TERMIUM Plus^®

Record 1,  Textual support,  English

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Pertaining to a geometrical shape whose structure is such, that magnification of the detail by a given factor reproduces the original object.  2, record 1, English, - fractal

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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 1, English, - fractal

Record 1,  Textual support,  French

Record number: 1, 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 1, French, - fractale

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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 1, French, - fractale

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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 1, French, - fractale

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

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The fractal dimension of random structures can also be estimated from their density-density correlation function c(r).  2, record 2, English, - correlation%20function

Record 2,  Textual support,  French

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Fonction permettant d'évaluer la similitude.  2, record 2, French, - fonction%20de%20corr%C3%A9lation

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Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 CONT

The technique of virtual memory is exploited to handle the extremely large numbers of iterates needed for the convergence of the algorithms. They study quantitatively the oscillations which appear in the usual linear regressions of the log-log plot and which are inherent in lacunar fractal sets. These oscillations are the cause of previous underestimates of the Renyi dimensions and in fact make accurate dimension estimates an elusive goal.  1, record 3, English, - lacunar%20fractal%20set

Record 3,  Textual support,  French

Record number: 3, Textual support number: 1 OBS

Tissu lacunaire, lacune : petite cavité du tissu cellulaire, espace interstitiel entre les cellules.  2, record 3, French, - ensemble%20fractal%20lacunaire

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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

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

Record 4,  Textual support,  French

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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

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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

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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

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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

A method for solving the Laplace equation without using an underlying lattice. Applied in simulation techniques involving aggregation of particles and fractal pattern formation. The interfacial pattern is approximated as a piecewise linear with uniform monopole sources. A given interface uniquely determines the source distribution which, in turn, uniquely determines the velocity distribution along the interface. Based on Green’s function, an integro-differential equation, and on the Dirac delta function.  1, record 5, English, - boundary%20integral%20method

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Investigations based on the boundary integral method demonstrate that noise is not a necessary ingredient of an algorithm producing DLA-type patterns since they can be grown using deterministic equations. This result is supported by multifractal analysis. The fractal dimension of off-lattice DLA clusters in the asymptotic limit may be approximately equal to 1. 65.  1, record 5, English, - boundary%20integral%20method

Record 5,  Textual support,  French

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Record 6,  Textual support,  English

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Fractal crowds, such as those produced by SLOGRO, can be categorized by a dimension that characterizes their rate of growth.  1, record 6, English, - fractal%20crowd

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Record 7,  Textual support,  English

Record number: 7, Textual support number: 1 CONT

Fractal length-area relation. To pinpoint the argument, consider a collection of geometrically similar islands with fractal coastlines of dimension D>1. The standard ratio(length)/(area) _1/2 is infinite in this context, but I propose to show it has a useful fractal counterpart. We denote as G-length the coast length measured with a yardstick length of G, and as G-area the island area measured in units of G₂.  1, record 7, English, - G%2Dlength

Record 7,  Textual support,  French

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Record 8,  Textual support,  English

Record number: 8, Textual support number: 1 DEF

A finite size fractal consisting of disconnected parts embedded into one-dimensional space.  2, record 8, English, - Cantor%20set

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One of the simplest and best known fractals is the so called triadic Cantor set which is a finite size fractal consisting of disconnected parts embedded into one-dimensional space(d=1). Various Cantor sets with the same fractal dimension can be constructed as well.  2, record 8, English, - Cantor%20set

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See also dyadic Cantor set and Cantor ternary set.  3, record 8, English, - Cantor%20set

Record 8,  Textual support,  French

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Ensemble borné de dimension fractale comprise entre 0 et 1, constitué d'éléments discontinus enchâssés ou emboîtés dans un espace unidimensionnel.  3, record 8, French, - ensemble%20de%20Cantor

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Un ensemble de Cantor classique, croissant, dyadique, extrapolé, généralisé, homéomorphe, interpolé, non uniforme, tétradique, triadique, uniforme.  3, record 8, French, - ensemble%20de%20Cantor

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produit cartésien de l'ensemble de Cantor.  3, record 8, French, - ensemble%20de%20Cantor

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Record 9,  Textual support,  English

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The Brownian trajectory is a random fractal in spaces whose embedding dimension is larger than two.  2, record 9, English, - Brownian%20trajectory

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See Brownian path.  3, record 9, English, - Brownian%20trajectory

