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This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems. How can one decide whether one surface or spatial object is more complex than another? What does it require to measure the spatial complexity of small maps, and why does this matter for nature, science and technology? Drawing from algorithmics, geometry, topology, probability and informatics, and with examples from everyday life, the reader is invited to cross the borders into the bewildering realm of spatial complexity, as it emerges from the study of geographic maps, landscapes, surfaces, knots, 3D and 4D objects. The mathematical and cartographic experiments described in this book lead to hypotheses and enigmas with ramifications in aesthetics and epistemology. .

System theory. --- Geography. --- Topology. --- Cognitive psychology. --- Biodiversity. --- Complex Systems. --- Geography, general. --- Cognitive Psychology. --- Biological diversification --- Biological diversity --- Biotic diversity --- Diversification, Biological --- Diversity, Biological --- Biology --- Biocomplexity --- Ecological heterogeneity --- Numbers of species --- Psychology, Cognitive --- Cognitive science --- Psychology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Cosmography --- Earth sciences --- World history --- Systems, Theory of --- Systems science --- Science --- Philosophy

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This is the first book on spatial entropy in the scientific literature. It links spatial entropy with landscape analysis, landscape diversity and geo-information. It gives all the essential tools that a researcher needs in order to study the spatial entropy of physical as well as artificial landscapes (created with artificial life, swarm intelligence etc). This book explores the fascinating world of the interplay between spatial entropy, spatial information, self-organization and emergence and gives geographers and landscape scientists several alternative mathematical methods to study them, i.e. Shannon's formula, measures from non-extensive thermodynamics, from directional statistics and network theory. An essential book for researchers in landscape analysis and geo-informatics. The author Dr. Dr. Fivos Papadimitriou is at the University of Tübingen and he is the author of "Spatial Complexity: Theory, Mathematical Methods and Applications" (Springer).

Environmental planning --- Social geography --- ruimtelijke ordening --- geografie

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Geography --- Topology. --- Mathematics.

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