scraps of paper). I have had a real block with translating it into knitting, since the principle of fractals means increasing amounts of negative space; so fair isle would work on the small scale, but on the larger scale it would mean intarsia. Or else making smaller blocks and joining together. Ugh to both, since it seems very inelegant. I just realized, while answering a question on what to do with two colors other than intarsia or fair isle, that the solution is double-knitting! *slaps forehead* Though for larger projects, joining blocks might be the way to go.
The other issue is distortion; I was thinking of a felting project, since the typical felting shrinkage results in stitch height becoming about equal to width, instead of stretched 2:3 for stockinette. Perhaps done in garter? That would be awfully stretchy for a large project. Must think more on this issue. The distortion does not matter to the fractal, it would still be self-similar, but it might not be pleasing to the eye.
The Fractal patterns I was thinking of knitting were based on the Cantor set, where in each iteration, the middle third of the line is removed and becomes negative space. This could make a really striking cuff or neckband. Or a sideways knit scarf. I was thinking of using the Sierpinski triangle on the side of a felted bag (I'm now working on a cellular automata pattern, though). The Sierpinski carpet would make a stunning afghan. Or, the triangle could be tiled into a hexagon, which would also be gorgeous.