As a continuation of my explorations in the geometry of pattern design, I am studying line group symmetries.
Textbook examples tend to use friezes to demonstrate the seven line groups. Those examples do not answer a basic question for artists: How do you turn the corner? That is, if you want to create an illustrated rectangular border based on the symmetry of a particular line 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 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.
Artworks
Calladium 1
41 x 51 cm
Silverpoint Drawing on Coated Paper
2015
This original hand-drawn image includes a border which illustrates Group t2mm (sometimes noted as p2mm) from the seven line groups. The generator, or fundamental region, is a single leaf which becomes a 4-leaf motif. It demonstrates three reflections.
Curiously, there is the optical illusion that the generators moving vertically are different from the generators moving horizontally. In fact, they are identical.
My drawing process began by coating the paper with a metalpoint ground based on a Renaissance bone ash formula. For the drawing, I used a stylus of sterling silver wire. The rough texture of the ground allowed tiny particles of metal to adhere.
Ginko 1
51 x 41 cm
Silverpoint Drawing on Coated Paper
2015
This original hand-drawn image includes a border which illustrates Group t (sometimes noted as p) from the seven line groups. The generator, or fundamental region, is a 2-leaf motif formed of a diagonal mirror image of a single leaf, within an implied square. The operation is translation of that generator.
A property of the Group t 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.
My drawing process began by coating the paper with a metalpoint ground based on a Renaissance bone ash formula. I drew with a stylus of sterling silver wire. The rough texture of the ground allowed tiny particles of metal to adhere.
