Search results for "fractale"
showing 10 items of 40 documents
Dimensions fractales et réalités périurbaines. L'exemple du Sud de Bruxelles
2004
This exploratory paper aims at showing how the fractal dimension can be used to characterise the spatial structure of built-up areas within the periurban fringe. The southern periphery of Brussels is considered here. Two estimation techniques (correlation and dilation) are applied to surface areas, and one (correlation after dilation) to the borders of built-up areas. They are applied to windows of fixed size. Fractal dimensions are then compared with traditional socio-economic and morphological indicators. The results are interpreted in the context of urban sprawl and polycentric development of the peripheries. These analyses confirm the usefulness of the fractal approach for describing bu…
Estimation des dimensions en présence d'erreurs
2018
Journées du GDR Analyse Multifractale, Nouan-le-Fuzelier, FRANCE, 16-/09/2018 - 20/09/2018; Nous nous posons la question de l'estimation des différentes dimensions fractales lorsque nous sommes en présence de bruit additif (à une itération donnée) ou multiplicatif ( qui se propage à travers les itérations), en testant, sur des fractales construites, les méthodes classiques d'estimation et en analysant la structure des résidus d'estimation.
La morphologie des tissus urbains et périurbains à travers une lecture fractale
2005
Urban expansion produces an irregular urban fabric. This phenomenon influences areas which are distant from urban centres, a problem for sustainable development. Solutions proposed to reduce urban expansion are modelled on the pattern of the compact town. Generally, it is believed that these solutions are unacceptable to the people concerned. In this article we present an alternative approach to the study of urban fabric, which shows that, despite their irregular form, it is possible to describe their development using fractal analysis. This permits understanding of the socio-economic causes of this process and the development an alternative conceptual approach to the management of urban ex…
Espaces tangents pour les formes auto-similaires
2013
The fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. It finds applications in many branches of science as objects of such complex structure often poses interesting properties. In 1988 Barnsley presented the Iterative Func-tion System (IFS) model that allows modelling complex fractal shapes with only a limited set of contractive transformations. Later many other models were based on the IFS model such as Language-Restricted IFS,Projective IFS, Controlled IFS and Boundary Controlled IFS. The lastto allow modelling complex shapes with control points and specific topol-ogy. These models cover classical geometric models such as B-…
Theoretical approaches for geometric optimization of urban forms : towards a fractal development of the city
2017
This thesis aims to establish a urban structure that optimizes inhabitant's preferences. In other words, we want to find out which city shape answers the best the residents' aspirations, according to their consumption preferences for urban and green amenities. By considering a theoretical field of study and by characterizing the population by a Cobb-Douglas behavioral pattern, we will build step by step a city, assuming successive arrivais of new individuals, in order to find out which geometric shape gives the most suitable answer. The final goal of this thesis is there to suggest a city with a fractal shape as an appro- priate answer to the resident's expectations. We will show that this …
Méthodes de contrôle de la rugosité à partir des propriétés différentiels de courbes autosimilaires.
2023
La rugosité a de nombreuses applications, l’industrie l’utilise comme outil pour avoir des propriétés de surface recherchés ou pour le contrôle qualité, le domaine de l’informatique graphique s’intéresse à la synthétiser pour la génération de terrains ou la génération de textures et aussi à simuler ses effets sur la lumière avec les BRDF. . . Dans cette présentation, nous proposeronsun rappel sur la rugosité, notamment sa définition plus précise que "surface ou courbe non lisse" et ses outils de quantification suivi d’une comparaison de certaines de ses méthodes de génération, illustrant l’intérêt d’une approche fractale pour l’étudier. Nous commencerons par des méthodes simples mais offran…
Analyse de la distribution spatiale des implantations humaines : apports et limites d’indicateurs multi-échelles et trans-échelles
2020
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 whic…
Tangentes à une courbe fractale
2007
http://www.irit.fr/REFIG/index.php/refig/article/view/10; National audience; Nous nous intéressons au calcul des tangentes à une courbe fractale définie à l'aide d'un IFS. Généralement, les courbes fractales sont nulle part dérivables, mais sous certaines conditions on peut montrer qu'elles admettent, en un ensemble de points, des demi-tangentes à droite et à gauche. Nous proposons une méthode permettant de déterminer ces demi-tangentes.
Use of fractal geometry to dissolution study of a sweetener excipient
2002
International audience
Etude de la morphologie de l'interface reactive de dissolution en utilisant le concept de géométrie fractale
1995
National audience