Lana Holden
I find my creativity is enhanced, rather than inhibited, by the imposition of structure. Much of my work pairs a standard idea from knitting or crochet design repertoire with a mathematical idea in a compatible but unexpected way. I try to make specific connections between the mathematics and fiber arts concepts, rather than simply exploring random combinations, for the most spectacular results.
This work is the first in a series that applies the Japanese continuous-motif crochet technique to Sierpinski fractals. Although it appears to be composed of 216 small pentagonal motifs created individually and then joined, each connected section is in fact crocheted with a continuous strand (i.e., all of the light blue is a single length of yarn). The planning of a continuous traversal involves mapping the figure to a planar digraph and inspecting the graph. We suspect that the existence of such a traversal for every iteration of the Sierpinski pentaflake (and others) can be proven using elementary graph theoretic results about Eulerian paths.