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Record 1,  Textual support,  English

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 CONT

Les surfaces fractales sont obtenues par subdivision récursive d'une figure géométrique initiale (ex. : triangle, quadrilatère).  1, record 1, French, - surface%20fractale

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 DEF

Pertaining to a geometrical shape whose structure is such, that magnification of the detail by a given factor reproduces the original object.  2, record 2, English, - fractal

Record number: 2, Textual support number: 1 PHR

fractal algorithm, fractal art, fractal attractor, fractal boundary, fractal cove, fractal city, fractal concept, fractal curve, fractal definition, fractal dimension, fractal domain, fractal fern, fractal geometry, fractal goose, fractal graphics, fractal growth, fractal heaven, fractal hell, fractal hexagon, fractal image, fractal Julia set, fractal Koch flake, fractal landscape, fractal lattice measure, fractal modeling, fractal monster, fractal motion, fractal noise, fractal number, fractal object, fractal paradox, fractal pattern, fractal self-similarity, fractal stable, fractal structure, fractal surface, fractal time, fractal tree, fractal vision.  2, record 2, English, - fractal

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 DEF

Relatif aux structures et aux systèmes dynamiques dont les éléments présentent une certaine similarité à l'ensemble quelle que soit l'échelle de l'examen.  3, record 2, French, - fractale

Record number: 2, Textual support number: 1 OBS

S'applique aux changements spatio-temporels tels le bruit électronique dans les semi-conducteurs, les fluctuations de voltage dans les membranes neurales, les crues périodiques des eaux, les variations des indices économiques et du trafic routier, les battements du cœur, etc. Selon B. Mandelbrot, créateur du terme en 1975, le concept n'a pas encore de définition mathématique généralement acceptée. Le terme est dérivé du latin «fractus» qui signifie «fragmenté», «irrégulier». Le masculin pluriel est «fractals», le féminin pluriel, fractales».  3, record 2, French, - fractale

Record number: 2, Textual support number: 1 PHR

aérogel fractal, agrégat fractal, aire fractale, algorithme fractal, analyse fractale, arbre fractal, art fractal, attracteur fractal, autosimilarité fractale, bruit fractal, chaos fractal, codimension fractale, compression d'images fractale, courbe fractale, continent fractal, côte fractale, croissance fractale, débit fractal, densité fractale, diffraction fractale, dimension fractale, distribution fractale, échelle fractale, ensemble fractal, éponge fractale, équation fractale, espace-temps fractal, fonction fractale, figure fractale, flèche du temps fractale, fonction d'interpolation fractale, forme fractale, fromage fractal, front de diffusion fractal, frontière fractale, générateur fractal, génération fractale, géométrie fractale, groupe fractal, hasard fractal, île fractale, image fractale, imagerie fractale, infographie fractale, interface fractale, intermittence du bruit fractale, lac fractal, langage fractal, ligne fractale, masse fractale, mesure fractale, modèle fractal, modélisation fractale, monstre fractal, montagne fractale, motif fractal, musique fractale, nature de la turbulence fractale, nombre fractal, objet fractal, ordinateur fractal, ordre fractal, pavage fractal, paysage fractal, périmètre fractal, plaque fractale, profil fractal, reconnaissance d'image fractale, rythme fractal, segmentation fractale, structure fractale, surface fractale, synthèse fractale, système fractal, tambour fractal, temps fractal, texture fractale, théorie fractale, tortuosité fractale, trajectoire fractale, transformation fractale, transformée fractale, vidéocompression fractale, vision fractale, zone fractale.  3, record 2, French, - fractale

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 DEF

Any solution of the Laplace equation which has continuous derivatives of first and second order.  3, record 3, English, - harmonic%20function

Record number: 3, Textual support number: 1 CONT

... it is quite natural to look at GSPD as a fractal measure... with infinitely many types of singularities. Probing the surface with many random walks is equivalent to the estimation of the corresponding solutions of Laplace's equation... which are usually called harmonic functions. Consequently, the name harmonic measure is also used for GSPD.  2, record 3, English, - harmonic%20function

Record number: 3, Textual support number: 1 OBS

To calculate the harmonic measure and its characteristic properties one can follow two numerical methods. i) After having generated a DLA cluster one releases further particles ... whose diffusional motion is simulated by the same technique ... which is used for growing the aggregate. These probe particles, however, are eliminated when they arrive at the surface, and a record is kept of how many times each of the surface sites is contacted in this way. The normalized number of contacts is then regarded as the growth probability.  2, record 3, English, - harmonic%20function

Record 3,  Textual support,  French

Record number: 3, Textual support number: 1 DEF

Fonction formée par quatre points d'une droite, d'un faisceau de droites, d'une moyenne, etc.  1, record 3, French, - fonction%20harmonique

