Analysis Of Pattern Structure By Geometric Symmetries

INTRODUCTION While a large literature exists on the technologies different peoples use to manufacture woven fabrics (cf. Emery 1966), little attention has been given to developing equally systematic ways to study the patterns produced. This paper outlines one approach to pattern analysis which utilizes mathematical symmetries to describe the way design parts are arranged in a pattern. The advantages of this method are discussed and examples of a number of problems that such an analysis of pattern structure can address are described. SYMMETRY ANALYSIS: Symmetry analysis is a mathematically based description of the structure of a pattern. It specifies the geometries which organize, that is, repeat, the parts in a pattern. Only patterns whose design elements repeat regularly can be described by this geometry. For the purposes of textile pattern analysis, I am considering that textiles are flat—in mathematical terms they are two-dimensional planar surfaces. (Textural elaborations should not affect this classification scheme, unless one considers that these render the piece a three-dimensional object, in which case the three-dimensional symmetries should be used for the classification.) There are four symmetry motions that move the parts of a design onto themselves and produce the repetition of the parts in the pattern. Geometers call these motions distance preserving motions because the distance between any two parts is always the same. These motions are translation (a shift by a given distance along a line) (Figure 1a), rotation about a point in the plane (Figure 1b), mirror reflection across a line in a plane (Figure 1c) and glide reflection (translation followed by mirror reflection) (Figure 1d