Analysis of the relations among spatial tessellations

A spatial tessellation is a set of regions that are collectively exhaustive and mutually exclusive except for the boundaries. In geographical analysis, it may represent such administrative units as census tracts, postal zones, and electoral or school districts. Spatial tessellations of a certain area are often closely related to each other. Areas of local communities are related to school districts, market areas of retail stores, and administrative units. Postal zones and census tracts are determined by collecting or dividing administrative units. Analysis of such relations among tessellations often reveals their underlying spatial phenomena. To this end, this paper proposes a new exploratory method for analyzing the relations among spatial tessellations. It aims to detect spatial patterns, especially those with a hierarchical structure, and to provide a tessellation classification scheme. Topological relations and similarity measures are introduced to evaluate the relations between tessellation pair. For more tessellations, tree representations are proposed. These not only visualize relations, but also provide a means of classifying tessellations. The method is applied to the analysis of two sets of spatial tessellations: one with five hypothetical tessellations, and another with 34 candidate plans for the new Doshusei administrative system in Japan. The application reveals the properties of the method and quantitative measures used in analysis.