Relevant bibliographies by topics / Fractal system

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fractal system'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Fractal system.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Fractal system"

1

Suny, Vian Hafid, Kosala Dwidja Purnomo, and Firdaus Ubaidillah. "PEMANFAATAN METODE ITERATED FUNCTION SYSTEM (IFS) PADA PEMBANGKITAN KURVA NAGA." Majalah Ilmiah Matematika dan Statistika 20, no. 2 (September 29, 2020): 89. http://dx.doi.org/10.19184/mims.v20i2.15780.

Full text
Abstract:
Fractals have two types, namely fractals sets (artificial fractals) and natural fractals. Each type of fractal has a variety of fractal objects. One of the fractal objects is the Dragon Curve. Fractal objects can be generated through two methods, namely the Lindenmayer System (L-System) and the Iterated Function System (IFS). In previous studies, the Dragon curve can be generated through the L-System approach. The method is to start from determining the rotation angle, then determining the initial string, and the last one, which is determining the production rules. In this study, the Dragon curve is generated using IFS with Affine Transformation. The Affine transformation used in this study is dilation and rotation. Some variation is given on the scale of dilation and rotation angle. The variation is using a fixed angle with a variety of scale and using a fixed scale with a variation of angle. Each variation gives a different effect. This influence results in a varied visualization of the Naga curve. If the scale and angle that is varied approach a scale of one and an angle of 90° then the fractal formed approaches the Dragon curve of a scale of one with an angle of 90°. Conversely, if the scale and angle are varied away from one scale and angle of 90°, the fractal formed away from the Dragon curve of scale one with an angle of 90°. Keywords: Affine transformation, dragon curve, IFS method.
APA, Harvard, Vancouver, ISO, and other styles
2

Benguigui, L. "A Fractal Analysis of the Public Transportation System of Paris." Environment and Planning A: Economy and Space 27, no. 7 (July 1995): 1147–61. http://dx.doi.org/10.1068/a271147.

Full text
Abstract:
An analysis of the railway networks of the public transportation system of Paris, based on the notion of fractals, is presented. The two basic networks, (metropolitan and suburban) which have different functions, have also a different fractal dimension: 1.8 for the metropolitan network, and 1.5 for the suburban network. By means of computer simulation, it is concluded that the true dimension of the metro network is probably 2.0. A fractal model of the suburban network, with the same features and the same fractal dimension, is proposed. This supports the conclusion that this network is fractal.
APA, Harvard, Vancouver, ISO, and other styles
3

Zhao, Shanrong, Jin Tan, Jiyang Wang, Xiaohong Xu, and Hong Liu. "A Dendrite with "Sierpinski Gasket" Fractal Morphology in Matt Glaze of LiAlSiO4-SiO2 System." Fractals 11, no. 03 (September 2003): 271–76. http://dx.doi.org/10.1142/s0218348x03001525.

Full text
Abstract:
In this paper, we introduce a dendritic crystal, formed in matt glaze of LiAlSiO 4- SiO 2, having "Sierpinski gasket" fractal morphology. The crystal structure of this "Sierpinski gasket" dendrite is β-quartz. β-quartz can grow two kinds of fractal patterns: snow-shaped dendrite and "Sierpinski gasket" dendrite, depending on different supercooling conditions. These two kinds of fractals can develop together in one dendritic crystal. The evolution of the boundary morphologies between these two kinds of fractal dendrites can be described by another fractal — Koch curve. The "Sierpinski gasket" dendrite is a rather new fractal growth pattern which can introduce new opportunities to fractal growth research of nonlinear sciences.
APA, Harvard, Vancouver, ISO, and other styles
4

Giona, Massimiliano. "Chemical Engineering, Fractal and Disordered System Theory." Fractals 05, no. 03 (September 1997): 333–54. http://dx.doi.org/10.1142/s0218348x97000334.

Full text
Abstract:
This article critically discusses the applications of fractal and disordered system theory to chemical engineering problems in order to highlight some promising research directions and the difficulties that may be encountered. Starting from the analysis of transport and reaction kinetics, the question is addressed, with the aid of some examples, of whether and how engineering research could help in the study of complex phenomenologies on fractals and disordered systems. The effects of thermodynamical nonidealities in transport and adsorption, and the influence of nonlinearities in reaction kinetics are discussed in some detail. Examples of typical engineering problems in which fractal analysis may help towards a better understanding of the physical phenomenologies in the presence of complex porous substrata and fluid mixtures are discussed. The role played by the boundary conditions on transport phenomena involving fractal structures is also analyzed. A critical discussion on the perspectives in the characterization of disordered and fractal porous structures, and in the study of turbulent transport and mixing is also developed.
APA, Harvard, Vancouver, ISO, and other styles
5

Cherny, A. Yu, E. M. Anitas, V. A. Osipov, and A. I. Kuklin. "Scattering from surface fractals in terms of composing mass fractals." Journal of Applied Crystallography 50, no. 3 (June 1, 2017): 919–31. http://dx.doi.org/10.1107/s1600576717005696.

