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Dissertations / Theses on the topic 'Fractal mathematics'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

McClure, Mark. "Fractal measures on infinite-dimensional sets /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu148785391310164.

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2

Liao, Haoke. "Fractal simulation of plants." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-91410.

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We study two methods of simulation of plants in R2 , the Lindenmayer system and the iterated function system. The algorithm for a L-system simulates fast and efficiently the growth structure of the plants. The iterated function system can be done by deterministic iteration or by the so called chaos game.

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3

Donovan, George C. "Fractal functions, splines, and wavelet." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30411.

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4

Mullins, Edmond N. "Derivation bases, interval functions, and fractal measures /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487942182325914.

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5

Wessel, Ralf. "Formation and flow of fractal aggregates." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240023.

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6

Blunt, Martin Julian. "The growth and properties of fractal boundaries." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293638.

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7

Piacquadio, Losada Maria N. "P.D.E. in planar regions with fractal boundary." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/91885/.

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8

Xiao, Yimin. "Fractal Measures and Related Properties of Gaussian Random Fields /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487935573769563.

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9

Peng, Na. "Fractal Gauges for Hyperspace: One Limit Point." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1278387275.

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10

Cesbron, Fred́eŕique Chantal. "Multiresolution fractal coding of still images." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15508.

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11

Cohen, Dolav. "An exploration of fractal dimension." Kansas State University, 2013. http://hdl.handle.net/2097/16194.

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Master of Science<br>Department of Mathematics<br>Hrant Hakobyan<br>When studying geometrical objects less regular than ordinary ones, fractal analysis becomes a valuable tool. Over the last 30 years, this small branch of mathematics has developed extensively. Fractals can be de fined as those sets which have non-integral Hausdor ff dimension. In this thesis, we take a look at some basic measure theory needed to introduce certain de finitions of fractal dimensions, which can be used to measure a set's fractal degree. We introduce Minkowski dimension and Hausdor ff dimension as well as explore

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12

Burkhead, Darrell. "An Object Oriented Implemtation of Fractal Image Compression." TopSCHOLAR®, 1995. http://digitalcommons.wku.edu/theses/897.

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The technique of Fractal Image Compression, although new, has been described in several ways. Thus far, all descriptions of this compression algorithm read by the author have been in procedural form. The purpose of this paper is to present the Fractal Image Compression algorithm in an object-oriented form and to point out the advantages of this organization. The main advantages of taking an object-oriented approach to this problem are flexibility and maintainability. Different aspects of this algorithm are handled by different objects, thereby allowing for easy customization and testing of eac

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13

Vaughn, Leonard Lewis. "Development of algorithms for the analysis of fractal data." Thesis, University of Hertfordshire, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275140.

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14

Kerss, Alexander. "Fractal activity time and integer valued models in finance." Thesis, Cardiff University, 2014. http://orca.cf.ac.uk/68211/.

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The role of the financial mathematician is to find solutions to problems in finance through the application of mathematical theory. The motivation for this work is specification of models to accurately describe the price evolution of a risky asset, a risky asset is for example a security traded on a financial market such as a stock, currency or benchmark index. This thesis makes contributions in two classes of models, namely activity time models and integer valued models, by the discovery of new real valued and integer valued stochastic processes. In both model frameworks applications to optio

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15

Chen, Hua, and Chun Yu. "Asymptotic behaviour of the trace for Schrödinger operator on fractal drums." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2615/.

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16

Fetbrandt, Joshua Taylor. "Hölder Extensions for Non-Standard Fractal Koch Curves." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/4097.

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Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is a strictly increasing function of n; this prevents us from demonstrating uniform convergence in

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17

Constantine, William L. B. "Wavelet techniques for chaotic and fractal dynamics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/7124.

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18

Piché, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.

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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wav

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Pich??, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.

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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wav

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20

Jones, Cameron Lawrence, and cajones@swin edu au. "Image analysis of fungal biostructure by fractal and wavelet techniques." Swinburne University of Technology, 1997. http://adt.lib.swin.edu.au./public/adt-VSWT20051107.093036.

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Filamentous fungal colonies show a remarkable diversity of different mycelial branching patterns. To date, the characterization of this biostructural complexity has been based on subjective descriptions. Here, computerized image analysis in conjunction with video microscopy has been used to quantify several aspects of fungal growth and differentiation. This was accomplished by applying the new branch of mathematics called Fractal Geometry to this biological system, to provide an objective description of morphological and biochemical complexity. The fractal dimension is useful for describing ir

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21

Phillips, Jason D. "Intersections of Deleted Digits Cantor Sets With Their Translates." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1308100597.

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22

Luz, Emanueli Vallini da [UNESP]. "A geometria fractal como fator minimizador das dificuldades referentes a conceitos geométricos." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/143826.