Record 3,  Textual support,  Spanish

Record 4,  Textual support,  English

Record number: 4, Textual support number: 1 CONT

It is generally found that natural objects possess self-similarity and self-affinity in their structures. Fractal analysis, a technique based on these properties, has been widely used in various research applications. In the active remote sensing of the earth terrain, it is possible to extract this fractal information from the images obtained. In this application, fractal surface dimension, an important parameter in fractal analysis, can be employed as an additional feature to classify different landuse areas. This fractal surface dimension is generally related to the roughness of the surface. By keeping the x and y coordinates of the pixels of the image, and taking the grey level of each pixel as its z coordinate, a three-dimensional surface can be constructed. The calculation of fractal surface dimension can then be carried out on that surface.  2, record 4, English, - fractal%20analysis

Record number: 4, Textual support number: 1 OBS

fractal analysis: term officially approved by the RADARSAT-2 Terminology Approval Group (RTAG).  3, record 4, English, - fractal%20analysis

Record 4,  Textual support,  French

Record number: 4, Textual support number: 1 CONT

L'analyse fractale repose sur l'étude des fluctuations locales des pixels pour la recherche de la répétition d'un motif lorsqu'on observe l'image à différentes résolutions. Ce codage met en valeur les fluctuations dans les deux directions privilégiées correspondant aux deux directions physiques du radar (distance et azimut).  2, record 4, French, - analyse%20fractale

Record number: 4, Textual support number: 2 CONT

L'apparition des images à très haute résolution spatiale en télédétection a substantiellement compliqué l'analyse automatique des images optiques. La difficulté de l'analyse fractale [Kaplan, 1999], etc. ne semble pas pouvoir s'adapter à toutes les formes de textures. La grande variation locale des niveaux de gris des objets présents dans les images optiques à très haute résolution spatiale, rend obsolètes les méthodes d'analyse précédemment citées. Dans [Pentland, 1984], il est montré que la dimension fractale peut être utilisée pour caractériser des scènes naturelles; toutefois, ce type d'analyse n'est plus efficace lorsque l'image à étudier est très irrégulière. Pour analyser des signaux possédant une régularité variant fortement d'un point à un autre, il est préférable d'utiliser l'analyse multifractale. Nous proposons un nouvelle approche à la segmentation d'images de télédétection basée sur l'analyse des composants fractals de l'image. Elle ne nécessite aucune connaissance a priori sur l'image, et étudie la régularité locale et globale par le biais de l'exposant de Hölder et du spectre multifractal. Les singularités et les irrégularités d'un signal sont souvent porteuses de la plus grande part d'information.  3, record 4, French, - analyse%20fractale

Record number: 4, Textual support number: 1 OBS

analyse fractale : terme uniformisé par le Groupe de travail de la terminologie de RADARSAT-2 (GTTR).  4, record 4, French, - analyse%20fractale

Record 4,  Textual support,  Spanish

Record number: 4, Textual support number: 1 CONT

Ya están desarrollados los nuevos métodos de procesamiento y transmisión de la imagen, tales como el análisis fractal, la transformación de pequeñas ondas, la codificación orientada a objetos,...  1, record 4, Spanish, - an%C3%A1lisis%20fractal

Record 5,  Textual support,  English

Record number: 5, Textual support number: 1 DEF

The residual set of an Apollonian packing.  2, record 5, English, - Apollonian%20gasket

Record number: 5, Textual support number: 1 CONT

The Apollonian construction concludes with five circles, three given and two Apollonian, which together define six circular triangles. Repeating the same procedure, we draw the largest inscribed circle in each triangle. Infinite further repetition is called Apollonian packing. To the resulting infinite collection of circles one adds its limit points, and one obtains a set I call Apollonian net. A portion of net within a circular triangle ... is to be called Apollonian gasket.  3, record 5, English, - Apollonian%20gasket

Record number: 5, Textual support number: 2 CONT

Formation of an Apollonian gasket : the points that are never inside any of the circles form a set of zero area which is, as it were, more than a line, but less than a surface. Its fractal dimension therefore lies between 1 and 2, though its exact value is not known. It is approximately 1. 3.  4, record 5, English, - Apollonian%20gasket

Record number: 5, Textual support number: 1 OBS

See Sierpinski gasket.  5, record 5, English, - Apollonian%20gasket

Record 5,  Textual support,  French

Record number: 5, Textual support number: 1 DEF

L'ensemble non dénombrable des points à surface nulle qui restent non couverts par un bourrage apollonien.  2, record 5, French, - tamis%20apollonien

Record number: 5, Textual support number: 1 OBS

Voir bourrage, entassement.  3, record 5, French, - tamis%20apollonien

Record 5,  Textual support,  Spanish

Record 6,  Textual support,  English

Record number: 6, Textual support number: 1 CONT

The notion of fractal dimension provides a numerical measure of the wiggliness of a curve or the roughness of a surface. It fits within the intuitive idea that a crinkly curve somehow covers more of a given area than a smooth curve and that a rough surface fills more space than a smooth one. Beyond that, a fractal dimension is a way of expressing the fact that a fractal is self-similar, or contains copies of itself. It reflects the relationship between the whole and its parts.  3, record 6, English, - fractal%20dimension

