Relevant bibliographies by topics / Fractals

Contents

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

Academic literature on the topic 'Fractals'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Fractals"

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MITINA, OLGA V., and FREDERICK DAVID ABRAHAM. "THE USE OF FRACTALS FOR THE STUDY OF THE PSYCHOLOGY OF PERCEPTION: PSYCHOPHYSICS AND PERSONALITY FACTORS, A BRIEF REPORT." International Journal of Modern Physics C 14, no. 08 (2003): 1047–60. http://dx.doi.org/10.1142/s0129183103005182.

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The present article deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. The experimental research for construction of functional relations between objective parameters of fractals' complexity (fractal dimension and Lyapunov exponent) and subjective perception of their complexity was conducted. As stimulus material we used the program based on Sprott's algorithms for the generation of fractals and the calculation of their mathematical characteristics. For the research 20 fractals were selected which had differen
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Жихарев, Л., and L. Zhikharev. "Fractals In Three-Dimensional Space. I-Fractals." Geometry & Graphics 5, no. 3 (2017): 51–66. http://dx.doi.org/10.12737/article_59bfa55ec01b38.55497926.

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It has long been known that there are fractals, which construction resolve into cutting out of elements from lines, curves or geometric shapes according to a certain law. If the fractal is completely self-similar, its dimensionality is reduced relative to the original object and usually becomes fractional. The whole fractal is often decomposing into a set of separate elements, organized in the space of corresponding dimension. German mathematician Georg Cantor was among the first to propose such fractal set in the late 19th century. Later in the early 20th century polish mathematician Vaclav S
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Husain, Akhlaq, Manikyala Navaneeth Nanda, Movva Sitaram Chowdary, and Mohammad Sajid. "Fractals: An Eclectic Survey, Part II." Fractal and Fractional 6, no. 7 (2022): 379. http://dx.doi.org/10.3390/fractalfract6070379.

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Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales. This paper is the second (and last) part of a series of two papers dedicated to an eclectic survey of fractals describing the infinite complexity and amazing beauty of fractals from historical, theoretical, mathematical, aesthetical and technological aspects, including their diverse applications in various fields. In this article, our focus is on engineering, industrial, commercial and futuris
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Жихарев and L. Zhikharev. "Generalization to Three-Dimensional Space Fractals of Pythagoras and Koch. Part I." Geometry & Graphics 3, no. 3 (2015): 24–37. http://dx.doi.org/10.12737/14417.

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Fractals are geometric objects, each part of which is
 similar to the whole object, so that if we take a part and increase
 its size to the size of the whole object, it would be impossible to
 notice a difference. In other words, fractals are sets having scale
 invariance. In mathematics, they are associated primarily with
 non-differentiable functions. The concept of "fractal" (from the
 Latin "Fractus" meaning «broken») had been introduced by Benoit
 Mandelbrot (1924–2010), French and American mathematician,
 physicist,
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Fraboni, Michael, and Trisha Moller. "Fractals in the Classroom." Mathematics Teacher 102, no. 3 (2008): 197–99. http://dx.doi.org/10.5951/mt.102.3.0197.

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What exactly is a fractal? Traditionally, students learn about the familiar forms of symmetry: reflection, translation, and rotation. Intuitively, fractals are symmetric with respect to magnification. A magnification of a small part of the fractal looks essentially the same as the entire picture. More formally, fractals have the property of self-similarity—that is, a fractal is any shape that is made up of smaller copies of itself. Self-similarity is what distinguishes fractals from most conventional Euclidean figures and makes them appealing. Do fractals hold the same characteristics as other
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Fraboni, Michael, and Trisha Moller. "Fractals in the Classroom." Mathematics Teacher 102, no. 3 (2008): 197–99. http://dx.doi.org/10.5951/mt.102.3.0197.

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What exactly is a fractal? Traditionally, students learn about the familiar forms of symmetry: reflection, translation, and rotation. Intuitively, fractals are symmetric with respect to magnification. A magnification of a small part of the fractal looks essentially the same as the entire picture. More formally, fractals have the property of self-similarity—that is, a fractal is any shape that is made up of smaller copies of itself. Self-similarity is what distinguishes fractals from most conventional Euclidean figures and makes them appealing. Do fractals hold the same characteristics as other
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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 (2017): 919–31. http://dx.doi.org/10.1107/s1600576717005696.