Full text
Abstract:
It is argued that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of a surface fractal is shown to be a sum of the amplitudes of the composing mass fractals. Various approximations for the scattering intensity of surface fractals are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of a power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensityI(q) ∝ q^{D_{\rm s}-6}, where 2 <Ds< 3 is the surface-fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution dN(r) ∝r−τdr, withDs= τ − 1. The distribution is continuous for random fractals and discrete for deterministic fractals. A model of the surface deterministic fractal is suggested, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and its scattering properties are studied. The present analysis allows one to extract additional information from SAS intensity for dilute aggregates of single-scaled surface fractals, such as the fractal iteration number and the scaling factor.
APA, Harvard, Vancouver, ISO, and other styles
6

HUYNH, HOAI NGUYEN, and LOCK YUE CHEW. "ARC-FRACTAL AND THE DYNAMICS OF COASTAL MORPHOLOGY." Fractals 19, no. 02 (June 2011): 141–62. http://dx.doi.org/10.1142/s0218348x11005178.

Full text
Abstract:
In this paper, we present an idea of creating fractals by using the geometric arc as the basic element. This approach of generating fractals, through the tuning of just three parameters, gives a universal way to obtain many novel fractals including the classic ones. Although this arc-fractal system shares similar features with the well-known Lindenmayer system, such as the same set of invariant points and the ability to tile the space, they do have different properties. One of which is the generation of pseudo-random number, which is not available in the Lindenmayer system. Furthermore, by assuming that coastline formation is based purely on the processes of erosion and deposition, the arc-fractal system can also serve as a dynamical model of coastal morphology, with each level of its construction corresponds to the time evolution of the shape of the coastal features. Remarkably, our results indicate that the arc-fractal system can provide an explanation on the origin of fractality in real coastline.
APA, Harvard, Vancouver, ISO, and other styles
7

Skydan, Oleg, Olga Nykolyuk, Oleksandr Chaikin, and Vasyl Shukalovych. "Concept of fractal organization of organic business systems." Agricultural and Resource Economics: International Scientific E-Journal 7, no. 2 (June 20, 2021): 59–76. http://dx.doi.org/10.51599/are.2021.07.02.04.

Full text
Abstract:
Purpose. The purpose of the article is determining the possibilities of fractal approach, as the one that enables not only flexibility and viability, but also, management efficiency improvement, new competencies of the company formation, self-renewal ability formation and conflicts of interest between structural subdivisions in complex vertically integrated structures elimination, to the organization of implementation of organic business entities. Methodology / approach. The methodological basis of the research is general scientific and specific methods of economic phenomena and processes cognition. Therefore, the following methods have been applied: logical generalization (in determining the properties and benefits of agricultural business systems of the fractal type); comparison (when the practice of functioning of properties of organic products is analyzed); abstract-logical (when features of the functioning of network structures in fractally organized business systems are designed); monographic (in the study of the recent concepts of the functioning of fractal organized business systems); graphic (for visual presentation of the cooperation network of vertically integrated structure members); heuristic (when formulating conclusions and generalizations, as well as when justifying the directions for future research of the business system). Results. The essence of fractal business organization and the properties of fractal type business systems have been identified which include heterarchy, structure complexity, self-organization, self-optimization, openness, as well as autonomy and elements. The fractally organized business systems benefits in agribusiness compared with agrarian business systems with a traditional structure and management system have been determined. The existence of objective prerequisites for organic farms fractalization has been substantiated, which is already inherent in some of fractally organized business systems properties. The properties and features of fractally organized business systems of network structures functioning have been defined. Originality / scientific novelty. For the first time the substantiation of fractal type business systems formation in agriculture is proved, organic production in particular (previously expediency of fractal type business systems was studied only for industrial enterprises use). In particular, potential subjects of fractalization in organic production are identified, which include complex diversified agricultural business systems; the properties and advantages of fractally organized organic farms are identified and formalized, that are defined for a single fractal as well as a business system in general; the network structure of fractally organized organic farms is substantiated, particularly the relationship structure, network interaction rules, properties and values of fractally organized business structures in organic farming. In addition, the identification and formalization of the factors that affect Ukrainian organic production development got further development. Practical value / implications. To ensure the fulfillment of obligations by all parties as well as maintaining the basic principles of fractal organization in the field of goal-setting the function of the institutional environment is proposed. As PE “Gallex-Agro” is the vivid example of interconnections network that corresponds to the features of fractal business systems design, vertically integrated structure of member’s interaction network is designed at its case.
APA, Harvard, Vancouver, ISO, and other styles
8

