Table of Contents. General Introduction... Part 1. Introduction... 3

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1 Table of Contents General Introduction... xi PART 1. THE STRUCTURE OF THE GEOGRAPHIC SPACE... 1 Part 1. Introduction... 3 Chapter 1. Structure and System Concepts The notion of structure In mathematics and in physics In computer science In human, social and life sciences The systemic paradigm The systemic triangle The whole is greater than the sum of its parts The notion of organization Structure and organization Sequential organizations Organization in classes and partitions Organizations in trees Network organization Hierarchical organizations The use of the graph theory for complex organizations Complexity of an organization, from determinism to chaos Chapter 2. Space and Geometry Different theories of space Euclidian models Metric spaces... 32

2 vi Simulation of Complex Systems in GIS Normed spaces Pseudo-Euclidian spaces Riemann s spaces Topological spaces About equality in a space Geometry and its data structures Planes structure The elevation model (2D½) Non-Euclidian space, anamorphoses and gravitation field Possible morphologies of a finite space without limits Neat geometry and fuzzy geometry Chapter 3. Topological Structures: How Objects are Organized in Spatial Systems Topology Metrics and topologies Calculated topology, structural topology Square grid Hexagonal grid Neighborhood structure for an irregular mesh Neighborhood operator for an irregular mesh Vector-topological model of a meshing of random zones Network topological model Hierarchization Chapter 4. Matter and Geographical Objects Geographic matter The material field Hypothesis of spatial and temporal differentiation of matter The notion of observation The geographic object: Definitions and principles Identification Spatial base of an object Material content of an object Material geographic object and layers of objects The principle of separation The principle of mixing The principle of impenetrability The dimensionality of an object The principle of embedding Evaluated geographic object Description forms of the object... 94

3 Table of Contents vii Chapter 5. Time and Dynamics Time Temporalities Life interval T Minimum time step dt Time base B T Activity support of a phenomenon σ Phenomenon with discrete (or isolated) support Phenomenon with continuous or piecewise continuous support Events, processes Morphological discretization of a phenomenon Billiard balls example Temporality of a spatial process Decomposition of a complex process An epistemic choice: reciprocal dependency between the complexity levels of a phenomenon Chapter 6. Spatial Interaction Presentation of the concept Definition of macroscopic interaction The four elementary (inter)actions Microscopic interaction like a multigraph Composition of successive interactions The configurations and the trajectories of a simulation are categories Intermediary level matrix representation Examples of interactions Flux and transport Movement of an object in space Collision between two objects Accumulation by confluence Centrifugal distribution Equalization through communication vases First definition of the notion of spatial system Part 1. Conclusion: Stages of the Ontogenesis PART 2. MODELING THROUGH CELLULAR AUTOMATA Chapter 7. Concept and Formalization of a CA Cellular automata paradigm

4 viii Simulation of Complex Systems in GIS 7.2. Notion of finite-state automata Mealy and Moore automata A simple example of CA: the game of life Different decompositions of the functions of a cell Threshold automaton, window automaton Micro level and Stochastic automaton Macro level and deterministic automaton General definition of a geographic cellular automaton Different scheduling regimes of the internal tasks of the system Ports, channels, encapsulation Interaction Space associated with a geographic cellular automaton Topology and neighborhood operator of a GCA The notion of cellular layer Hierarchized GCA models Spatial hierarchization Temporal hierarchization Hierarchization of the control Chapter 8. Examples of Geographic Cellular Automaton Models SpaCelle, multi-layer cellular automaton Description Choice of metrics and the notion of neighborhood in SpaCelle Universe Structures Definition of cellular behavior with SpaCelle General structure of a model Cellular behavior, birth, life and death, law of the most pertinent rule Deterministic or stochastic functioning Rule syntax Calculation of the pertinence of a transition rule Strict or fuzzy evaluation of a neighborhood The rule base The SpaCelle meta-model Outputs Example: the evolution model of the Rouen agglomeration From the map to the cellular automaton The rule base Evolution observed in the Rouen space between 1950 and Current assessment of SpaCelle use

5 Table of Contents ix 8.3. RuiCells Presentation of the model Recognition of soil occupation and surface development Functioning The outputs GeoCells The generic GeoCells model The GeoCells-Europe model The GeoCells-Votes model Part 2. Conclusion PART 3. A GENERAL MODEL OF GEOGRAPHIC AGENT SYSTEMS Part 3. Introduction Chapter 9. Theoretical Approach of an Integrated Simulation Platform For an integrated platform of simulation General specifications Chapter 10. A Formal Ontology of Geographic Agent Systems The conceptual framework The notion of a geographic agent system A generalization of the notion of process The notion of a geographic agent When the geographic object becomes an agent The agent dynamics The agent-organization duality The formalization of the geographic agent The formalization of the notion of organization Re-examining the concept of organization Social organization, spatial organization Formalization Two examples of organization Predefined spatial organization Predefined social organization The formalization of behavior The evaluation The decision The action The formalization of a basic behavior

6 x Simulation of Complex Systems in GIS Formalization of a general AOC model The Schelling model example Part 3. Conclusion General Conclusion Acronyms Bibliography Index

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