The Roman Villa found in Chedworth, England comprises several pavement mosaics that contain a variety of geometric patterns. The most notable of these patterns is the intricate swastika meander found in the dining room, recently subjected to an explicit geometrical analysis. However, the remaining mosaics in the villa, characterized by their uniqueness and apparent variety, have not received the attention they deserve. In this paper, the remaining pavements of this ancient villa are analyzed from a transformation-geometry point of view, thus filling this lacuna. Although the patterns exhibit considerable perceptual differences, the analysis reveals that they are closely related, and may be easily morphed from each other by means of a few simple geometric transformations. It is also shown that they are closely related to patterns found in Basque and Islamic decorative arts, as well as to families of curves well studied in the mathematics literature. Finally, it is shown how these patterns may be incorporated into a modular design process that yields many new and interesting pattern designs.