Geographical Models with Mathematica

Geographical Models with Mathematica provides a fairly comprehensive overview of the types of models necessary for the development of new geographical knowledge, including stochastic models, models for data analysis, for geostatistics, for networks, for dynamic systems, for cellular automata and for multi-agent systems, all discussed in their theoretical context.

The author then provides over 65 programs, written in the Mathematica language, that formalize these models. Case studies are provided to help the reader apply these programs to their own studies.

• Provides theoretical, stochastic and dynamic system models
• Covers data science, both in a spatial and spatio-temporal analysis
• Presents a microstructural understanding of the mechanical behavior of granular materials

Students, teachers and researchers in geography; the user community of Wolfram language and Mathematica students, teachers and researchers in geosciences and social sciences

Introduction

• I.1 The scientific practice of the geographer
• I.2 The three forms of geography projects
• I.3 Plan of the work
• I.4 How should this work be read?
• I.5 Appendix 1: a general modeling language Mathematica

Part 1: Modeling the Relationships between Societies and Nature

Introduction

1: The Theoretical Context of Classical Geography

• Abstract
• 1.1 Environmentalism – a theory that is still rejected
• 1.2 The theoretical double paradox of classical geography
• 1.3 The general theory of systems and the theories derived therefrom
• 1.4 Conclusion
• 1.5 Appendix 2: Importing data within Mathematica

2: Statistical and Probability Models for Given Relationships Between Societies and the Natural Environment

• Abstract
• 2.1 Acknowledging the probability model for recorded data
• 2.2 Modeling the relationships between two or several variables
• 2.3 Temporalities and time series models
• 2.4 Conclusion
• 2.5 Appendix 3: chronological program processing

3: Models of Ordinary Dynamic Systems

• Abstract
• 3.1 Four lines of questioning to understand the behavior of a dynamic system
• 3.2 Initiation in the modeling of dynamic systems
• 3.3 Assets and restrictions of ODE models
• 3.4 More realistic models of geographical systems
• 3.5 Conclusion
• 3.6 Appendix 4: crowd behavior in catastrophic situations

Part 2: Modeling Geographic Locations

Introduction

4: Theories of Geographical Locations

• Abstract
• 4.1 Introduction to spatial economic theories
• 4.2 A new urban economy and a new economic geography
• 4.3 Conclusion

5: Theoretical Geolocation Models

• Abstract
• 5.1 Von Thünen and d’Alonso’s monocentric and polycentric models
• 5.2 Steiner’s model generalizes Weber’s
• 5.3 Central place models in the making
• 5.4 Conclusion

Part 3: Spatial Structures and Territorial Dynamics

Introduction

6: Theories Used to Understand Territorial Structures and Dynamics

• Abstract
• 6.1 From terrestrial to geographical space
• 6.2 Some theories drawn from various fields and used to explain simple territorial forms
• 6.3 From morphology to morphogenesis
• 6.4 An overview of morphogenetic theories
• 6.5 Conclusion
• 6.6 Appendix 5: globalization at the root of a paradox: homogenization and global fracturing

7: Models of Basic Structures: Points and Fields

• Abstract
• 7.1 Modeling the point structures of a geographical space
• 7.2 Modeling geographical fields
• 7.3 Conclusion
• 7.4 Appendix 6: Introduction to the morphometric analysis of the Grenoble Alps

8: Models of Basic Structures: Networks

• Abstract
• 8.1 The two aspects of a network: graphs and matrices
• 8.2 Modeling the structure of a spatial network
• 8.3 Qualitative geographical models and graph theory
• 8.4 Modeling network dynamics
• 8.5 Conclusion
• 8.6 Appendix 7: A geometric approach to the network of French metropolises

9: Geographical Space as a Mixture of Basic Spatial Structures

• Abstract
• 9.1 Testing links between two elementary spatial structures
• 9.2 Modeling complex spatial structures: machine learning and choremes
• 9.3 Modeling multiscale spatial structures
• 9.4 Conclusion

10: Morphogenetic Macro- and Micro-models

• Abstract
• 10.1 Time series typical of morphogenetic theories
• 10.2 Modeling the dynamics of territorial systems: from ODEs to PDEs
• 10.3 Cellular automata, Brownian motions and multi-agent systems
• 10.4 Conclusion
• 10.5 Appendix 8: simulating urban growth along the French Riviera with a cellular automata model