# 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.

A combinatorial problem first proposed by Dudeney involves ‘necklaces’ of colored beads. Suppose N beads of two colors are strung together in a circle to form a necklace. In how many ways can this be done for different values of N? This piece presents the answer for two cases, showing all arrangements of 4 and 8 beads. The semi-regular tessellation composed of octagons and squares provides the layout. Each of the octagons represents one of the 30 solutions for 8 beads. The beads are shown as octagon-sections, colored either white or indigo blue. The squares show the 6 possibilities for 4 beads (using two shades of blue-gray). Various visual elements in the design are used to reflect the symmetry properties of the necklaces.

This work is based on a magic square of order 8, expressed in a visual format similar to a traditional quilt pattern. The magic square, known as the Gwalior Square, is an 8x8 array of numbers from 0 to 63, such that every row and column adds up to 252, the ‘magic constant.’ The two main diagonals, as well as every broken diagonal, also sum to 252. The numbers in the square are represented in base 2 and base 4. Nested squares serve as the number places in the base systems, and suggest the Log Cabin quilt structure. For each of the 64 squares, half is shown in base 2 and the other half in base 4. The squares are oriented to create the ‘pinwheel’ quilt pattern. This pattern groups together 2x2 arrays of 4 numbers, all of which sum to 126.