Now that I'm halfway done this project and no longer routinely swearing and ripping it out, I think it's time to show off my progress. The project was partially conceived out of a desire to play with triangle-based fractals and partially out of a desire to make myself more comfortable with lace. The bottom panel is a Sierpinski sieve after three iterations of the algorithm. Each panel goes back one iteration, until nothing remains but a triangle. I'm currently knitting said triangle. After I'm done that, I'll go forward two iterations into the 2-dimensional Koch curve (or Koch snowflake). At the size I'm knitting, I only have the resolution to knit two Koch curves. However, the Koch curve pattern (which I've sketched, but not yet plotted out with all its decreases) has the fortuitous property of being half again as large as the Sierpinski triangle. Hence, two Koch curves will be as long as three Sierpinski triangles. I had a few false starts with the Sierpinski pattern, though. First, I misguessed how to angle the decreases, resulting in a random web of yarn. Second, I saw that once I'd knitted more than half the triangle, the corners of the fabric drooped dramatically. To fix that, I spread out and flattened the scarf, then placed a straight edge from the middle over the drooping corners and noted the row that it intersected. Having done that, I cast on with twice the number of stitches that that row had outside the pattern (twice 14 --$gt; 28). From there, I increased every row without a corresponding decrease, until the scarf was 45 stitches across, the width of the pattern. I intend to, on the second Koch curve, decrease every pattern row for the last third of the pattern, giving it the opposite curve to the bottom of the scarf, rather than the simple curve that would result from casting off on a flat edge.