Record 9,  Textual support,  French

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Trajectoire de mouvement brownien  2, record 9, French, - trajectoire%20brownienne

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Record 10,  Textual support,  English

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The residual set of an Apollonian packing.  2, record 10, English, - Apollonian%20gasket

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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 10, English, - Apollonian%20gasket

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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 10, English, - Apollonian%20gasket

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See Sierpinski gasket.  5, record 10, English, - Apollonian%20gasket

Record 10,  Textual support,  French

Record number: 10, Textual support number: 1 DEF

L'ensemble non dénombrable des points à surface nulle qui restent non couverts par un bourrage apollonien.  2, record 10, French, - tamis%20apollonien

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Voir bourrage, entassement.  3, record 10, French, - tamis%20apollonien

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Record 11,  Textual support,  English

Record number: 11, Textual support number: 1 CONT

Some of the basic properties of objects with anomalous dimension were noticed and investigated at the beginning of this century mainly by Hausdorff (1919) and Besicovich (1935). They were considered "monstruous" and "pathological".  1, record 11, English, - anomalous%20dimension

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See fractal dimension, anomalous diffusion law, anomalous scaling.  1, record 11, English, - anomalous%20dimension

Record 11,  Textual support,  French

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Anomal : se dit d'une forme ou d'une construction qui présente un caractère aberrant par rapport à un type ou à une règle (sans être incorrecte ou anormale).  2, record 11, French, - dimension%20anomale

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Record 12,  Textual support,  English

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(...) the objects we are going to consider will offer a succession of different dimensions. The novelty will be that certain zones of transition will be reinterpreted as being fractal zones within which the fractal dimension is greater than the topological dimension.  1, record 12, English, - fractal%20zone

Record 12,  Textual support,  French

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Les objets dont cet Essai traite ont, eux aussi, toute une suite de dimensions différentes; la nouveauté sera que là où - jusqu'à présent - l'on ne voyait que des zones de transition, sans structure bien déterminée, s'identifie des zones fractales, dont la dimension est, soit une fraction, soit un entier "anormal", lui aussi descriptif d'un état irrégulier ou interrompu.  2, record 12, French, - zone%20fractale

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Record 13,  Textual support,  English

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... a family of sets which covers the plane with no gaps....  2, record 13, English, - covering

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A number of experimental techniques have been used to measure the fractal dimension of scale invariant structures grown in various experiments. The most widely applied methods can be divided into the following categories :(a) digital image processing of two-dimensional pictures,(b) scattering experiments,(c) covering the structures with monolayers, and(d) direct measurement of dimension-dependent physical properties.  3, record 13, English, - covering

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covering map, theorem, transformation.  4, record 13, English, - covering

Record 13,  Textual support,  French

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Disposition la moins dense d'unités (boules, carrés, cellules, disques ou sphères identique) dans un espace, de telle sorte que tout point de l'espace se trouve soit à l'intérieur soit à la surface d'une unité.  2, record 13, French, - recouvrement

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remplissage fermé, fini, ouvert, particulier, privilégié.  3, record 13, French, - recouvrement

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remplissage de boules, d'un ensemble.  2, record 13, French, - recouvrement

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Record 14,  Textual support,  English

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Since measuring the volume of fractals embedded into a dimensional Euclidean space leads to the conclusion that they are objects having no integer dimension, we assume that the dimensionality of fractals is usually given by a noninteger number D that will be called fractal dimension.  2, record 14, English, - dimensionality

Record 14,  Textual support,  French

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Caractéristique d'un objet qui a des dimensions.  3, record 14, French, - dimensionnalit%C3%A9

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dimensionalité fractale, dimensionalité spatio-temporelle, dimensionalité spectrale.  3, record 14, French, - dimensionnalit%C3%A9

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dimensionalité de l'espace.  3, record 14, French, - dimensionnalit%C3%A9

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Record 15,  Textual support,  English

Record number: 15, Textual support number: 1 CONT

A strange attractor is an attractor for which the iterates X_n depend sensitively on the initial X₀ that is, arbitrarily close initial values will become macroscopically separated for a sufficiently large N. Strange attractors are fractal dusts with a fractal dimension smaller than the Euclidean dimension of the embedding space.  2, record 15, English, - strange%20attractor

