Geographical Models with Mathematica

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