Towards four-dimensional modeling of geospatial phenomena: An integration of voxel automata and the geo-atom theory

Geographic Information Systems (GIS) are widely used in both the management of spatial data as well as in the study and analysis of spatiotemporal processes. However, contemporary spatial data models are based on the principles of traditional two-dimensional cartography that simplify space to the horizontal Cartesian plane. This is partly due to the limitations in the way spatial phenomena are generally conceptualized and represented in GIS databases using the vector and raster geospatial data models. Over the last two decades, various methods of modeling the third dimension, incorporating the temporal component, and linking the field and object perspectives have been proposed but they have received little integration in GIS software applications. The main objective of this dissertation is to develop modeling approaches that can represent dynamic spatial phenomena in the four-dimensional (4D) space-time domain (three-dimensional space plus time) using a theoretical geospatial data model and the principles of complex systems and geographical automata theory. Using the theory of complex systems and the geo-atom concepts, this dissertation proposes and implements a voxel-based automata modelling approach for the study and analysis of 4D spatial dynamic phenomena. The data are structured using the geo-atom model, a theoretical geospatial data model that links the object and field perspectives of space and explicitly models the four dimensions of the space-time continuum. The results from implementing voxel-based automata indicate their usefulness in simulating dynamic processes, the management of geographic data, and the development of three-dimensional landscape indices and spatiotemporal queries. The significance of the study is that it provides a robust platform that demonstrates the potential of the voxel automata and geo-atom spatial data model to represent spatial dynamic phenomena in 4D.