Record 15,  Textual support,  French

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Objet mathématique à structure transverse fractale extrêmement enchevêtrée qui consiste en une infinité de points, chacun d'eux représentant un état du système turbulent considéré, et dont la dimension reste basse (et souvent, fractionnaire) même lorsque l'espace des phases du système possède une grande dimension, parfois infinie. Les trajectoires de phase sont attirées vers l'attracteur; les paires de trajectoires initialement voisines divergent rapidement sur l'attracteur étrange.  2, record 15, French, - attracteur%20%C3%A9trange

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Concept découvert par S. Smale et utilisé en 1971 par D. Ruelle et F. Takens pour montrer que chaos peut survenir dès qu'un système dynamique comporte au moins trois paramètres. Contrairement aux attracteurs des systèmes non turbulents, un attracteur étrange est infiniment sensible aux conditions initiales. Selon B. Mandelbrot (1983:197), dans la plupart des cas, un attracteur est étrange lorsqu'il est fractal, mais la réciproque n'est pas nécessairement vraie. L'étrange présuppose des propriétés topologiques inhabituelles auxquelles peuvent s'ajouter des propriétés fractales inhabituelles.  2, record 15, French, - attracteur%20%C3%A9trange

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L'attracteur étrange se contracte, crée des plis (à l'intérieur d'autres plis), se déplie, se déploie, se développe, se dilate, s'enroule, s'étire, évolue, intègre une immense incertitude, se plie, prend une direction dilatante/contractante; se replie, subsiste.  2, record 15, French, - attracteur%20%C3%A9trange

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construire, découvrir, développer, sauter d'un attracteur étrange à un autre attracteur étrange.  2, record 15, French, - attracteur%20%C3%A9trange

Record number: 15, Textual support number: 3 PHR

direction, feuillet, fronce, plis, point figuratif, structure lacunaire, trajectoire d'un attracteur étrange.  2, record 15, French, - attracteur%20%C3%A9trange

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Record 16,  Textual support,  English

Record number: 16, Textual support number: 1 CONT

For strictly self-similar mathematical fractals, such as the Sierpinski gasket and the Cantor dust, the mass dimension is the same as the Hausdorff dimension(and any other fractal dimension considered here). They are all given by the similarity dimension of the scaling law, defined by the initiator and the generator that generates the fractal.  2, record 16, English, - scaling%20law

Record 16,  Textual support,  French

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Loi de la géométrie, selon laquelle les propriétés physiques telles la masse ou la conductivité dépendent de la taille du système de façon algébrique.  2, record 16, French, - loi%20d%27%C3%A9chelle

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Par exemple, la masse d'un cube est proportionnelle à la longueur de côté élevée à une puissance D (dimension fractale) - un nombre positif et inférieur à la valeur 3 qui correspond à la dimension euclidienne à laquelle obéissent les objets homogènes.  2, record 16, French, - loi%20d%27%C3%A9chelle

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Record 17,  Textual support,  English

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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 17, English, - fractal%20dimension

Record 17,  Textual support,  French

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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 17, French, - dimension%20fractale

Record number: 17, 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 17, French, - dimension%20fractale

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La dimension fractale s'accentue, augmente, croît, décroît, diminue, quantifie, renseigne sur la répartition de la masse, tend vers zéro, varie.  2, record 17, French, - dimension%20fractale

Record number: 17, Textual support number: 2 PHR

calculer, correspondre à, évaluer, extraire, obtenir une dimension fractale.  2, record 17, French, - dimension%20fractale

Record number: 17, Textual support number: 3 PHR

dimension fractale chimique, spectrale.  2, record 17, French, - dimension%20fractale

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dimension fractale d'empilement, d'étalement, de tortuosité.  2, record 17, French, - dimension%20fractale

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Record 18,  Textual support,  English

Record 18,  Textual support,  French

Record number: 18, Textual support number: 1 DEF

Existence d'une hiérarchie de singularités et de dimensions fractales.  1, record 18, French, - multifractalit%C3%A9

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Propriété postulée pour la turbulence et les attracteurs étranges.  1, record 18, French, - multifractalit%C3%A9

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Record 19,  Textual support,  English

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Curve for which the fractal dimension exceeds the topological dimension...  2, record 19, English, - fractal%20curve

Record 19,  Textual support,  French

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(...) dans le schéma d'un espace des phases, l'attracteur étrange est repéré par le point qui représente le système. Au cours de son déplacement, le point du système se plie et se replie dans l'espace des phases avec une complexité infinie. Un attracteur étrange est donc une courbe fractale.  2, record 19, French, - courbe%20fractale

