# 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.

Some years I ago 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. I intend to continue to explore the expression of my ideas in a range of media including prints, books, and textiles.

The traditional quilt pattern “Broken Dishes” and certain edge-matching puzzles share a common visual element – a square subdivided along its main diagonals to form 4 right triangles. This work presents 4 puzzle solutions using this visual element in a format suggesting Broken Dishes quilts. Edge-matching puzzles based on the square were introduced by MacMahon in the 1920s. One challenge was to arrange a set of 24 three-colored squares (all the possibilities) in a rectangle with same colors matching on the edges and a single color appearing around the border. If this is generalized to four colors, the complete set of puzzle pieces jumps to 70. These can be arranged in a 7x10 rectangle, providing a nice quilt proportion. This set of four designs is based on different matching “rules” ranging from strict matching to random placement, while maintaining the border requirement. To produce richer colors, each design is overlaid with a translucent scrim of the next design in the sequence.

This design is based on four ELOP tables arranged in a pinwheel format. The term “ELOP” comes from “ELementary OPerations” and the tables have been expressed in four modulus systems. The symbols used for the underlying numbers are triangle slices; for example, the operation result “3 modulus 4” would be represented as a 3/4 slice of a right triangle. Six elementary arithmetic operations (+, -, *, /, …) are shown in the composite tables of nested squares, with inverse operations paired together and both possible operand orders expressed. For each modulus order, a design is generated with the overall appearance of an array of jagged pinwheels. The four composite tables for modulus orders 2, 3, 4, and 5 have been scaled to the same outer dimension, and they are themselves arranged in a pinwheel. There is a “fractal” element to this design, as the composite table for each order becomes more fragmented than the previous one, and similar, but not strictly identical, shapes can be found.