Simulation of Complex Systems in GIS

Patrice Langlois

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848212237
• eBook ISBN: 9781118600993
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geography
• Index: Geography

This book provides a comprehensive view of the field of geographical modeling by dividing the topic into three parts.

The first part of the work establishes the foundations of geographical modeling through the use of more general concepts, including: structure, organization, system, geometries, topologies, metrics, material, and object. Finally, introduction of the concept of time leads to the theories of process and spatial interaction, which are fundamental in geography.

The second part of the book tackles the use of computer tools for dynamic model building, which are the geographic cellular automata (GCA), and presents several models applied to various themes, such as urban growth, natural risks by flood simulations, as well as more political themes, such as the use of European funds, or the development of voting patterns in France.

Finally, a general model of the geographic agents system (GAS) which can be used as a basis for the construction of a model-building platform for dynamic spatial models is presented.

PART 1

The Structure of the Geographic Space

Geometry and movement are the two inseparable problems in geographic theory. Regardless of the movement, they leave their mark on the terrestrial surface. They produce a geometry, then the geometry produces movements: circulations in states are created by national frontiers, and in return they contribute to create these frontiers.

William Bunge

Part 1

Introduction

The concept of geographic space has been used by geographers and spatial economists since the end of the 19th century, by such people as von Thunen, Weber, Losch, Christaller and many others. It is mostly done through network studies, taking into account locations, distances, and terrestrial surfaces. There are also “functional distances” which are no longer expressed in kilometers, but in transport cost, in travel time, in energy spent, etc. Surfaces are measured not only in hectares or in square kilometers but also in population size, density and revenues. Thus, geographic space appears as though it has been constituted by all of its “geographic matter”, (natural or constructed, human or social). It is a space of diverse activities that consumes energy and thus possesses an economic dimension. Then, there is a sort of generalized or abstract roughness that expresses the degree of difficulty to deal with the fundamentally heterogeneous space. For example, Jacques Levy speaks of different pedestrianized “metrics” to express this notion. This has led to different types of cartographic representations where geometric space is deformed in order to better visualize this spatial roughness through anamorphosic methods (Tobler, Charlton, Cauvin–Raymond, Langlois, etc.).

Also, the concept of space is not totally foreign to the concept of geographic objects, which has been used for a long time in human geography. We will elaborate on the precise and concrete definition of this notion of geographic object later on in geomatics. In addition, the notion of objects is also a central concept in computer science, where object–oriented languages have an important place, and are well adapted to multi–agent modeling. In the context of geographic phenomena modeling, the use of the term “object” may cause confusion. Nevertheless, we use it here not to refer to oriented–object programming, but in a more general, systemic and auto–referential “physics” sense. We will demonstrate how the object is the central concept through which the first concepts of space, time and energy–matter were structured. It is also the interface between the observation and modeling levels of reality.

The object is not only defined as its inanimate material element but covers the whole disciplinary field, as we believe that in the field of computer modeling the same elementary principles of structuring and function are applicable, from a pebble to a social group. The important differences between objects come from the differences in the levels of complexity and not because they come from the essence or from fundamental epistemic differences, in particular between inanimate and living things. We must then be able to formalize and program them with the same methods and modeling language, on the same platform of computer modeling.

If we were to reflect upon the concept of a modeling platform, we would need a clear conceptual and mathematic formalization of the concepts of space, spatial structure, objects and spatial systems. We could then elaborate on the notions of dynamics, process and behavior, which gives these objects an “agent” status.

Chapter 1

Structure and System Concepts

1.1. The notion of structure

According to Raymond Boudon, “structure appears as indispensable in all human sciences, judging by the increase of its employment, and it being difficult to pinpoint”. Amongst the definitions contained in the Universalis Encyclopedia, there are four concerning our subject:

– complex organization (administrative structure);

– the way in which things are organized to form a set (abstract or concrete);

– in philosophy the stable set of interdependent elements, such that each one is dependent on its relation with others;

– in mathematics, a set composed of certain relations or laws of composition.

Let us observe at which point these definitions converge towards our subject. The first reintroduces complexity; the second brings us back to the notion of an organized set; the third, in its simplified version, refers to the structuralist theories (Saussure, Merleau–Ponty, Piaget, Lévi–Strauss, etc.) but does not contradict the way in which mathematics formalizes it through the fourth definition. Furthermore, it corresponds to a contemporary trend consisting of defining an object, not by its intrinsic properties, but by its connections with others. Its function is defined because it consumes and produces on the outside and not by its content or its internal mechanism of functioning. In particular, it is the systemic paradigm of the “black box”.

1.1.1. In mathematics and in physics

1.1.1.1. The mathematical structure of group and physics invariants

It is interesting to see how mathematics approaches this notion of structure. There is a great diversity of meanings that are more or less general but each of them is precisely defined, such as must be done in mathematics. The most general definition is the following: a structure is a set composed of relations between its elements. In the case of an algebraic structure, it is the operations (additions, multiplications, etc.) that define the relations between the elements. Thus, the number 5 is related to a couple of numbers (2, 3) by the addition operation. However most of these operation properties are important (commutativity, associativity, etc.). The example of the group's structure¹ is emblematic because it is both simple and plays a fundamental role in mathematics and physics, translating a certain invariance and symmetry properties in natural phenomena. We also speak of invariance in Euclidian geometry by the group of trips (translations and rotations) that operate on the points of space, or by the group of rotations that operate on the vectors (the vectors already being invariant by translation). This means that a rigid object, such as a box's x width, y depth and z length, doesn't change its dimension (its diagonal length l being calculated by the Pythagorean theorem: l² = x² + y² + z² ). This is translated by the invariance of length l when we operate its displacement of the box.

The group structure can be enriched if we add other operations such as a multiplication or a scalar product, etc. We then see a swarm of algebraic structures with flourishing images, such as modules, rings, bodies, algebra, vectorial space, topologic space, Hibert space, etc. All of these structures play an essentially intellectual role in mathematics and physics. If we can establish a bijection between two sets of objects (often in very different domains), that can conserve their respective algebraic structure (isomorphisms). We can apply all of these acquired results from one domain to the other. Furthermore, each of these domains enlightens the other one under a new representation and then improves the comprehension of each of them.

1.1.2. In computer science

In computer science the notion...

Table of contents

• Cover
• Title Page
• Copyright
• General Introduction
• PART 1: The Structure of the Geographic Space
• PART 2: Modeling Through Cellular Automata
• PART 3: A General Model of Geographic Agent Systems
• General Conclusion
• Acronyms
• Bibliography
• Index