# Margaret Kepner

I enjoy exploring the possibilities for expressing ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a wealth of subject matter. My lifelong interest in art gives me a vocabulary to utilize in my work. I particularly like to combine ideas from seemingly different areas and try to find parallels and relationships. 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. Topics that I have explored include: tesselations, symmetry patterns, combinatorics, edge-matching, group theory, dissections, magic squares, modular systems, knots, fractals, and number theory. For the most part, I use inkjet printing to produce my artwork. I have also experimented with screen printing, textile constructions, digital printing on fabric, and book making in order to produce pieces at a larger scale and/or with more physical variety.

The book “17” is a visual exploration of the 2D symmetry groups -- the so-called "wallpaper" groups. These 17 groups have interesting mathematical properties, and the associated patterns are widely used in the decorative arts. A symmetry pattern can be transformed by (1 or more) of the motions of translation, reflection, rotation, or glide-reflection, while still preserving the overall pattern. For this book, the same “seed” shape, a 30-60-90 triangle, is used for all patterns. There is a page for each symmetry group, with a large square containing a representative pattern for that group. Smaller squares on the page show other variations, achieved due to the effect of using different initial orientations of the seed shape, plus variations in spacing and coloring. In the lower right-hand corner, each group’s name is shown according to a commonly used system: p1, pgg, p3m1, etc. Graphic index pages precede and follow the group pages. The book uses the Japanese Stab Binding method.

“Quilt 100” is an accordion-fold book with 100 pages. The book’s subject matter is a “quilt” of 10 rows and 10 columns, composed of pairs of nested squares filled with 10 different colors. The structure and coloring of the quilt is based on a pair of Mutually Orthogonal Latin Squares of order 10. Such pairs were once thought to be impossible for all orders of the form (4k+2), based on a 1782 conjecture by Euler. Although it was proven that the order 6 case (36 Officer Puzzle) has no solution, examples of MOLS of orders 10, 14, etc. were found in 1959. They were dubbed “Euler’s spoilers.” In the flat quilt, due to the properties of MOLS, each color occurs in the outer squares exactly once in each row and column, and similarly for the inner squares. All 100 possible color combinations occur. To make the 2D quilt into a 3D book, a system of cuts and accordion folds is used. The two double-squares not on the quilt’s main diagonal are given special “bookend” roles in the folded book.

“Hex Study with Circles” is derived from a shape-packing problem. The 35 small shapes in each circle are called “hexominoes.” They represent all the shapes that can be formed from six squares joined along their edges, neglecting rotations and flips. Mathematicians have explored ways to pack these shapes efficiently inside various envelopes. This design is based on a tight packing of the hexominoes into a circle. The packing has been exploded slightly, creating space around the original “packed” pieces. Small random rotations have been added to loosen up the design and suggest motion. The patterns in the two circles are reflections of each other. One might imagine that the black pieces in the upper circle are expanding outward, escaping from a smaller, tightly packed circle. Perhaps the white ones in the lower circle are moving in the opposite direction, condensing inward. Tensions are created in this design between white and black, rectilinear and round, expansion and contraction.