Elizabeth Whiteley
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.
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.
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.