Spatial chromatic model in high-dimensional spaces and the uniqueness of chromatic code: a new perspective of geographic entity–space relationship

Abstract

The abstraction, representation, and computation of entity–space relationship are keystones of geographic information science (GIS). The newly proposed spatial chromatic tessellation (SCT) provides a novel model to explore this relationship. SCT has demonstrated a variety of potential applications in GIS, such as reasoning spatial topology, point pattern analysis, and Voronoi diagrams. This study aims to theoretically investigate SCT by focusing on two aspects: (1) extending SCT to higher dimensional spaces. Results show that cells missing in lower dimensional spaces are hidden in higher dimensional spaces; (2) exploring the uniqueness of chromatic codes, particularly the chromatic codes of 2-cell and 3-cell clusters: their codes are proved to be unique. In a mathematical perspective, the observed phenomena from the above two aspects bring some new thoughts into the first law of geography and spatial heterogeneity. Based on these new understandings of entity–space relationship, SCT is replaced by spatial chromatic model (SCM) in which spaces are created by entities themselves rather than by partitioning the space preexisted. This makes a change from an absolute geographic space to a relative geographic space.

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