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Submitted by EMANUELI VALLINI DA LUZ null (manuvallini@hotmail.com) on 2016-09-05T16:03:06Z No. of bitstreams: 1 LUZ_Emanueli Vallini.pdf: 1946551 bytes, checksum: fddaa535ea085475a08b5129e3c35fa6 (MD5)<br>Rejected by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: No campo “Versão a ser disponibilizada online imediatamente” foi informado que seria disponibilizado o texto completo porém no campo “Data para a disponibilização do texto completo” foi informado que o texto completo deverá ser dis

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23

Murteza, Noor Danielle. "Designer Fractal Patterns: Ecological Validity and the Psychological Wellbeing Effect of Fractal Patterns in Interior Spaces." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu159422878465947.

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24

Leifsson, Patrik. "Fractal sets and dimensions." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7320.

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<p>Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.</p><p>In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and com

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25

Golds, Jeffrey A. "Estimation of the fractal dimension of selected classes of Julia sets using spectral radius calculations." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1321900008.

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26

Tao, Yu. "Feature extraction in pattern recognition and document analysis by fractal and wavelet." HKBU Institutional Repository, 2001. http://repository.hkbu.edu.hk/etd_ra/284.

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27

Gras, Fabrice Roger Pierre Fernand. "Fractal segmentation using Fourier and wavelet spectra." Thesis, Queensland University of Technology, 1997.

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28

Nicola, Celso Henrique. "Conhecendo fractal no ensino médio árvore pitagórica." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5949.

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Made available in DSpace on 2016-06-02T20:29:24Z (GMT). No. of bitstreams: 1 5485.pdf: 1729103 bytes, checksum: b09e1b153530a221dce99193f3506fe6 (MD5) Previous issue date: 2013-08-26<br>Financiadora de Estudos e Projetos<br>This work has objective to show results of a didactic experience that consider the use of a dynamic geometric software in a restrict area of the Mathematic, named fractal . This study presents a great complexity and beauty in your geometric structures. Therefore, we present some fractals, in particular, the Pythagorean Tree that arouses the interest of students. For geom

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29

Mežanec, Jolita. "Paviršių profilogramų tyrimas fraktalinės geometrijos metodais." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050627_121625-86882.

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In this work we used the profilogramms of surfaces, which were gained after the surface was processed (coarsened) with abrasive paper of 24, 36, 40, 60 and 100 numbers. We assessed fractal dimensions of all profilogramms and founded dependence of fractal dimension on abrasive paper number. We found that the more is the coarse of the surface the smaller is fractal dimension. As we didn’t want to do experiment which ask many resources – we modeled theoretically researched profilogramms–fractals, calculated and modeled dimensions of fractal profilogramms. We created programmable tools for theoret

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30

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.

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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, an

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31

Antanavičius, Karolis. "Elektrokardiogramos variacijos pobūdžio tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060606_171848-70560.

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In our research we analyse electrocardiograms (ECG). The aim of this research is to apply the fractal dimension computing method to electrocardiograms, i.e. to create an algorithm, due to which it would be possible to get a few parameters describing ECG. Then, to check, whether the created the mathematical model for computing fractal dimension classify the possessed data. According to Hausdorf “capacity dimension” we compute and analyze “capacity coefficient”. The research of the plane “capacity coefficient” was carried out in this work (it is a fractal dimension, which was computed at the fix

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32

Jančiukaitė, Giedrė. "Teoriniai ir praktiniai fraktalinių interpoliacinių funkcijų sudarymo aspektai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050608_161133-37268.

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This thesis introduces fractal interpolation functions, exposes advantages of fractal interpolation of real world objects and presents some newly developed procedures, associated with fractal interpolation process. The work briefly presents the context needed for introduction of fractal approach and relevant definitions. Also, the detailed description of fractal generating algorithms (deterministic, random iteration, “escape time”) as well as fractal classifications is presented. Since the research object is theoretical and practical aspects of fractal interpolation function analysis, special

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Luz, Emanueli Vallini da. "A geometria fractal como fator minimizador das dificuldades referentes a conceitos geométricos /." São José do Rio Preto, 2016. http://hdl.handle.net/11449/143826.

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Orientador: José Roberto Nogueira<br>Banca: Daniel Dos Santos Viais Neto<br>Banca:Cristiane Nespoli Morelato França<br>Resumo: É incontestável a importância da Geometria Euclidiana para a vida e a evolução da humanidade, e em consequência da defasagem dos alunos em relação a este conteúdo, o presente trabalho, desenvolvido no âmbito da Educação Matemática, iniciou-se com a finalidade de inserir a Geometria Fractal no ensino básico, de modo a viabilizar o processo de ensino e aprendizagem de conceitos da Geometria Clássica, minimizando as dificuldades e promovendo reflexões a respeito da sua ge

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Alexander, Simon. "Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1180.

