Fractal Collars

Last weekend, I had an extraordinary experience.  At the College Arts Association Conference, I met several people through my Fractal Necklaces. That’s not the extraordinary part though.

As many of you who actually know me in person know, I’ve long been obsessed with pattern and structure in Fiber, be it beads, crochet, or paper.  Before I moved to Spain in 2005, my friend Rowena taught me to knit.  And, like any good Fiber Artist who is obsessed with structure, I wanted to push the limits of my new-found skill.  I knitted a fractal headpiece with some ombreéd Red Heart yarn that promptly got dropped into my closet and maybe even thrown away because it wasn’t really wearable (at the time).

It looked a lot like my current iteration of the same knit-formula (see above), but it was icky yarn, and at the time, statement jewelry wasn’t à la mode.

Well last weekend, I wore a couple different versions of my coral-like Fractal Collars, and several of the professors at the conference came up to me and said that I should look at Daina Taimina (from Cornell), and the Institute for Figuring (at Cal Arts).  One even told me that I was wrong and my necklace isn’t a fractal, but an expression in Hyperbolic Space.  She asked me to explain why I thought it was a fractal.

This is what I told her:

If you look at the most simple of fractals, they take a mathematical formula and repeat it on every iteration of the fractal.  One book I read showed how even a tree or grass is a simple branching fractal.  In fact, what I’m doing is doubling every row, adding a branch at each level.  A Julia set or a Mandelbrot fractal uses a more complex formula, but it is basically the repetition of a formula across every iteration of the fractal.

The models we look at of Julia sets or Mandelbrot sets  are actually like a derivative in calculus.  They are modeled in 2 dimensions of something that is actually probably at least 3 dimensions.  It’s like slicing through the shadow of a light.  For all you non-math people, it’s like taking a slice of bread, you only get part of the idea of what the whole loaf looked like.

So knitting and crochet (or using a modified peyote stitch in beading) are a perfect way to model these shapes because they aren’t limited to two dimensional space, but the pattern can be limited to something easy to write down as a single line of repeating formula.

So basically, the formula I use is a simple quadratic, well even simpler.  It’s a geometric increase that is modeled using a set pattern which in turn creates the hyperbolic space that Margaret Wertheim and Daina Taimina are talking about. There’s a TED video here that was excellent!

Watching this video today made me very excited that the world is indeed a very small place.  If I had still been in Chicago years ago instead of in Spain, I might have heard about this sooner, but it is wonderful to hear about the links that other people have made to things that I think about, and to learn from what they’ve discovered.

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