Bolotov, V. N., and Yu V. Tkach. "Fractal communication system." Technical Physics 53, no. 9 (September 2008): 1192–96. http://dx.doi.org/10.1134/s1063784208090107.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Navascués, M. A. "Fractal Haar system." Nonlinear Analysis: Theory, Methods & Applications 74, no. 12 (August 2011): 4152–65. http://dx.doi.org/10.1016/j.na.2011.03.048.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Shevchenko, Svitlana, Yulia Zhdanovа, Svitlana Spasiteleva, Olena Negodenko, Nataliia Mazur, and Kateryna Kravchuk. "MATHEMATICAL METHODS IN CYBER SECURITY: FRACTALS AND THEIR APPLICATIONS IN INFORMATION AND CYBER SECURITY." Cybersecurity: Education, Science, Technique, no. 5 (2019): 31–39. http://dx.doi.org/10.28925/2663-4023.2019.5.3139.

Full text
Abstract:
The article deals with the application of modern mathematical apparatus in information and cyber security namely fractal analysis. The choice of fractal modeling for the protection of information in the process of its digital processing is grounded. Based on scientific sources, the basic definitions of the research are analyzed: fractal, its dimension and basic properties used in the process of information protection. The basic types of fractals (geometric, algebraic, statistical) are presented and the most famous of them are described. The historical perspective of the development of fractal theory is conducted. Different approaches to the application of fractal theory in information and cyber security have been reviewed. Among them are: the use of fractal analysis in encryption algorithms; development of a method of protecting documents with latent elements based on fractals; modeling the security system of each automated workplace network using a set of properties that can be represented as fractals. The considered approaches to the application of fractal analysis in information and cyber security can be used in the preparation of specialists in the process of research work or diploma work.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Fractal system"

1

Zaks, Michael. "Fractal Fourier spectra in dynamical systems." Thesis, [S.l.] : [s.n.], 2001. http://pub.ub.uni-potsdam.de/2002/0019/zaks.ps.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Karavas, Costas. "Fractal chaotic systems : investigation of the geological system and its sedimentation behaviour." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60052.

Full text
Abstract:
Chaos theory has only recently been related to various phenomena in the earth sciences. Here, using systems theory in a description of geological processes, we study the chaotic development of sedimentary sequences.
The geosystem is treated as a partially specified system in order to apply qualitative stability analysis in the investigation of sedimentation behaviour and interactions among geological processes. The analysis suggests that the sedimentary system is unstable. This instability in conjunction with the system's sensitive dependence to internal fluctuations (i.e., those generated within the system) provide supporting evidence to suggest a chaotic behaviour for the sedimentation system.
We suggest that chaos could act as the common underlying mechanism which is manifest as the fractal-flicker noise character observed in reflectivity well logs. Acoustic impedance variations--the geophysical measures of lithologic variability--represent the internal organization of the interacting geological processes. This organization under a chaotic regime is responsible for the common statistical character found in various sedimentary basins.
APA, Harvard, Vancouver, ISO, and other styles
3

Landais, François. "Lois d’échelles et propriétés statistiques multifractales de la topographie des planètes." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS453/document.