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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
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Joy, Elizabeth K., and Dr Vikas Garg. "FRACTALS AND THEIR APPLICATIONS: A REVIEW." Journal of University of Shanghai for Science and Technology 23, no. 07 (2021): 1509–17. http://dx.doi.org/10.51201/jusst/21/07277.

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In this paper, I have discussed about fractals. The two key properties of fractals have been stated. A brief history about fractals is also mentioned. I have discussed about Mandelbrot fractal and have plotted it using python. A computer-generated fern is compared to a real fern to show how much fractals resemble the real-world objects. Various applications of fractal geometry have also been included.
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BANAKH, T., and N. NOVOSAD. "MICRO AND MACRO FRACTALS GENERATED BY MULTI-VALUED DYNAMICAL SYSTEMS." Fractals 22, no. 04 (2014): 1450012. http://dx.doi.org/10.1142/s0218348x14500121.

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Given a multi-valued function Φ : X ⊸ X on a topological space X we study the properties of its fixed fractal[Formula: see text], which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals [Formula: see text] and [Formula: see text] for a contracting compact-valued function Φ : X ⊸ X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual t
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Chen, Yanguang. "Fractal Modeling and Fractal Dimension Description of Urban Morphology." Entropy 22, no. 9 (2020): 961. http://dx.doi.org/10.3390/e22090961.

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The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of lo
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Dissertations / Theses on the topic "Fractals"

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Moraes, Leonardo Bastos. "Antenas impressas compactas para sistemas WIMAX." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26122013-161125/.

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Alcançar altas taxas de dados em comunicações sem fio é difícil. Altas taxas de dados para redes locais sem fio tornou-se comercialmente um sucesso por volta do ano de 2000. Redes de longa distância sem fio ainda são projetados e utilizados principalmente para serviços de voz em baixas taxas. Apesar de muitas tecnologias promissoras, a realidade de uma rede de área ampla que atenda muitos usuários com altas taxas de dados e largura de banda e consumo de energia razoáveis, além de uma boa cobertura e qualidade no serviço ainda é um desafio. O objetivo do IEEE 802.16 é projetar um sistema de com
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Дядечко, Алла Миколаївна, Алла Николаевна Дядечко, Alla Mykolaivna Diadechko, D. Tokar, and V. R. Tarasenko. "Fractals." Thesis, Видавництво СумДУ, 2011. http://essuir.sumdu.edu.ua/handle/123456789/13436.

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Zanotto, Ricardo Anselmo. "Estudo da geometria fractal clássica." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/6058.

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Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-08-31T19:46:48Z No. of bitstreams: 2 Dissertação - Ricardo Anselmo Zanotto - 2015.pdf: 7706833 bytes, checksum: 26c6e884d0e3a03a3daebaa4ab5764a4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-08-31T19:47:01Z (GMT) No. of bitstreams: 2 Dissertação - Ricardo Anselmo Zanotto - 2015.pdf: 7706833 bytes, checksum: 26c6e884d0e3a03a3daebaa4ab5764a4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made avail
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LONG, LUN-HAI. "Fractals arithmetiques." Université Louis Pasteur (Strasbourg) (1971-2008), 1993. http://www.theses.fr/1993STR13249.

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Dans cette these, nous etablions d'abord un modele mathematique a partir d'un ensemble de points entiers, et d'un nombre fini de couples composes par une application strictement contractante et un ensemble borne. On applique ensuite ce modele a l'etude de la construction de la foret d'arbres. On obtient ainsi une grande classe de fractals qui contient presque tous les fractals classiques, par exemples, les ensembles a similitudes internes, les ensembles auto-affines, les ensembles recurrents de dikking, les ensembles de julia, les attracteurs, etc. Nous etudions ensuite deux familles particuli
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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.

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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.
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Mucheroni, Laís Fernandes [UNESP]. "Dimensão de Hausdorff e algumas aplicações." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151653.

