# Elizabeth Whiteley

Studio Artist
Washington DC
As a continuation of my explorations in the geometry of pattern design, I am studying Frieze Group symmetries.

Textbook examples tend to use line patterns to demonstrate the seven Frieze Groups Those examples do not answer a basic question for artists: How do you turn the corner? That is, if you want to create a 2-D illustrated rectangular border based on the symmetry of a particular frieze group, what happens at the vertices?

My research uncovered solutions in a book on tessellations for quilt makers. I applied that guidance to borders on my original botanical art drawings. The corners are transitional focal points which indicate a change of axial direction as the viewer’s eye moves horizontally or vertically around the border.
Halesia carolina 1
51 x 41 cm
Silverpoint Drawing on Coated Paper
2016
The Halesia carolina tree, or Carolina Silverbells, is breathtaking in the spring when there are white blooms which hang gracefully. For the border of this original hand-drawn artwork, I chose a symmetry group, mt, that would illustrate the sense of numerous blooms at the same time.

Frieze Group mt contains a horizontal mirror line. The operation is reflected translation. A property of the Frieze Group mt border is that in order to have the corner turn symmetrically, there must be a mirror of the generator at the center of each of the 4 sides. The corners will then match.

I used a Renaissance metalpoint drawing technique with a sterling silver stylus.
Symmetry Breaking 1
51 x 41 cm
Silverpoint Drawing on Coated Paper
2016
For this drawing, I chose Datura metel buds, with a seemingly 3-fold symmetry. In full flower, though, there are clearly five sections. Between the two states there is a symmetry breaking point as the flower finds its way to its most stable shape.The image of symmetry breaking is in the center of the drawing; the border motif is a birds’ eye view of the opening bud.

The border of this original hand-drawn artwork illustrates Frieze Group tm. The operation is translation of a reflection. A property of the Frieze Group tm border is that in order to have the corner turn symmetrically, there must be a mirror of the generator at the center of all sides.

I used a Renaissance metalpoint drawing technique with a sterling silver stylus.