Full text
Abstract:
Au cours des 20 dernières années, le développement des méthodes de télédétection et le succès des missions spatiales ont considérablement enrichi nos connaissances sur les surfaces planétaires révélant une immense diversité de morphologies. Etant le reflet de l'interaction et de la compétition entre des processus géologiques dont les modalités sont variables d'un corps à l'autre, elles sont largement étudiées pour retracer l'histoire géologique des planètes telluriques. En particulier, des informations précieuses sur la nature des processus et sur les lois générales qui contrôlent la formation et l'évolution des paysages sont enregistrées dans le champ topographique qui peut être analysé en tant que champ statistique. Nous rapportons dans cette thèse les résultats d'une étude comparative des propriétés statistiques de la topographie des principaux corps du système solaire en nous appuyant sur le volume croissant de données altimétriques et photogrammétriques. Notre approche est centrée sur la notion de loi d'échelle qui vise à caractériser les symétries du champ en traduisant le caractère auto-similaire des surfaces naturelles : les détails d'une surface ressemblent en général à des versions réduites de l'ensemble. Nous mettons en oeuvre plusieurs méthodes d'analyse de données dites «multifractales» pour dégager le meilleur modèle statistique capable de décrire la topographie dans différents contexte et proposons de nouveaux indicateurs de rugosité à l'échelle globale, régionale et locale. Nous montrons qu'en dépit de leur diversité, les surfaces du système solaire respectent des lois statistiques similaires que nous explicitons. En particulier nous montrons que la distribution globale des pentes d'un corps respecte en général des lois multifractales pour les échelles supérieures à 10-20km et présente une structure statistique différente pour les échelles inférieures. Enfin nous proposons une méthode pour générer des topographies synthétique sphériques dont le propriétés statistiques sont similaires aux topographie planétaire du système solaire
Over the past 20 years, the development of remote sensing methods and the success of space missions have considerably enriched our knowledge of planetary surfaces revealing an immense diversity of morphologies. Being the reflection of the interaction and the competition between geological processes whose modalities are variable from one body to the other, they are widely studied to trace the geological history of the telluric planets. In particular, precise information on the nature of processes and general laws controlling the formation and evolution of landscapes is recorded in the topographic field which can be analyzed as a statistical field. We report in this thesis the results of a comparative study of the statistical properties of the topography of the main bodies of the solar system based on the increasing volume of altimetric and photogrammetric data. Our approach focuses on the notion of scaling law which aims to characterize the symmetries of the field by translating the self-similar nature of natural surfaces: the details of a surface generally look like reduced versions of the whole. We use several methods of analyzing so-called "multifractal" to derive the best statistical model capable of describing the topography in different contexts and propose new indicators of roughness at the global, regional and local scale. We show that in spite of their diversity, the surface of the solar system respects similar statistical laws. In particular, we show that the overall distribution of the slopes of a body generally respects multifractal laws for scales greater than 10-20 km and presents a different statistical structure for the lower scales. Finally, we propose a method for generating spherical synthetic topographies whose statistical properties are similar to the topographies in the solar system
APA, Harvard, Vancouver, ISO, and other styles
4

Joanpere, Salvadó Meritxell. "Fractals and Computer Graphics." Thesis, Linköpings universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-68876.

Full text
Abstract:
Fractal geometry is a new branch of mathematics. This report presents the tools, methods and theory required to describe this geometry. The power of Iterated Function Systems (IFS) is introduced and applied to produce fractal images or approximate complex estructures found in nature. The focus of this thesis is on how fractal geometry can be used in applications to computer graphics or to model natural objects.
APA, Harvard, Vancouver, ISO, and other styles
5

Machado, Bruno Brandoli. "Texture analysis using complex system models: fractal dimension, swarm systems and non-linear diffusion." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-24112016-113253/.

