Eureka!

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.

Comments

[alice]

I am so glad that I stumbled onto your blog (courtesy of Fillyjonk). Your latest entry and comment makes me wonder if you have seen the work that is being done on string-or-nothing? She is knitting an hexagonal bedspread....I think I will now graph and color squares in ordr to fit the math into my brain :)

[Sahara]

The Sierpinsky Carpet sounds fascinating to me. How would you do it? The most obvious would be brocade (knit and purl sts), as it's easier to show square forms and I'm thinking of the smallest units as 1 stitch. In fairisle, you would have to deal with the floats, although intarsia knitting for the larger blocks would take care of that.

Double knitting sounds like the ticket, to me, for certain fractals. Or circular knitting, from the smallest units, outward. Hmmm.

[thomasina]

Sahara, I hadn't even thought of brocade. Of course, I only saw my first really striking brocade pattern today, a celtic key piece designed by Alice Starmore. It seems like getting good results with a brocade would be very dependent on the type of yarn. I wish I had knit with a wider variety of yarns - it seems like it would need something with a sheen would be best. Like the Clip Egyptian Cotton, which would not really make a good afghan!

Alice, I had not seen string-or-nothing.blog-city.com before (okay, I did see just the dragon skin-modified Rouge in passing before, but not the rest of the site). Thank you so much for pointing this out to me. I have been enjoying reading up on her design programs, and watching how her projects develop. And her counter stitch markers were the final bit of inspiration to get me started on my own stitch markers.