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Submitted by LAÍS FERNANDES MUCHERONI (lais.mucheroni@gmail.com) on 2017-09-18T17:23:23Z No. of bitstreams: 1 dissertacao_mestrado_lais.pdf: 1067574 bytes, checksum: 952e3477ef0efeafd01d052547e8f2e5 (MD5)<br>Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-09-19T20:08:28Z (GMT) No. of bitstreams: 1 mucheroni_lf_me_rcla.pdf: 1067574 bytes, checksum: 952e3477ef0efeafd01d052547e8f2e5 (MD5)<br>Made available in DSpace on 2017-09-19T20:08:28Z (GMT). No. of bitstreams: 1 mucheroni_lf_me_rcla.pdf: 1067574 bytes, checksum: 952e3477ef0efeafd01d052547e8f2e5 (MD5)
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Berbiche, Amine. "Propagation d'ondes acoustiques dans les milieux poreux fractals." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4758.

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La méthode de minimisation de l'intégrale d'action (principe variationnel) permet d’obtenir les équations de propagation des ondes. Cette méthode a été généralisée aux milieux poreux de dimensions fractales, pour étudier la propagation acoustique dans le domaine temporel, en se basant sur le modèle du fluide équivalent. L'équation obtenue réécrite dans le domaine fréquentiel représente une généralisation de l'équation d'Helmholtz. Dans le cadre du modèle d'Allard-Johnson, l'équation de propagation a été résolue de manière analytique dans le domaine temporel, dans les régimes des hautes et des
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Prehl, geb Balg Janett. "Diffusion on Fractals." Master's thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200701033.

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We study anomalous diffusion on fractals with a static external field applied. We utilise the master equation to calculate particle distributions and from that important quantities as for example the mean square displacement . Applying different bias amplitudes on several regular Sierpinski carpets we obtain maximal drift velocities for weak field strengths. According to ~t^(2/d_w), we determine random walk dimensions of d_w&lt;2 for applied external fields. These d_w corresponds to superdiffusion, although diffusion is hindered by the structure of the carpet, containing dangling ends. This se
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Yin, Qinghe. "Fractals and sumsets." Title page, contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phy51.pdf.

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Beaver, Philip Frederick. "Fractals and chaos." Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/28232.

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Books on the topic "Fractals"

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A, Pickover Clifford, ed. Fractal horizons: The future use of fractals. St. Martin's Press, 1996.

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Feder, Jens. Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6.

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Dekking, Michel, Jacques Lévy Véhel, Evelyne Lutton, and Claude Tricot, eds. Fractals. Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0873-3.

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O'Connell, Richard. Fractals. Atlantis Editions, 2002.

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Stephen, Pollock, and British Broadcasting Corporation, eds. Fractals. [British Broadcasting Corporation, 1990.

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Feder, Jens. Fractals. Plenum Press, 1988.

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Feder, Jens. Fractals. Plenum Press, 1988.

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Mac Cormac, Earl, and Maxim I. Stamenov, eds. Fractals of Brain, Fractals of Mind. John Benjamins Publishing Company, 1996. http://dx.doi.org/10.1075/aicr.7.

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Barnsley, Michael. Fractals everywhere. 2nd ed. Academic Press, 1993.

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Barnsley, Michael. Fractals everywhere. Dover Publications, 2012.

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Book chapters on the topic "Fractals"

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

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Tharaniya, P., G. Jayalalitha, Pethuru Raj, and B. Sundaravadivazhagan. "Fractals and Fractal Geometry." In Advanced Fractal Graph Theory and Applications. Chapman and Hall/CRC, 2024. https://doi.org/10.1201/9781003481096-3.

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Courtens, Eric, and René Vacher. "Fractons in Real Fractals." In Random Fluctuations and Pattern Growth: Experiments and Models. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2653-0_4.

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Feder, Jens. "Introduction." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_1.

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Feder, Jens. "Self-Similarity and Self-Affinity." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_10.

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Feder, Jens. "Wave-Height Statistics." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_11.

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Feder, Jens. "The Perimeter-Area Relation." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_12.

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Feder, Jens. "Fractal Surfaces." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_13.

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Feder, Jens. "Observations of Fractal Surfaces." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_14.

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Feder, Jens. "The Fractal Dimension." In Fractals. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2124-6_2.