Full text
Abstract:
Texture is one of the primary visual attributes used to describe patterns found in nature. Several texture analysis methods have been used as powerful tools for real applications involving analysis and computer vision. However, existing methods do not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures by means of measures such as the fractal dimension. Fractality-based measures allow a non-integer geometric interpretation with applications in areas such as mathematics, physics, and biology. With this gap in mind, the central hypothesis of this thesis is that textures can be described as irregular fractal surfaces due to their complex geometry; such geometry can be exploited for image analysis and computer vision. By exploring such possibilities, pushing the limits of the state-of-the-art, this thesis starts with an analysis of texture features achieved by means of agents on image surfaces. To do so, we used the Bouligand-Minkowski fractal dimension, swarm-system Artificial Crawlers, and non-linear diffusion of Perona-Malik, techniques that led to methodologies with efficacy and efficiency comparable to the state-of-the-art. Our first method combines fractal dimension with random walks on the surface of images. In a second approach, non-linear diffusion is used to represent texture images at different scales, which are described via their fractal dimension for image classification purposes. In a third proposal, we employ fractal dimension concepts over multiple scales derived from the same image for a richer texture description. One of the purposes is the automatic detection of diseases in soybean leaves. Finally, texture characteristics were exploited in a method based on complex networks used to analyze the agglomeration of particles in nanotechnology images. The results achieved in the four methodologies described in this thesis demonstrated the potential of using texture features in tasks of classification and pattern recognition. The contributions of this work shall support significant advances in materials engineering, computer vision, and agriculture.
A textura é um dos principais atributos visuais para a descrição de padrões encontrados na natureza. Diversos métodos de análise de textura têm sido usados como uma poderosa ferramenta para aplicações reais que envolvem análise de imagens e visão computacional. Entretanto, os métodos existentes não conseguem discriminar com sucesso a complexidade dos padrões de textura. Tais métodos desconsideram a possibilidade de se descrever estruturas de imagens por meio de medidas como a dimensão fractal. Medidas baseadas em fractalidade permitem uma interpretação geométrica não-inteira que possui aplicações encontradas em áreas como matemática, física, e biologia. Sobre esta lacuna metodológica, a hipótese central desta tese é que texturas presentes na natureza podem ser medidas como superfícies fractais irregulares devido à sua geometria complexa, o que pode ser explorado para fins de análise de imagens e visão computacional. Para superar tais limitações, avançando o estado da arte, esta tese se inicia com uma análise das características de texturas baseada em caminhadas aleatórias de agentes sobre superfícies de imagens. Esta primeira análise leva a um método que combina dimensão fractal com caminhadas de agentes sobre a superfície de imagens. Em uma segunda abordagem, usa-se a difusão não-linear para representar imagens de texturas em diferentes escalas, as quais são descritas via dimensão fractal para fins de classificação de imagens. Em uma terceira proposta, emprega-se a dimensão fractal sobre múltiplas escalas derivadas de uma mesma imagem com o propósito de se realizar a descrição multi-escala de texturas. Um dos propósitos específicos foi a detecção automática de doenças em folhas de soja. Por último, as características de textura foram exploradas segundo uma metodologia baseada em redes complexas para análise de aglomeração de partículas em imagens de nanotecnologia. Os resultados alcançados nesta tese demonstraram o potencial do uso de características de textura. Para tanto foram usadas técnicas de dimensão fractal de Bouligand-Minkowski, multiagentes Artificial Crawlerse difusão não-linear de Perona-Malik, os quais alcançaram eficácia e eficiência comparáveis ao do estado da arte. As contribuições obtidas devem suportar avanços significativos nas áreas de engenharia de materiais, visão computacional, e agricultura.
APA, Harvard, Vancouver, ISO, and other styles
6

USUI, Shin'ichi, Masayuki TANIMOTO, Toshiaki FUJII, Tadahiko KIMOTO, and Hiroshi OHYAMA. "Fractal Image Coding Based on Classified Range Regions." Institute of Electronics, Information and Communication Engineers, 1998. http://hdl.handle.net/2237/14996.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Fraser, Jonathan M. "Dimension theory and fractal constructions based on self-affine carpets." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3869.

Full text
Abstract:
The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively well-understood world of self-similar sets and the far from understood world of general self-affine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, and they display many interesting and surprising features which the simpler self-similar constructions do not have. For example, they can have distinct Hausdorff and packing dimensions and the Hausdorff and packing measures are typically infinite in the critical dimensions. Furthermore, they often provide exceptions to the seminal result of Falconer from 1988 which gives the `generic' dimensions of self-affine sets in a natural setting. The work in this thesis will be based on five research papers I wrote during my time as a PhD student. The first contribution of this thesis will be to introduce a new class of self-affine carpets, which we call box-like self-affine sets, and compute their box and packing dimensions via a modified singular value function. This not only generalises current results on self-affine carpets, but also helps to reconcile the `exceptional constructions' with Falconer's singular value function approach in the generic case. This will appear in Chapter 2 and is based on a paper which appeared in 'Nonlinearity' in 2012. In Chapter 3 we continue studying the dimension theory of self-affine sets by computing the Assouad and lower dimensions of certain classes. The Assouad and lower dimensions have not received much attention in the literature on fractals to date and their importance has been more related to quasi-conformal maps and embeddability problems. This appears to be changing, however, and so our results constitute a timely and important contribution to a growing body of literature on the subject. The material in this Chapter will be based on a paper which has been accepted for publication in 'Transactions of the American Mathematical Society'. In Chapters 4-6 we move away from the classical setting of iterated function systems to consider two more exotic constructions, namely, inhomogeneous attractors and random 1-variable attractors, with the aim of developing the dimension theory of self-affine carpets in these directions. In order to put our work into context, in Chapter 4 we consider inhomogeneous self-similar sets and significantly generalise the results on box dimensions obtained by Olsen and Snigireva, answering several questions posed in the literature in the process. We then move to the self-affine setting and, in Chapter 5, investigate the dimensions of inhomogeneous self-affine carpets and prove that new phenomena can occur in this setting which do not occur in the setting of self-similar sets. The material in Chapter 4 will be based on a paper which appeared in 'Studia Mathematica' in 2012, and the material in Chapter 5 is based on a paper, which is in preparation. Finally, in Chapter 6 we consider random self-affine sets. The traditional approach to random iterated function systems is probabilistic, but here we allow the randomness in the construction to be provided by the topological structure of the sample space, employing ideas from Baire category. We are able to obtain very general results in this setting, relaxing the conditions on the maps from `affine' to `bi-Lipschitz'. In order to get precise results on the Hausdorff and packing measures of typical attractors, we need to specialise to the setting of random self-similar sets and we show again that several interesting and new phenomena can occur when we relax to the setting of random self-affine carpets. The material in this Chapter will be based on a paper which has been accepted for publication by 'Ergodic Theory and Dynamical Systems'.
APA, Harvard, Vancouver, ISO, and other styles
8

