Lois d'échelle et transitions fractal-non fractal en géographie

Abstract

Résumé. Le concept de transition fractal -non fractal fut introduit initialement dans un cadre de physique fondamentale. Il est fondé sur le constat que le monde est globalement organisé de manière scalaire (comme fonction de l'échelle). Cette transition décrit le passage d'états non fractals (indépendants de l'échelle) à des états fractals (explicitement dépendants de l'échelle) et se manifeste localement sur des gammes d'échelles assez courtes. Ce concept permet de comprendre comment certains systèmes peuvent paraître non fractals à certaines échelles et fractals à d'autres.Abstract. The concept of fractal -non fractal transition has been initially introduced in a physical framework. It is based on the fact that the world is generally organized according to scales. This transition describes the passage from non fractal (scale independent) states to fractal (scale-dependent) states and manifests itself locally on rather short ranges of scales. It allows one to understand how some systems may seem to be non-fractal at some scales and fractal at others. We establish three possible fractal laws of fractal -non fractal transitions, which we fit to geographic (urban and physical) data in order to demonstrate the essential character for geography of these structuring in scale. Mots

Macroscopic Quantum-Type Potentials in Theoretical Systems Biology

“…In this case the fractal dimension is no longer constant, but varies in a linear way in terms of the logarithm of resolution. Many manifestations of such a behavior have been identified in human and physical geography [ 19 , 20 ]. law of “scale dynamics” involving a scale harmonic oscillator: For ε ≪ λ 0 it gives the standard scale invariant case = 0 (λ 0 / ε ) τ 0 , i.e.…”

Dupont et les modèles systémiques

“…Sur toutes ces innovations, parfois délaissées, se greffent de nouveaux développements : des modèles conceptuels graphiques sont approfondis par la théorie des graphes, et les systèmes dynamiques spatiaux bénéficient des avancées dans le calcul des équations différentielles partielles. Les jeunes DUPONT et les moins jeunes continuent d'innover, notamment en modélisant et en approfondissant les théories des systèmes complexes multi-échelles avec les approches fractales [Forriez & Martin, 2010, Dauphiné, 2011. Ils bénéficient des nombreux travaux effectués dans les disciplines voisines.…”

Scale Relativity and Fractal Space-Time: Theory and Applications

“…The application of the various tools and methods of the scale relativity theory to history and geography has been proposed by Martin and Forriez [34,61,35,36]. Forriez has shown that the chronology of some historical events (various steps of evolution of a given site) recovered from archeological and historical studies can be fitted by a log-periodic deceleration law with again g ≈ 1.7 and a retroprediction of the foundation date of the site from the critical date [34,35].…”

“…Forriez has shown that the chronology of some historical events (various steps of evolution of a given site) recovered from archeological and historical studies can be fitted by a log-periodic deceleration law with again g ≈ 1.7 and a retroprediction of the foundation date of the site from the critical date [34,35]. Moreover, the various differential equation tools developed in the scale relativity approach both in scale and position space, including the nonlinear cases of variable fractal dimensions, have been found to be particularly well adapted to the solution of geographical problems [61].…”

“…The scale relativity theory has also been recently applied to sciences other than physical sciences, including sciences of life, sciences of societies, historical [34] and geographical sciences [61,35,36] and human sciences [125,87,95,102]. We refer the interested reader to the books [85,99], to parts of review papers or books [83,90,97] and full review papers on this specific subject [6,101] for more details.…”