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Record 20,  Textual support,  English

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We call embedding dimension that Euclidian dimension d of the space the fractal can be embedded in. In addition, d has to be the smallest such dimension.  3, record 20, English, - embedding%20dimension

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Le procédé part d'une propriété élémentaire qui caractérise le concept de dimension euclidienne dans le cas d'objets géométriques simples et possédant une homothétie interne.  3, record 20, French, - dimension%20euclidienne

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Record 21,  Textual support,  English

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Again the global dimension is D=1, and the local dimension is fractal and D-1/H. This dimension is sometimes called the latent fractal dimension.  1, record 21, English, - global%20dimension

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Bouligand introduit par ailleurs une dimension locale, pour pouvoir obtenir une borne inférieure de la dimension globale à l'aide d'une connaissance locale de l'ensemble.  1, record 21, French, - dimension%20globale

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Record 22,  Textual support,  English

Record number: 22, Textual support number: 1 CONT

For strictly self-similar mathematical fractals, such as the Sierpinski gasket and the Cantor dust, the mass dimension is the same as the Hausdorff dimension.... They are all given by the similarity dimension of the scaling law, defined by the initiator and the generator that generates the fractal. But for practical fractals, there are significant differences....  2, record 22, English, - mass%20dimension

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Record 23,  Textual support,  English

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Again the global dimension is D=1, and the local dimension is fractal and D-1/H. This dimension is sometimes called the latent fractal dimension.  1, record 23, English, - local%20dimension

Record 23,  Textual support,  French

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Bouligand introduit par ailleurs une dimension locale, pour pouvoir obtenir une borne inférieure de la dimension globale à l'aide d'une connaissance locale de l'ensemble.  1, record 23, French, - dimension%20locale

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Record 24,  Textual support,  English

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To interpret [the] value we recall that investigations of the diffusion-limited CCA model with relatively high densities showed that structures with a fractal dimension about 1. 7 are formed in the system close to its gelation point, i. e., when a cluster spanning the whole cell is formed.  1, record 24, English, - gelation%20point

Record 24,  Textual support,  French

Record 24,  Textual support,  Spanish

Record 25,  Textual support,  English

Record number: 25, Textual support number: 1 CONT

... the fractal dimension... is determined from an implicit equation derived from the condition that the right-angled hypercone should be at zero potential.  1, record 25, English, - hypercone

Record number: 25, Textual support number: 2 CONT

... hypercone representing the tips of the needle-like arms of the aggregate.  1, record 25, English, - hypercone

Record 25,  Textual support,  French

Record 25,  Textual support,  Spanish

Record 26,  Textual support,  English

Record number: 26, Textual support number: 1 CONT

The notion of fractal dimension is explored for various fractal curves or dusts that are not self-similar, but are diagonally self-affine. A diagonal self-affinity stretches the coordinates in different ratios.  1, record 26, English, - diagonal%20self%2Daffinity

Record number: 26, Textual support number: 2 CONT

The most typical self-affine structures ... are diagonally self-affine. This means that they are invariant under a transformation whose invariant sets include any collection of straight lines parallel to the coordinate axes.  2, record 26, English, - diagonal%20self%2Daffinity

Record 26,  Textual support,  French

Record number: 26, Textual support number: 1 OBS

Voir "auto-affinité".  1, record 26, French, - auto%2Daffinit%C3%A9%20diagonale

Record 26,  Textual support,  Spanish

Record 27,  Textual support,  English

Record number: 27, Textual support number: 1 DEF

A non-zero but finite s-dimensional Hausdorff measure.  2, record 27, English, - Besicovitch%20measure

Record number: 27, Textual support number: 1 OBS

A fractal measure devised in 1935 by Besicovitch based on Felix Hausdorff's work(1919) on non-integer dimensions for geometrically very complex objects. See fractional dimension, fractal dimension, Hausdorff dimension.  3, record 27, English, - Besicovitch%20measure

Record 27,  Textual support,  French

Record number: 27, Textual support number: 1 CONT

Dans le contexte triadique de Cantor, partons d'une masse distribuée sur (0,1) avec la densité uniforme égale à 1. Effacer le tiers central divise cette masse en parties égales .. réparties avec les densités 3/2, o, et 3/2 [...] Quand on aura répété la procédure à l'infini, la masse formera ce que nous allons appeler une mesure de Besicovitch [...] Il est clair, pour commencer, qu'aucun intervalle ouvert ne constitue une intermission absolue.  1, record 27, French, - mesure%20de%20Besicovitch