Sellami, Tarek. "Dynamique commune des fractals de rauzy de même matrice d' incidence." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4030/document.

Full text
Abstract:
On sait que la matrice d'incidence associée à une substitution ne suffit pas pour déterminer complètement le système dynamique associé, même dans des cas très simples, il existe plusieurs substitutions associées à une même matrice car il existe de nombreux mots ayant le même abélianisé. Dans cette thèse, on étudie les points communs de deux lignes brisées associées à deux substitutions $sigma_1$ et $sigma_2$ irréductibles unimodulaires de type Pisot qui ont la même matrice d'incidence. On identifie les points communs de ces deux lignes brisées à partir d'un algorithme. On montre ainsi que l'intersection de ces deux lignes brisées est aussi une ligne brisée associée au point fixe d'une nouvelle substitution. On montre plus précisément que si $sigma_1$ vérifie la conjecture Pisot et $0$ est un point intérieur à son fractal de Rauzy alors ces points communs peuvent être engendrés par une substitution définie sur un alphabet appelé alphabet des paires équilibrées. Cette substitution est obtenue à partir d'un algorithme, l'algorithme des paires équilibrées. On obtient ainsi l'intersection des intérieurs des deux fractals de Rauzy. En prenant la clôture de cet ensemble on obtient un ensemble substitutif. La condition que $0$ est un point intérieur au fractal de Rauzy associé à la substitution $sigma_1$ nous permet de montrer que l'intersection des deux fractals de Rauzy est de mesure positive. Dans une deuxième partie du travail on s'intéresse à l'étude de la frontière du fractal de Rauzy. Le fractal de Rauzy est dit fractal mais c'est en fait sa frontière qui est fractale
The matrix of a substitution is not sufficient to completely determine the dynamics associated with it, even in the simplest cases since there are many words with the same abelianization. In this paper we study the common points of the canonical broken lines associated with two different irreducible Pisot unimodular substitutions σ1 and σ2 having the same incidence matrix. We prove that if σ1 verifies the Pisot conjecture and 0 is an inner point to the Rauzy fractal associated with the substitution σ1 then these common points can be generated with a substitution on an alphabet of so-called balanced pairs, and we obtain in this way the intersection of the interior of two Rauzy fractals
APA, Harvard, Vancouver, ISO, and other styles
9

Caputo, Jean-Guy. "Dimension et entropie des attracteurs associés à des écoulements réels : estimation et analyse de la méthode." Grenoble 1, 1986. http://www.theses.fr/1986GRE10057.

Full text
Abstract:
On s'interesse a la caracterisation des regimes chaotiques par lesquels un ecoulement atteint la turbulence. On montre qu'un regime chaotique de convection de rayleigh-benard est decrit par un attracteur dont on determine la dimension et l'entropie. En vue de caracteriser des attracteurs de dimension plus elevee on determine les conditions d'obtention de resultats corrects sur des exemples precis
APA, Harvard, Vancouver, ISO, and other styles
10

Barreiras, Carmen da Piedade Maceiras. "O conjunto de cantor." Master's thesis, Universidade de Évora, 2011. http://hdl.handle.net/10174/15448.

