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Spatial Complexity

Theory, Mathematical Methods and Applications

  • Presents an accessible mathematical foundation of Spatial Complexity
  • Provides simple methods for assessing the Spatial Complexity of small maps
  • Examines Spatial Complexity in an interdisciplinary manner, with applications in natural sciences, technology, and humanities

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxi
  2. Introducing Spatial Complexity

    1. Front Matter

      Pages 1-1
    2. What is Spatial Complexity?

      • Fivos Papadimitriou
      Pages 3-18
  3. The Mathematical Basis of Spatial Complexity

    1. Front Matter

      Pages 37-37
    2. The Geometric Basis of Spatial Complexity

      • Fivos Papadimitriou
      Pages 39-50
    3. The Probabilistic Basis of Spatial Complexity

      • Fivos Papadimitriou
      Pages 51-61
    4. The Topological Basis of Spatial Complexity

      • Fivos Papadimitriou
      Pages 63-79
    5. The Algorithmic Basis of Spatial Complexity

      • Fivos Papadimitriou
      Pages 81-99
    6. Exploring Spatial Complexity in 3d

      • Fivos Papadimitriou
      Pages 101-113
    7. Spatial Complexity in 4-and-Higher-Dimensional Spaces

      • Fivos Papadimitriou
      Pages 115-123
  4. Numbers Behind Spatial Complexity

    1. Front Matter

      Pages 125-125
    2. The Spatial Complexity of 3 × 3 Binary Maps

      • Fivos Papadimitriou
      Pages 163-178
  5. Understanding Spatial Complexity

    1. Front Matter

      Pages 193-193
    2. Enigmas of Spatial Complexity

      • Fivos Papadimitriou
      Pages 195-207
    3. Taming Spatial Complexity

      • Fivos Papadimitriou
      Pages 209-225
  6. Epistemological, Psychological, Geophilosophical and Aesthetic Perspectives on Spatial Complexity

    1. Front Matter

      Pages 227-227

About this book

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. 

Reviews

“With this book, Dr Papadimitriou shows that the examination of spatial complexity is a problem on its own, and that, although the basic theory for its assessment should (expectedly) be mathematical, its connections with non-mathematical concepts and ideas leads us to a trove of applications for geography never imagined before.” (John Lidstone, IRGEE International Research in Geography and Environmental Education, August 20, 2021)

Authors and Affiliations

  • Forschungsbereich Geographie, Mathematisch-Naturwissenschaftliche Fakultät, Universität Tübingen, Tübingen, Germany

    Fivos Papadimitriou

About the author

 Dr.Dr. Fivos Papadimitriou, B.Sc. (Athens), M.Sc. (Athens), M.Sc. (Paris), M.Ed. (Patras), Ph.D. (Budapest), Ph.D. (Oxford), is at the University of Tübingen. He has created new mathematical formulas, models and methods for measuring landscape complexity and spatial complexity.

Bibliographic Information

  • Book Title: Spatial Complexity

  • Book Subtitle: Theory, Mathematical Methods and Applications

  • Authors: Fivos Papadimitriou

  • DOI: https://doi.org/10.1007/978-3-030-59671-2

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-59670-5Published: 03 November 2020

  • Softcover ISBN: 978-3-030-59673-6Published: 03 November 2021

  • eBook ISBN: 978-3-030-59671-2Published: 02 November 2020

  • Edition Number: 1

  • Number of Pages: XXI, 298

  • Number of Illustrations: 29 b/w illustrations, 149 illustrations in colour

  • Topics: Complex Systems, Geography, general, Topology, Cognitive Psychology, Biodiversity

Buy it now

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access