Theory, Mathematical Methods and Applications, Fivos Papadimitriou, Springer, 2020Spatial complexity is the complexity of spatial entities (with dimension two or higher).
This book offers, for first time ever, a unified theory of spatial complexity, based on geometric, topological, probabilistic and algorithmic determinants.
Consequently, the mathematical theory of spatial complexity entails formulas and methods for the assessment of the complexity of simple spatial objects, complemeted by a theory for creating spatial complexity from numbers and square maps, what the author calls “Spatium Numerorum”.
The book is written by adopting an inter-disciplinary perspective, therefore making it accessible to a wide readership and essential guide to all those who need to explore the spatial complexity of spatial objects (maps, landscapes, photographs, knots, braids, higher-genus surfaces, 3d and 4d objects etc).
The applications presented are manifold, ranging from geography, ecology and medicine to psychology, aesthetics, philosophy and epistemology, leading to the exploration of tricks, limits, enigmas, hypotheses and conjectures opening avenues for future research.