# Margaret Kepner

I enjoy exploring the possibilities for conveying ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a never-ending supply of subject matter. My lifelong interest in art gives me a vocabulary and references to utilize in my work. I particularly like to combine ideas from seemingly different areas. I coined the term “visysuals” to describe what I do, meaning the “visual expression of systems” through attributes such as color, geometric forms, and patterns. My creative process involves moving back and forth between a math concept that intrigues me and the creation of visual images that interpret that concept in interesting ways.

The Catalan numbers are a sequence of positive integers that provide answers to certain combinatorial questions. For example, in how many ways can a polygon with n+2 sides be cut into triangles? A hexagon (setting n=4) can be triangulated in fourteen different ways, so the 4th Catalan number is 14. Other types of problems also lead to the Catalan numbers: counting binary trees, balancing parentheses, finding paths through a grid, shaking hands in a circle, etc. This piece is composed of diagrams representing seven different problems; for each of these, the answer is the 4th Catalan number. The solution sets for the problems are displayed in diagonal bands. The columns indicate correspondences between elements in different solution sets.

A geometric dissection is a subdivision of a shape into pieces that can be reassembled to create a different shape. This design is based on dissections of nine squares into regular polygrams, or stars. For each square, the sub-pieces are colored, and the corresponding star-shape is shown using the colored outlines of the reassembled pieces. For example, the rightmost square is cut into seven subparts; these pieces can be regrouped to form an 8-pointed star, as the line-figure directly to the right illustrates. Visually, the dissected squares resemble the random patchwork patterns that compose traditional Crazy Quilts. In this case, however, the pieces are not so “crazy” – they have a clear purpose, which is to create stars.