Record 6,  Textual support,  French

Record number: 6, Textual support number: 1 DEF

Nombre qui sert à quantifier le degré d'irrégularité et de fragmentation d'un ensemble géométrique, d'un objet naturel ou d'un système dynamique. Ce nombre, qui mesure la manière dont ces entités remplissent l'espace dans lequel elles se trouvent, n'est pas nécessairement un entier.  2, record 6, French, - dimension%20fractale

Record number: 6, Textual support number: 1 OBS

Par exemple, la dimension des courbes de Koch est D = 1,26 ..., celle des nuages varie entre 2,2 et 2,3, celle des montagnes se trouve entre 2,1 et 2,3. Il existe plusieurs définitions de la dimension fractale qui ne sont pas formellement équivalentes et qui conduisent à des valeurs numériques différentes aussi bien du point de vue mathématique que pour des cas concrets. Certaines définitions soulignent la connectivité intrinsèque d'un objet (dimension d'étalement, ou chimique), d'autres considèrent plutôt la façon dont l'objet emplit l'espace ambiant (dimension d'empilement, de tortuosité, dimension spectrale). Les recherches en cours étudient des aspects très importants pour la description des systèmes dynamiques tels l'élasticité sous déformation et l'intermittence. D'autre part, il existe déjà des méthodes très simples pour construire des lignes, des surfaces et des volumes à dimension fractale.  2, record 6, French, - dimension%20fractale

Record number: 6, Textual support number: 1 PHR

La dimension fractale s'accentue, augmente, croît, décroît, diminue, quantifie, renseigne sur la répartition de la masse, tend vers zéro, varie.  2, record 6, French, - dimension%20fractale

Record number: 6, Textual support number: 2 PHR

calculer, correspondre à, évaluer, extraire, obtenir une dimension fractale.  2, record 6, French, - dimension%20fractale

Record number: 6, Textual support number: 3 PHR

dimension fractale chimique, spectrale.  2, record 6, French, - dimension%20fractale

Record number: 6, Textual support number: 4 PHR

dimension fractale d'empilement, d'étalement, de tortuosité.  2, record 6, French, - dimension%20fractale

Record 6,  Textual support,  Spanish

Record 7,  Textual support,  English

Record number: 7, Textual support number: 1 CONT

DLA and the Harmonic Measure. How can we best characterise the surface or perimeter of... fractal structures? The harmonic measure affords a method of quantitatively characterising such surfaces. This(probability) measure is defined(with respect to a particular cluster) as the probability,... of a random walker approaching the cluster from infinity first striking the cluster between the points... along the boundary of the cluster.  1, record 7, English, - probability%20measure

Record 7,  Textual support,  French

Record 7,  Textual support,  Spanish

Record 8,  Textual support,  English

Record number: 8, Textual support number: 1 CONT

The term diffractals was coined in Berry 1979 to denote waves that are either reflected by a fractal surface or refracted by a slab of transparent material with fractally turbulent refractive index. Diffractals are a new wave regime in which ever finer levels of structures are explored and geometrical optics is never applicable.  2, record 8, English, - diffractal

Record 8,  Textual support,  French

Record number: 8, Textual support number: 1 DEF

Structure créée par diffraction des ondes réfléchies par une surface fractale et dont la description échappe à la géométrie optique.  2, record 8, French, - diffractale

Record number: 8, Textual support number: 1 OBS

Terme formé vers 1979 par M. Berry à partir de «fractale de diffraction».  2, record 8, French, - diffractale

Record number: 8, Textual support number: 2 OBS

Néologisme créé par analogie à diffracté, diffractif, diffraction, diffractomètre (voir le Grand Robert, volume 3, page 531).  3, record 8, French, - diffractale

Record 8,  Textual support,  Spanish

Record 9,  Textual support,  English

Record number: 9, Textual support number: 1 CONT

A fractal flake in which the altitude would be analytically the same as on the above Pangaea but with a scale of the order of magnitude of half the radius would have a surface of dimension D=5/2 and would look overall like one of the irregular moons of the outer planets.  1, record 9, English, - fractal%20flake

Record 9,  Textual support,  French

Record number: 9, Textual support number: 1 OBS

Voir flocon de neige.  1, record 9, French, - flocon%20fractal

Record 9,  Textual support,  Spanish

Record 10,  Textual support,  English

Record number: 10, Textual support number: 1 OBS

See self-affine fractal.  2, record 10, English, - self%2Daffine%20surface

Record 10,  Textual support,  French

Record number: 10, Textual support number: 1 OBS

Voir aussi surface fractale et fractale auto-affine.  1, record 10, French, - surface%20auto%2Daffine

Record 10,  Textual support,  Spanish

Record 11,  Textual support,  English

Record number: 11, Textual support number: 1 OBS

See fractal surface.  1, record 11, English, - stochastic%20fractal%20surface

Record 11,  Textual support,  French

Record number: 11, Textual support number: 1 CONT

Surfaces fractales stochastiques où le facteur de dispersion est variable.  1, record 11, French, - surface%20fractale%20stochastique

Record 11,  Textual support,  Spanish