Search results for " fractal"
showing 10 items of 45 documents
The p-Laplacian with respect to measures
2013
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
L’approche fractale des tissus urbains – réflexions conceptuelles et analyses morphologiques
2014
International audience
Growing a Project-Based Translation Pedagogy: A Fractal Perspective
2012
Le présent article propose un cheminement fractal à travers la psychologie et la philosophie éducative, avec l’intention de faire la lumière sur une représentation arborescente de sources d’inspiration interdisciplinaires et complémentaires pour une pédagogie de la traduction par projets. Commençant par la méthode d’apprentissage socioconstructiviste proposée au tournant du millénaire, notre propos tente de brosser un vaste portrait des influences synergiques sous-jacentes à l’approche émergente « holistique-expérientielle » de la formation en traduction. Le post-modernisme, l’énaction dans les sciences cognitives, la théorie de la complexité, la théorie éducative transformationnelle et l’é…
Analyse morphologique de talwegs et comportement scalant : applications des dimensions non-entières à la géographie physique
1999
Morphological talweg analysis and scaling behaviour: applying non-integer dimension to physical geography. -- The organisation of the talweg network is fundamental to the erosion system on the silty loamy plateaux of north-western France. The morphology of the Pays de Caux is a good example of successive runoff concentration caused by the nesting of small dry valleys. These are inherited from a periglacial climate and their general direction is governed by tectonics. However the detailed pattern of these forms remains complex and without obvious explanation. Non-integer dimensions may offer a ceratin logic to this relatively chaotic pattern. This paper has therefore sought to demonstrate th…
Encriptación óptica empleando llaves Weierstrass-Mandelbrot
2013
[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to enc…
Aménités urbaines et périurbaines dans une aire métropolitaine de forme fractale
2002
In the THÜNEN tradition, Urban Economy is a striking abstraction, giving models that keep the main features of the wide diversity of real word cities. Nevertheless, this paradigm less suits the modern urban spatial structures (polycentrism, weak centripetal forces, etc.), particularly the peri-urban form of metropolitan areas, which are an urban/rural integrated space. In this paper, we propose a classical micro-economic urban model combined with a " SIERPINSKI's carpet " geometry, a fractal form which suits for fit together urban and rural areas in a hierarchical structure. Subject to a budget constraint, a household maximises a Cobb-Douglas/CES function, where household's taste for divers…
L'analyse fractale des zones métropolitaines: un aperçu méthodologique
1993
National audience; La croissance des agglomérations se manifeste dans la plupart des cas par J'apparition d'un tissu urbain amorphe et fragmenté même si le plan initial de la ville était conçu selon une géométrie régulière comme les bastides ou les villes nouvelles. Cette morphologie irrégulière de la surface bâtie ne semble pas liée à une situation lùstorique particulière et elle apparaît souvent en dépit des intentions des urbanistes qui tentent souvent d'imposer des plans compacts et réguliers. Ceci incite à supposer que la morphogenèse urbaine est le résultat de processus d'auto-organisation qui devraient se manifester par un principe d'ordre interne, si irrégulière que paraisse la morp…
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
L'analyse fractale, un nouvel outil pour l'analyse spatiale des agglomérations urbaines
1997
The fractal approach. A new tool for the spatial analysis of urban agglomerations. Fractal geometry is a new approach for the study of spatial distributions. The basic model is a law of hierarchical distribution corresponding to Pareto's law which is familiar to urban geographers and demographers. The methods of fractal analysis can be used to study the spatial organization of human activities across scales. The regularities and the discontinuities in the distributions can then be identified. These discontinuities can be spatially situated. Applying this concept to urbanized areas has shown that districts can be defined and classified according to their scaling relations, thereby allowing d…