Tesselation-based or area-based visual representations are common to many artistic or visualization applications. For example, Voronoi art uses a space-filling tessellation of the image by Voronoi cells. We present frayed cell diagrams as an aesthetic visual representation of the separating border between those space-filling regions. Our approach is based on a simple randomized algorithm that densely draws lines toward the reference points of cells. This algorithm is controlled by a few parameters whose effects are detailed in the paper: the density and size of cells, the degree of fraying, and the color coding. To demonstrate the usefulness of frayed diagrams for algorithmic art, we applied them to pieces of Voronoi art. Finally, we conducted a survey to assess the aesthetics of the frayed cell diagrams. As a result, we found out that the majority of the participants preferred a high degree of fraying, but that a nonnegligible subgroup preferred diagrams without any fraying.