Coded Symmetries

My recent Linear Lace artworks are explorations of the seven frieze symmetry types in traditional knitted lace. In my writing about these works, I use marked knitting charts to illustrate the symmetries in each pattern. Then it occurred to me; why not mark the lace itself?

Here, the glass beads show the symmetries in the seven lace patterns. The red lines are reflection axes, the orange lines are glide reflection axes, and the blue beads are centers of rotation. The teal beads along the edges of the designs mark their translational symmetries, with the minimal duplication needed to preserve reflections, glide reflections and rotations.

Coded Symmetries was knit by hand on 2.75 mm needles. I placed the beads into the fabric during the knitting process. This work was followed by a refinement, The Symmetries Diagram Themselves. Both works appear in my Bridges 2018 proceedings paper, Self-Diagramming Lace.