Horne began her studies in pure and applied mathematics, then turned to textile design for her graduate work, and went on to teach design construction techniques in the context of screen printed textiles. Here she develops mathematical ideas from such areas as geometry, graph theory, and topology and applies them in the context of repeating designs. She shows how the principles of rhythmic expansion, many developed in crystallography, can be applied to achieve balance and harmony within the design of textile and other forms of surface decorations. Her goal is to make complex theories and ideas easily accessible to artists and designers so that they can use them to increase their creativity and design potential