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This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have char

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Podkorytov, Sergey. "Espaces tangents pour les formes auto-similaires." Phd thesis, Université de Bourgogne, 2013. http://tel.archives-ouvertes.fr/tel-01005330.

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Nous nous intéressons à la modélisation de formes complexes de type structures arborescences, formes lacunaires ou surfaces rugueuses. Ces formes sont intéressantes de par leurs propriétés physiques particulières :objets légers, économie de matière, résistance mécanique, absorption acoustique importante. Les modèles basés sur le concept de la géométrie fractale permettent de générer de telles formes et notamment les formes auto-similaires. A partir des travaux de Barnsley sur les systèmes itérés de fonctions, Tosan et al, ont proposé une extension, Boundary Controled Iterated Funcions Systems

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36

Žavoronkov, Viktor. "Fraktalo vizualizavimas internete." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120723_105216-31163.

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Šio darbo uždavinys – sukurti internetinę programą, vaizduojančią trimatį fraktalą. Tam tikslui buvo išnagrinėti esami metodai ir technologijos trimatei grafikai internete vizualizuoti. Palyginus išnagrinėtus metodus ir technologijos,buvo parinktas tinkamas užduočiai realizuoti metodas, pateiktos išvados. Padaryta programavimo kalbų skirtu programavimui internete apžvalga, aprašytos jų savybės, principai ir palygintos jų teikiamos galimybės ir tinkamumas šiam darbui. Sukurtoje programoje vaizduojamas fraktalas-Mengerio kempinė. Pateiktas fraktalo konstravimo rekursinis algoritmas. Pateiktose p

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37

Siebert, Kitzeln B. "A modern presentation of "dimension and outer measure"." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1211395297.

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38

Singhal, Kritika. "Geometric Methods for Simplification and Comparison of Data Sets." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587253879303425.

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Степанов, Віталій Валерійович, Виталий Валерьевич Степанов, and Vitalii Valeriiovych Stepanov. "Mathematical analysis of the concept as a self-organized limitlessly branchable structure (on the basis of the fractal geometry by B. Mandelbrot)." Thesis, Izdevnieciba “Baltija Publishing”, 2019. https://essuir.sumdu.edu.ua/handle/123456789/85321.

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Тези доповіді розкривають механізм матричної реконструкції концепту ПОЛІТИКА як значення або інформації, активованих у свідомості англомовної спільноти мовним знаком (лексемою politics), лексико-семантичне поле якого слугує засобом його нескінченного самоподібного структурно-смислового розгалуження, що в лінгвістичному і математичному сенсі має фрактальний характер.<br>Тезисы доклада раскрывают механизм матричной реконструкции концепта ПОЛИТИКА как значения или информации, активированных в сознании англоязычного социума языковым знаком (лексемой politics), лексико-семантическое поле которого с

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Tipton, James Edward. "Reproducing Kernel Hilbert spaces and complex dynamics." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2284.

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Both complex dynamics and the theory of reproducing kernel Hilbert spaces have found widespread application over the last few decades. Although complex dynamics started over a century ago, the gravity of it's importance was only recently realized due to B.B. Mandelbrot's work in the 1980's. B.B. Mandelbrot demonstrated to the world that fractals, which are chaotic patterns containing a high degree of self-similarity, often times serve as better models to nature than conventional smooth models. The theory of reproducing kernel Hilbert spaces also having started over a century ago, didn't pick u

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

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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 ce

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Araújo, Jerrimar Moraes de. "Teoria matemática implícita na geometria fractal: construindo fractais com a ferramenta computacional Asymptote." Universidade Federal de Roraima, 2015. http://www.bdtd.ufrr.br/tde_busca/arquivo.php?codArquivo=308.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>O presente trabalho consiste em um relato sobre a origem da Geometria Fractal, tendo em destaque a figura de Benoît Mandelbrot, identificado como pioneiro nesta área, cujo fractal leva seu nome. Mostra os fractais pioneiros, assim como a construção destes através da ferramenta computacional "Asymptote". É necessário dizer que, a partir da construção destes, percebe-se, com facilidade um intenso uso de conteúdos presentes no currículo escolar do ensino básico, como por exemplo o cálculo de perímetro e de áreas de figuras planas, pot

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Medišauskas, Edvinas. "Koliažu grįstos fraktalinių interpoliacinių funkcijų generavimo procedūros sudarymas ir tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2007. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2007~D_20070816_143711-31633.