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Conference papers on the topic "Fractals"

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Wang, Yan. "3D Fractals From Periodic Surfaces." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29081.

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Fractals are ubiquitous as in natural objects and have been applied in designing porous structures such as micro antenna and porous silicon. The seemingly complex and irregular structures can be generated based on simple principles. In this paper, we present three approaches to construct 3D fractal geometries using a recently proposed periodic surface model. By applying iterated function systems to the implicit surface model in the Euclidean or parameter space, 3D fractals can be constructed efficiently. Porosity is also proposed as a metric in fractal design.
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"BACK MATTER." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_bmatter.

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WEST, BRUCE J. "MODELING FRACTAL DYNAMICS." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0002.

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MAINZER, KLAUS. "COMPLEXITY IN NATURE AND SOCIETY: Complexity Management in the Age of Globalization." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0010.

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PEARSON, MICHAEL. "FRACTALS, COMPLEXITY AND CHAOS IN SUPPLY CHAIN NETWORKS." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0011.

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SING, BERND. "ITERATED FUNCTION SYSTEMS IN MIXED EUCLIDEAN AND 𝔭-ADIC SPACES". У Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0024.

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LIEBOVITCH, L. S., V. K. JIRSA, and L. A. SHEHADEH. "STRUCTURE OF GENETIC REGULATORY NETWORKS: EVIDENCE FOR SCALE FREE NETWORKS." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0001.

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GORENFLO, RUDOLF, and FRANCESCO MAINARDI. "FRACTIONAL RELAXATION OF DISTRIBUTED ORDER." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0003.

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ALLEGRINI, P., F. BARBI, P. GRIGOLINI, and P. PARADISI. "FRACTIONAL TIME: DISHOMOGENOUS POISSON PROCESSES VS. HOMOGENEOUS NON-POISSON PROCESSES." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0004.

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PAPASIMAKIS, NIKITAS, and FOTINI PALLIKARI. "MARKOV MEMORY IN MULTIFRACTAL NATURAL PROCESSES." In Fractals 2006. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774217_0005.

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Reports on the topic "Fractals"

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Haussermann, John W. An Introduction to Fractals and Chaos. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada210257.

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Driscoll, John. Fractals as Basis for Design and Critique. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.7059.

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Moore, Charles. A Quantitative Description of Soil Microstructure Using Fractals. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada337825.

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Kostoff, Ronald N., Dustin Johnson, J. A. Del Rio, Louis A. Bloomfield, Michael F. Shlesinger, and Guido Malpohl. Duplicate Publication and 'Paper Inflation' in the Fractals Literature. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada440622.

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Oppenheim, Alan V., and Gregory W. Wornell. Signal Analysis, Synthesis and Processing Using Fractals and Wavelets. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada305490.

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Rao, C. R., and S. R. Kumara. Shape and Image Analysis using Neural Networks Fractals and Wavelets. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada392772.

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Yortsos, Y. C., and J. A. Acuna. Numerical construction and flow simulation in networks of fractures using fractals. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/6283188.

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Pardo Igúzquiza, Eulogio. Karst y fractales. Ilustre Colegio Oficial de Geólogos, 2022. http://dx.doi.org/10.21028/eog.2022.12.05.

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¿Qué tienen en común la distribución de galaxias en el universo, la red del metro de Madrid y la estrategia de caza de la tribu de los Hadza en el norte de Tanzania? La respuesta es que las tres están conectadas con el karst, tal y como se describe en este trabajo, a través del carácter fractal del mismo. En efecto, el karst presenta un comportamiento fractal tanto en superficie como en el subsuelo. En superficie, tanto la topografía kárstica como las depresiones cerradas (dolinas) que caracterizan el paisaje kárstico son fractales. En el karst subterráneo, la red de conductos kársticos (cueva
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Aminzadeh, Fred, Charles Sammis, Mohammad Sahimi, and David Okaya. Characterizing Fractures in Geysers Geothermal Field by Micro-seismic Data, Using Soft Computing, Fractals, and Shear Wave Anisotropy. Office of Scientific and Technical Information (OSTI), 2015. http://dx.doi.org/10.2172/1185274.

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Fisher, Yuval, and Albert Lawrence. Fractal Image Encoding. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada248003.

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