Record 27,  Textual support,  Spanish

Record 28,  Textual support,  English

Record number: 28, 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 28, English, - fractal%20flake

Record 28,  Textual support,  French

Record number: 28, Textual support number: 1 OBS

Voir flocon de neige.  1, record 28, French, - flocon%20fractal

Record 28,  Textual support,  Spanish

Record 29,  Textual support,  English

Record number: 29, Textual support number: 1 CONT

Mandelbrot 1965c suggested an alternative that has proved to be better in every way : the Lévy set. Once the dimension is prescribed, the Lévy set is the uniquely determined combination of two desirable properties. Like the randomized truncated Cantor set, it is a recurrent(renewal) random process. Like the Cantor set, it is a self similar fractal. Better than the Cantor set, this Lévy set is statistically identical to itself reduced in an arbitrary ratio r between O and 1.  1, record 29, English, - L%C3%A9vy%20set

Record 29,  Textual support,  French

Record number: 29, Textual support number: 1 CONT

Mandelbrot propose une construction dans le plan (ou l'espace) de l'ensemble de Lévy, en traçant, à partir d'un processus linéaire, des bandes (ou des plaquettes) dans des directions aléatoires du plan (ou de l'espace), construction qui, engendre des objets comparables à des réseaux de fractures hiérarchisés.  1, record 29, French, - ensemble%20de%20L%C3%A9vy

Record 29,  Textual support,  Spanish

Record 30,  Textual support,  English

Record number: 30, Textual support number: 1 CONT

In addition to the tips’ fractal dimension D, trees involve a parameter to be called the diameter exponent. When the tree is self-similar with a residue, [the diameter exponent] coincides with the D of the branch tips. Otherwise, [diameter exponent] and D are separate characteristics, and we deal with an instance of the phenomenon biologists call "allometry".  1, record 30, English, - diameter%20exponent

Record 30,  Textual support,  French

Record number: 30, Textual support number: 1 OBS

Voir fonction exponentielle.  2, record 30, French, - exponentielle%20de%20diam%C3%A8tre

Record 30,  Textual support,  Spanish

Record 31,  Textual support,  English

Record number: 31, Textual support number: 1 CONT

Fractional Brownian trails... constitutes an example of a statistically self similar fractal curve with the dimension D=1/0. 900=1. 1111. Its coordinate functions are independent fractional Brownian functions of exponent H=0. 9000, which implies that self intersections, though not strictly prohibited, are greatly discouraged by forcing the curve to be very persistent.  1, record 31, English, - fractional%20Brownian%20trail

Record 31,  Textual support,  French

Record number: 31, Textual support number: 1 CONT

vol brownien fractionnaire très persistant. Ce dessin constitue un exemple de courbe fractale, à homothétie statistique interne, dont la dimension est D=1/0,9=1,1 et pour laquelle la formation de boules sans être interdite - a été très fortement découragée, en imposant à cette courbe d'être très persistante.  1, record 31, French, - vol%20brownien%20fractionnaire

Record 31,  Textual support,  Spanish

Record 32,  Textual support,  English

Record number: 32, Textual support number: 1 CONT

Cirriform fractals. Clearly, a cirriform structure can, but need not, be present in a nonrandom fractal dust. It is absent from the Fournier model... which generates a collection of "lumps". By contrast, cirri are readily created by taking a Sierpinski carpet... and disconnecting its generator without brutality. Since the resulting fractal' s dimension can take essentially any value, we have made the important point that being cirriform is not a matter of dimension. Nevertheless, specifically built-in nonrandom cirri are too artificial to warrant attention.  1, record 32, English, - cirriform%20fractal

Record 32,  Textual support,  French

Record number: 32, Textual support number: 1 OBS

du lat. cirrus=filament.  2, record 32, French, - fractal%20cirriforme

Record number: 32, Textual support number: 2 OBS

La graphie "cirriforme" est courante en géologie où le terme qualifie les stipules qui s'allongent en vrilles, s'enroulent autour des corps voisins.  1, record 32, French, - fractal%20cirriforme

Record 32,  Textual support,  Spanish