Full text
Abstract:
O objectivo deste trabalho é o estudo aprofundado de um dos fractais mais conhecidos e estudados de sempre, o conjunto de Cantor. É feita uma abordagem histórica, onde são apresentados os marcos principais da vida e obra de Georg Cantor. Faz-se uma abordagem rigorosa do Conjunto de Cantor clássico e demonstram-se as suas principais propriedades, usando a de nição mais conhecida deste conjunto, como intersecção numerável de conjuntos fechados e encaixados. Estuda-se o conjunto de Cantor do ponto de vista dinâmico, isto é, como conjunto prisioneiro do sistema dinâmico discreto das iteradas de certas funções no intervalo. Fez-se o estudo do conjunto de Cantor enquanto fractal, estudando a sua dimensão de Hausdor¤, dimensão de capacidade e as propriedades de auto-semelhança. Finalmente propõem-se actividades de sala de aula no âmbito das matérias estudadas; ABSTRACT:The aim of this paper is a detailed study of one of the most known and studied fractals of all time, the Cantor set. It is made a historical approach, which presents the major landmarks of life and work of Georg Cantor. Is done a serious approach to the classical Cantor set and its main properties are proven, using the better known de nition of this set as a countable intersection of closed nested sets. The Cantor set is studied from the dynamic point of view, that means, as the prisoner set of a discrete dynamical system of the iterates of certain functions in the interval. It is made the study of the Cantor set as a fractal, studying its Hausdor¤ dimension, box-counting dimension and the properties of self-similarity. Finally, are proposed classroom activities within the subject matter.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Fractal system"

1

Lee, Kevin D. Fractal attraction: A fractal design system for the Macintosh. Boston: Academic Press, 1990.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Lee, Kevin D. Fractal attraction: A fractal design system for the Macintosh. Boston, MA: Academic Press, 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Barnsley, Michael. The desktop fractal design system. Boston, MA: Academic Press, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Dimri, V. P., ed. Fractal Behaviour of the Earth System. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/b137755.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Barnsley, Michael. The desktop fractal design system handbook: IBM PC version 2.0. Boston: Academic, 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Fractal fetishes: Essays on the organization of the system of information. Saarbrücken: VDM, Verlag Dr. Müller, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Andoniou, Constantine. Fractal fetishes: Essays on the organization of the system of information. Saarbrücken: VDM, Verlag Dr. Müller, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

The fractal organisation: Creating sustainable organisations with the viable system model. Hoboken, NJ: John Wiley & Sons, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Andoniou, Constantine. Fractal fetishes: Essays on the organization of the system of information. Saarbrücken: VDM, Verlag Dr. Müller, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

N, Mishra S., ed. L-system fractals. Amsterdam: Elsevier B. V., 2007.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Fractal system"

1

Liu, Shu-Tang, and Pei Wang. "Control on Julia Sets in Switching Complex System." In Fractal Control Theory, 263–76. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7050-1_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Pardo-Igúzquiza, Eulogio, Juan José Durán, Pedro Robledo, Carolina Guardiola, Juan Antonio Luque, and Sergio Martos. "Fractal Modelling of Karst Conduits." In Lecture Notes in Earth System Sciences, 217–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_50.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Ionescu, Clara Mihaela. "Time Domain: Breathing Dynamics and Fractal Dimension." In The Human Respiratory System, 139–67. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5388-7_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Losa, Gabriele A. "The Fractal Organization of the Nervous System." In Imagine Math 3, 121–28. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01231-5_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Soehle, Martin. "Fractal Analysis of the Cerebrovascular System Physiopathology." In Springer Series in Computational Neuroscience, 251–62. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-3995-4_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Bachmat, Eitan. "A Fractal Model for Storage System Activity." In Mathematical Adventures in Performance Analysis, 27–49. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09513-4_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Fedi, Maurizio, Donato Fiore, and Mauro La Manna. "Regularity Analysis Applied to Well Log Data." In Fractal Behaviour of the Earth System, 63–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26536-8_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Robledo-Ardila, Pedro A., Juan José Durán-Valsero, and Eulogio Pardo-Igúzquiza. "Evaluation of Fractal Dimension in Karst Aquifers." In Lecture Notes in Earth System Sciences, 211–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_49.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Hergarten, Stefan. "Fractals and Fractal Distributions." In Self-Organized Criticality in Earth Systems, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04390-5_1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Victor, Jonathan D. "The Geometry of System Identification: Fractal Dimension and Integration Formulae." In Advanced Methods of Physiological System Modeling, 147–64. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4613-9789-2_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Fractal system"

1

Han, Qing Kai, Hong Liang Yao, Zhi Wei Zhang, and Bang Chun Wen. "Experiment of Oil-Film Whirl in Rotor System and Wavelet Fractal Analyses." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85218.

