# Priscilla Newberger

I have intended to make mathematically inspired quilts since I started quilting several years ago. My academic training includes a bachelor's degree in mathematics and PhD in a physical oceanography, so that I naturally look for inspiration in mathematics and the sciences. After my retirement I expanded my long time interest in fiber arts to include traditional and art quilting. I find patchwork such as this quilt is ideal for displaying discrete mathematical objects. I plan to use other quilting forms such as applique, embroidery and crazy quilting to show other mathematical results such as vorticity fields from numerical models of the ocean or solutions to differential equations. I intend to focus on mathematically inspired quilts for the foreseeable future.

This quilt represents a tiling of the torus formed by identifying the top of the 16x16 array with the bottom edge and the left edge with the right. There are four different tiles (colors) used in the array so that there are 256 distinct colorings of a 2x2 square. The method of de Bruijn is used to select the arrangement of the colors so that each of the possible 2x2 sub-arrays occurs exactly once on the torus. If the array is denoted by A=a(i,j) and the sequence above the divider at the top of the quilt is denoted by B=b(i), the tile a(i,j)= b(j) if i+j is even and b(i) otherwise. The restrictions on the sequence B are that it is even (has no symmetric sub-sequences of odd length such as red-orange-red) and that each of the 16 possible two square colorings is in the sequence.

The design of this quilt includes aspects of both the American patchwork and crazy quilt traditions. Many traditional quilts, including Irish Chains, Nine Patch and Trip around the World use a rectangular array of squares to form a pattern. This quilt goes outside this tradition with embellishment of hand embroidery typically found in a crazy quilt. In this quilt the embroidered lines are along diagonals, emphasizing that each diagonal (and zigzag) in the array is in the order of the generating sequence B shown along the top border.