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RESEARCH PRODUCT

Analyse de la distribution spatiale des implantations humaines : apports et limites d’indicateurs multi-échelles et trans-échelles

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As human beings, it is easy for us to judge visually whether a distribution is dispersed or concentrated. However, the quantitative formalization of our impressions is problematic. It depends on the scales of the chosen analysis. This dependence of indicators on scales has changed. It is initially considered as a barrier to knowledge, it now reflects the multi-scale organisation of the distributions studied. The central objective of this thesis is to investigate the limits and contribution of multi-scale and trans-scale indicators to the study of the spatial distributions of human settlements.Spatial analysis aims at comparing spatial distributions to a uniform distribution. The way in which spatial distributions move away from this reference is used to characterize the multi-scale organization of the analyzed distributions. The application of these methods to human settlements has not been satisfactory. The use of an exogenous reference is not adapted to distributions that are very unevenly concentrated in space.Fractal analysis used in urban geography considers that the analysed distributions are their own measurement standard. Fractal dimensions measure how the space occupied by them evolves across scales. This type of analysis requires a regularity between scales, the invariance of scale whose existence is not verified on all territories. Trans-scale analysis generalises the principles of fractal analysis to all distributions and makes it possible to characterise the unequal concentration of human settlements in rural and urban territories.