Beaded Parquet Deformations

Inspired by research into mathematical art by Craig Kaplan, I set out to bead a design that morphs from one tiling pattern to another. M.C. Escher's use of this idea is famous in his designs, such as the Air and Water I (from the "Official M.C. Escher Website"). Craig writes about his research into formalizing deformations of planar tilings, and includes images that are beautiful partly because the design is regular, and partly because that regularity is lost as the design varies.

It was the Islamic Parquet Deformations that set me to beading. Here is the result, inspired by the  deformation shown here, from Craig's work.

Beaded Deformation: From Kepler's Star to the Night Sky
by Florence Turnour
6" by 1.5"

In this sampler, I explore techniques in bead weaving that allow me to express subtle changes in shape, and in particular in the "contact angle," that Craig describes. Unlike the deformations shown in Craig's image, the smallest changes I can make are limited by the sizes of the beads. The design travels from the Kepler's Star Weave (on the left)

Kepler's Star Weave (designed by Gwen Fisher)
Kepler's Star Patterns and Kits are available from beAd Infinitum

to the Night Sky Weave (on the right)

Night Sky Weave (designed by Gwen Fisher)
Night Sky Weave Patterns and Kits are available from beAd Infintum

I am drawn into the detailed regularity of these two flat angle weaves, but as I look at the Beaded Deformation I find my eye passing backwards and forwards across the three rows of tiles, finding spots that look like they will be regular, only to discover that they are not.

I may try to stretch the Night Sky end of this so that the end result has even more of a wedge shape. Perhaps then I could combine several such wedges to make a very ornate fan. Back to the bead board!