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Darbe pateikiamas naujas lokaliojo koliažo principu grįstas fraktalinių interpoliacinių funkcijų generavimo algoritmas (procedūra) su pilna kompiuterine realizacija. Siūlomas įrankis orientuotas į realaus pasaulio objektų (sistem��), pasižyminčių "atsikartojimu savyje" (fraktališkumu), modeliavimą. Atlikti preliminarūs eksperimentai patvirtina metodo perspektyvumą.<br>In the paper, a new method (tool) for the generation of fractal interpolation functions is presented. The proposed interpolation tool is oriented to process data arrays having links with real-world objects. The interpolation proc

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Li, Xiaolong. "Étude du processus de Mumford." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2006. http://tel.archives-ouvertes.fr/tel-00133522.

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Le processus de Mumford bidimensionnel est un processus gaussien réel à accroissements stationnaires généralisé qui a été introduit par Mumford et Gidas, en vue de modéliser certaines images naturelles comme les nuages. Nous nous propposons d'étudier la généralisation d'un tel processus.

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Gomes, Antônio do Nascimento. "Uma proposta de ensino envolvendo geometria fractal para o estudo de semelhança de figuras planas." Universidade Federal de São Carlos, 2010. https://repositorio.ufscar.br/handle/ufscar/4420.

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Made available in DSpace on 2016-06-02T20:02:48Z (GMT). No. of bitstreams: 1 3265.pdf: 8510958 bytes, checksum: fe5a45d4d8e220ad6a09c7098a54d28f (MD5) Previous issue date: 2010-07-02<br>Secretaria da Educação do Estado de São Paulo<br>The main objective of this research is develop a teaching material by exploring the Fractal Geometry helps students and teachers in teaching-learning process the concepts of Similarity of Figures, among others, present in the curriculum of 8th grade of Elementary School. In this sense, we work with Activities Sheets that connect content that are part of the cur

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Ohlsson, Patrik. "Computer Assisted Music Creation : A recollection of my work and thoughts on heuristic algorithms, aesthetics, and technology." Thesis, Kungl. Musikhögskolan, Institutionen för komposition, dirigering och musikteori, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kmh:diva-2090.

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Denna text är delvis en dokumentation av min egna resa inom datorbaserat tonsättande, specifikt inom algoritmisk komposition. Det är även ett utforskande av den tankevärld som finns i anknytning till dessa metoder – där estetiska koncept och konsekvenser diskuteras. Texten kommer huvudsakligen att beröra metoder som gynnas av eller möjliggörs av teknologi. Jag har försökt att närma mig dessa ämnen holistiskt genom att diskutera allt från estetik, teknik, till konkreta realiseringar av särskilda musikaliska idéer. Till detta tillkommer även många notexempel, lite kod, och illustrationer – speci

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Deheuvels, Thibaut. "Contributions à l'étude d'espaces de fonctions et d'EDP dans une classe de domaines à frontière fractale auto-similaire." Phd thesis, Université Rennes 1, 2013. http://tel.archives-ouvertes.fr/tel-00869946.

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Cette thèse est consacrée à des questions d'analyse en amont de la modélisation de structures arborescentes, comme le poumon humain. Plus particulièrement, nous portons notre intérêt sur une classe de domaines ramifiés du plan, dont la frontière comporte une partie fractale auto-similaire. Nous commençons par une étude d'espaces de fonctions dans cette classe de domaines. Nous étudions d'abord la régularité Sobolev de la trace sur la partie fractale de la frontière de fonctions appartenant à des espaces de Sobolev dans les domaines considérés. Nous étudions ensuite l'existence d'opérateurs de

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Ghanbarian-Alavijeh, Behzad. "Modeling Physical and Hydraulic Properties of Disordered Porous Media: Applications from Percolation Theory and Fractal Geometry." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1401380554.

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Suhr, Stephanie Marie. "A Fractal-Based Mathematical Model for Cancellous Bone Growth Considering the Hierarchical Nature of Bone." Wright State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=wright148467307435565.

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Ben, Slimane Mourad. "Étude du formalisme multifractal pour les fonctions." Phd thesis, Ecole Nationale des Ponts et Chaussées, 1996. http://pastel.archives-ouvertes.fr/pastel-00569006.

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L'objet de cette thèse est l'analyse multifractale des fonctions autosimilaires et l'étude de la validité du formalisme multifractal. Il s'agit d'abord de déterminer la régularité Hölderienne ponctuelle exacte pour des fonctions dont le graphe localement est grossièrement une contraction du graphe complet, à une fonction erreur près ; ensuite de calculer les dimensions de Hausdorff des ensembles de points où la fonction présente la même singularité; et enfin de vérifier les conjectures de Frish et Parisi et celle d'Arneodo, Bacry et Muzy, qui relient ces dimensions à des quantités moyennes ext

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