Full text
Abstract:
An oil-film whirl experiment is carried out in a rotor test rig and some nonlinear analyses are achieved in the paper. Firstly, the experiment schemes for measuring oil-whirl of a rotor system are introduced. The shaft vibrations are measured both in stable rotating process and running up and coast down. And then, the detailed signals of level 3, reconstructed by wavelet transform, representing the oil-film whirl motions are analyzed. At last, a wavelet fractal method is proposed, based on wavelet package transform and fractal geometry theory, and the correlative dimensions of signals in every frequency bands are calculated. This method describes the chaotic properties of the oil-film whirl vibration well, and wavelet fractals prove to be more effective than any other nonlinear parameters of the corresponding original shaft vibration signals.
APA, Harvard, Vancouver, ISO, and other styles
2

Hammel, Stephen, and P. W. Bo Hammer. "System identification in experimental data." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51022.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Monsef Khoshhesab, Mona, and Yaning Li. "Mechanical Modeling of Fractal Interlocking." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71844.

Full text
Abstract:
Topological interlocking is an effective joining approach in both natural and engineering systems. Especially, hierarchical/fractal interlocking are found in many biological systems and can significantly enhance the system mechanical properties. Inspired by the hierarchical/ fractal topology in nature, mechanical models for Koch fractal interlocking were developed as an example system to better understand the mechanics of fractal interlocking. In this investigation, Koch fractal interlocking with different number of iterations N were designed. Theoretical contact mechanics model was used to analytically capture the mechanical behavior of the fractal interlocking. Then finite element (FE) simulations were performed to study the deformation mechanism of fractal interlocking under finite deformation. It was found that by increasing the number of iterations, the contact area increases and the interlocking stiffness and strength also significantly increase. The friction coefficient of contact plays an important role in determining the mechanical properties of fractal interlocking.
APA, Harvard, Vancouver, ISO, and other styles
4

Usmanov, I. Yu, A. V. Scherbakov, V. B. Ivanov, and E. R. Yumagulova. "Fractal analysis of flavonoid biosynthesis system." In IX Congress of society physiologists of plants of Russia "Plant physiology is the basis for creating plants of the future". Kazan University Press, 2019. http://dx.doi.org/10.26907/978-5-00130-204-9-2019-446.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Melnikov, Alexander V. "Optical system of fractal image encoding." In Optical Information Science and Technology, edited by Andrei L. Mikaelian. SPIE, 1998. http://dx.doi.org/10.1117/12.302505.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Cao, T. N., and W. J. Krzysztofik. "Fractal Antenna of MIMO System WLAN." In 12th European Conference on Antennas and Propagation (EuCAP 2018). Institution of Engineering and Technology, 2018. http://dx.doi.org/10.1049/cp.2018.0457.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Lin Gu, Fangfang Dong, and Xing Li. "Analysis and prospect on fractal supply chain." In 2012 7th International Conference on System of Systems Engineering (SoSE). IEEE, 2012. http://dx.doi.org/10.1109/sysose.2012.6333570.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Moon, Yong H., Kyung S. Son, Hyung S. Kim, Yoon-Soo Kim, and Jae H. Kim. "Fractal image compression using human visual system." In IS&T/SPIE's Symposium on Electronic Imaging: Science & Technology, edited by Majid Rabbani, Edward J. Delp, and Sarah A. Rajala. SPIE, 1995. http://dx.doi.org/10.1117/12.204139.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Owens, Benjamin A. M., and Brian P. Mann. "Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70327.

Full text
Abstract:
This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.
APA, Harvard, Vancouver, ISO, and other styles
10

Zhou, Jiang, and Pei-wu Li. "Development and application of coastline fractal interpolation computing system based on GIS and fractal theory." In 2008 6th IEEE International Conference on Industrial Informatics (INDIN). IEEE, 2008. http://dx.doi.org/10.1109/indin.2008.4618068.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Fractal system"

1

Begeman, Carolyn, Marian Anghel, and Ishanu Chattopadhyay. Interpretable Deep Learning for the Earth System with Fractal Nets. Office of Scientific and Technical Information (OSTI), April 2021. http://dx.doi.org/10.2172/1769730.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Meisel, Lawrence V., and Mark A. Johnson. Fractal Scaling in Cellular Automata Simulations of Dissipative Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, July 1996. http://dx.doi.org/10.21236/ada315392.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Wilson, T. Fractal Analysis of Fracture Systems: Topical report, September 3, 1996. Office of Scientific and Technical Information (OSTI), December 1997. http://dx.doi.org/10.2172/620973.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Kearney, M., V. Kochergin, R. Hess, T. Foust, R. Herbst, and N. Mann. Industrial Membrane Filtration and Short-bed Fractal Separation Systems for Separating Monomers from Heterogeneous Plant Material. Office of Scientific and Technical Information (OSTI), March 2005. http://dx.doi.org/10.2172/838864.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Fractal system' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography