Relevant bibliographies by topics / Mandelbrot

Contents

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

Academic literature on the topic 'Mandelbrot'

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

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Journal articles on the topic "Mandelbrot"

1

Ford, Roger. "Activities for Students: Discovering and Exploring Mandelbrot Set Points with a Graphing Calculator." Mathematics Teacher 98, no. 1 (2004): 38–46. http://dx.doi.org/10.5951/mt.98.1.0038.

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The Mandelbrot set is one of the most beautiful and complicated objects in all of mathematics. The border of the set is infinite; no matter how many times you magnify the set, dazzling new images appear. Mandelbrot's discovery of the set and his subsequent work on fractals and recursive functions would not have been possible without the aid of the computer. Although the mathematics behind the Mandelbrot set is simple, creating the Mandelbrot set images involves millions of calculations.
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Mandelbrot, Benoit. "Benoit Mandelbrot." New Scientist 192, no. 2578 (2006): 72. http://dx.doi.org/10.1016/s0262-4079(06)61145-7.

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Taylor, Richard. "Benoit Mandelbrot." Physics Today 64, no. 6 (2011): 63–64. http://dx.doi.org/10.1063/1.3603925.

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LIU, XIANG-DONG, ZHI-JIE LI, XUE-YE ANG, and JIN-HAI ZHANG. "MANDELBROT AND JULIA SETS OF ONE-PARAMETER RATIONAL FUNCTION FAMILIES ASSOCIATED WITH NEWTON'S METHOD." Fractals 18, no. 02 (2010): 255–63. http://dx.doi.org/10.1142/s0218348x10004841.

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In this paper, general Mandelbrot and Julia sets of one-parameter rational function families associated with Newton's method were discussed. The bounds of these general Mandelbrot sets and two formulas for calculating the number of different periods periodic points of these rational functions were given. The relations between general Mandelbrot sets and common Mandelbrot sets of zn + c (n ∈ Z, n ≥ 2), along with the relations between general Mandelbrot sets and their corresponding Julia sets were investigated. Consequently, the results were found in the study: there are similarities between the Mandelbrot and Julia sets of one-parameter rational function families associated with Newton's method and the Mandelbrot and Julia sets of zn + c (n ∈ Z, n ≥ 2).
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Horgan, John. "Mandelbrot Set-To." Scientific American 262, no. 4 (1990): 30–34. http://dx.doi.org/10.1038/scientificamerican0490-30b.

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Garousi, Mehrdad. "A Mandelbrot Sunset." Math Horizons 18, no. 3 (2011): 5–7. http://dx.doi.org/10.4169/194762111x12954578042777.

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Westgaard, Odin. "A mandelbrot analog." Performance + Instruction 33, no. 8 (1994): 14–16. http://dx.doi.org/10.1002/pfi.4160330805.

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Barral, Julien, Antti Kupiainen, Miika Nikula, Eero Saksman, and Christian Webb. "Critical Mandelbrot Cascades." Communications in Mathematical Physics 325, no. 2 (2013): 685–711. http://dx.doi.org/10.1007/s00220-013-1829-4.

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Jha, Ketan, and Mamta Rani. "Control of Dynamic Noise in Transcendental Julia and Mandelbrot Sets by Superior Iteration Method." International Journal of Natural Computing Research 7, no. 2 (2018): 48–59. http://dx.doi.org/10.4018/ijncr.2018040104.

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Researchers and scientists are attracted towards Julia and Mandelbrot sets constantly. They analyzed these sets intensively. Researchers have studied the perturbation in Julia and Mandelbrot sets which is due to different types of noises, but transcendental Julia and Mandelbrot sets remained ignored. The purpose of this article is to study the perturbation in transcendental Julia and Mandelbrot sets. Also, we made an attempt to control the perturbation in transcendental sets by using superior iteration method.
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DOLOTIN, V., and A. MOROZOV. "ON THE SHAPES OF ELEMENTARY DOMAINS OR WHY MANDELBROT SET IS MADE FROM ALMOST IDEAL CIRCLES?" International Journal of Modern Physics A 23, no. 22 (2008): 3613–84. http://dx.doi.org/10.1142/s0217751x08040330.

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Direct look at the celebrated "chaotic" Mandelbrot Set (in Fig. 1) immediately reveals that it is a collection of almost ideal circles and cardioids, unified in a specific forest structure. In the paper arXiv:hep-th/0501235, a systematic algebro-geometric approach was developed to the study of generic Mandelbrot sets, but emergency of nearly ideal circles in the special case of the family x2 + c was not fully explained. In the present, paper, the shape of the elementary constituents of Mandelbrot Set is explicitly calculated, and difference between the shapes of root and descendant domains (cardioids and circles respectively) is explained. Such qualitative difference persists for all other Mandelbrot sets: descendant domains always have one less cusp than the root ones. Details of the phase transition between different Mandelbrot sets are explicitly demonstrated, including overlaps between elementary domains and dynamics of attraction/repulsion regions. Explicit examples of three-dimensional sections of Universal Mandelbrot Set are given. Also a systematic small-size approximation is developed for evaluation of various Feigenbaum indices.
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Dissertations / Theses on the topic "Mandelbrot"

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Reis, Márcio Vaiz dos. "Conjunto de Mandelbrot." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6343.

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Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-10-03T21:11:40Z No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-10-04T10:46:49Z (GMT) No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made available in DSpace on 2016-10-04T10:46:49Z (GMT). No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-29<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The purpose of this dissertation is to present an introductory approach to the complex dynamics and fractal geometry, especially the Mandelbrot set. With the goal to simplify and stimulate the introduction of complex number in high school, the approach adopted was: the definition of the Mandelbrot set and its characteristics; the relationship between the Mandelbrot set and Julia set; how to find by using the Mandelbrot set. One of the tools used to help the teaching was Geogeobra, a dynamic software that allows the student to build the Mandelbrot set. Through this study, it is expected to motivate the learning of complex numbers by using fractal obtained by the study of function ( ) . Obtaining, as a result, a differentiated and motivating way of learning for a better understanding and intellectual development of the students.<br>Esse trabalho apresenta uma abordagem introdutória para a dinâmica complexa e a geometria fractal, em especial o conjunto de Mandelbrot. Com objetivo de facilitar e motivar a interação dos alunos com o ensino dos números complexos, a abordagem adotada foi: a definição do conjunto de Mandelbrot e suas características; a relação entre o conjunto de Mandelbrot e o conjunto de Julia; a relação do conjunto de Mandelbrot e o número . Uma das ferramentas utilizadas para auxiliar o professor foi o Geogeobra, um software dinâmico que permite o aluno a construção do conjunto de Mandelbrot. Por meio deste trabalho, espera-se motivar o ensino dos números complexos através do fractal obtido pelo estudo da função ( ) . Obtendo assim, como resultado, uma forma diferenciada e motivadora do aprendizado do aluno, garantindo um melhor entendimento e desenvolvimento intelectual.
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Redona, Jeffrey Francis. "The Mandelbrot set." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1166.

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Jung, Wolf. "Homeomorphisms on edges of the mandelbrot set." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964996537.

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Knapp, Christian. "Creating Music Visualizations in a Mandelbrot Set Explorer." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-21135.

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The aim of this thesis is to implement a Mandelbrot Set Explorer that includes the functionality to create music visualizations. The Mandelbrot set is an important mathematical object, and the arguably most famous so called fractal. One of its outstanding attributes is its beauty, and therefore there are several implementations that visualize the set and allow it to navigate around it. In this thesis methods are discussed to visualize the set and create music visualizations consisting of zooms into the Mandelbrot set. For that purpose methods for analysing music are implemented, so user created zooms can react to the music that is played. Mainly the thesis deals with problems that occur during the process of developing this application to create music visualizations. Especially problems concerning performance and usability are focused. The thesis will reveal that it is in fact possible to create very aesthetically pleasing music visualizations by using zooms into the Mandelbrot set. The biggest drawback is the lack in performance, because of the high computation effort, and therefore the difficulties in rendering the visualization in real-time.
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Martineau, Étienne. "Bornes de la distance à l'ensemble de Mandelbrot généralisé /." Trois-Rivières : Université du Québec à Trois-Rivières, 2004. http://www.uqtr.ca/biblio/notice/resume/18442045R.pdf.

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Martineau, Étienne. "Bornes de la distance à l'ensemble de Mandelbrot généralisé." Thèse, Université du Québec à Trois-Rivières, 2004. http://depot-e.uqtr.ca/1224/1/000120872.pdf.

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Tingen, Larry L. "The Julia and Mandelbrot sets for the Hurwitz zeta function." View electronic thesis (PDF), 2009. http://dl.uncw.edu/etd/2009-3/tingenl/larrytingen.pdf.

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Liang, Xingang. "Propriétés asymptotiques des martingales de Mandelbrot et des marches aléatoires branchantes." Lorient, 2010. http://www.theses.fr/2010LORIS216.

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Dans cette thèse, nous étudions des propriétés asymptotiques de la limite Y d'une martingale de Mandelbrot généralisée, dans des cas divers : 1) les processus de branchement dans un environnement aléatoire ; 2) les cascades multiplicatives généralisées et les marches aléatoires branchantes sur R, au sens classique ou dans un environnement aléatoire ; 3) les cascades multiplicatives multi-dimensionnelles, les processus de branchement multi-types et les marches aléatoires branchantes multi-types ; 4) les cascades multiplicatives complexes et les marches aléatoires branchantes dans C. Dans chacun de ces cas, nous montrons une condition nécessaire ou/et suffisante pour l'existence de moments pondérés de la limite Y, de la forme E Y^{\alpha}\ell(Y) , où \alpha\ge1, \ell est une fonction positive à variation lente en \infty ; dans certains cas, nous montrons aussi une condition nécessaire ou/et suffisante pour que x^{\alpha} \P (|Y|&gt; x) \sim \ell (x) , x\rightarrow\infty<br>In this thesis, we study asymptotic properties of the limit Y of a generalized Mandelbrot's martingale in various cases : 1) the branching processes in a random environment ; 2) the generalized multiplicative cascades and the branching random walks on \ mathbb{R}, in the classical sense or in a random environment ; 3) the multi-dimensional multiplicative cascades, the multitype branching processes and the multitype branching random walks; 4) the complex valued multiplicative cascades and the branching random walks in \mathbb{C}. In each of the above cases, we show a necessary and/or sufficient condition for the existence of weighted moments of the limit Y of the form \E Y^{\alpha}\ell(Y), where \alpha\ge1, \ell is a positive function slowly varying at \infty; in certain cases, we show also a necessary and/or sufficient condition under which x^{\alpha}\P(|Y|&gt;x)\sim \ell(x), as x\rightarrow\infty
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Jones, Rafe. "Galois martingales and the hyperbolic subset of the p-adic Mandelbrot set /." View online version; access limited to Brown University users, 2005. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3174623.

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Barral, Julien. "Continuité, moments d'ordres négatifs et analyse multifractale des cascades multiplicative de Mandelbrot." Paris 11, 1997. http://www.theses.fr/1997PA112005.

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Les mesures de mandelbrot sont des mesures aleatoires obtenues par multiplications iterees de poids aleatoires repartis sur les sous-intervalles c-adiques de l'intervalle 0,1, c etant un entier superieur ou egal a 2. La premiere partie de cette these est consacree a l'etude de quelques proprietes des masses totales de ces mesures. En particulier, on exhibe des conditions suffisantes satisfaisantes pour que ces variables aient des moments d'ordres negatifs et pour que le processus qui a une famille de poids associe la masse totale de la mesure qu'elle definit soit continu. L'existence de moments d'ordres negatifs conditionne la plupart des resultats des parties deux et trois. Dans la seconde partie, on generalise la construction de mandelbrot en repartissant les memes poids, mais cette fois sur des intervalles aleatoires, structures en arbres comme le sont les intervalles c-adiques, et dont les longueurs sont elles-memes donnees par une mesure de mandelbrot. On prouve alors que si deux telles mesures sont construites sur les memes intervalles, l'une possede presque surement, presque partout par rapport a l'autre, un exposant de holder local. En corollaire, on calcule la plus petite dimension d'un borelien portant un morceau d'une telle mesure. Les troisieme et quatrieme parties sont consacrees a l'analyse multifractale de ces mesures : l'une d'entre elles etant fixee, on calcule la dimension de l'ensemble des points de son support ou elle possede un exposant de holder local donne. La cinquieme partie est une note aux comptes rendus de l'academie des sciences dans laquelle on s'interesse a certaines variantes du processus de multiplications. Enfin, dans la derniere partie, on generalise les resultats sur les moments d'ordres negatifs, les exposants de holder locaux et l'analyse multifractale dans le cas ou les mesures sont construites sur des intervalles dont le nombre de sous-intervalles est un entier c aleatoire.
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Books on the topic "Mandelbrot"

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Kasemets, Udo. Mandelbrot music. U. Kasemets, 1994.

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Stauffer, Dietrich, and H. Eugene Stanley. From Newton to Mandelbrot. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-11782-8.

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Stauffer, Dietrich, H. Eugene Stanley, and Annick Lesne. From Newton to Mandelbrot. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53685-8.

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Stauffer, Dietrich, and H. Eugene Stanley. From Newton to Mandelbrot. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-86780-4.

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Stauffer, Dietrich, and H. Eugene Stanley. From Newton to Mandelbrot. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-97262-1.

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Joana Mandelbrot und ich: Roman. Deutscher Taschenbuch, 2008.

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Vandervelde, Sam. The Mandelbrot problem book: A compilation of problems from the Mandelbrot Competition, 1995-2002. Greater Testing Concepts, 2002.

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Lesmoir-Gordon, Nigel. The colours of infinity: The beauty and power of fractals. Springer Verlag, 2010.

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Mandelbrot, Benoit B. Fractals and chaos: The Mandelbrot set and beyond. Springer, 2004.

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Tomboulian, Sherryl. Indirect addressing and load balancing for faster solution to Mandelbrot Set on SIMD architectures. ICASE, 1989.

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Book chapters on the topic "Mandelbrot"

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Peitgen, Heinz-Otto, Hartmut Jürgens, Dietmar Saupe, Evan M. Maletsky, Terry Perciante, and Lee Yunker. "Mandelbrot-Menge." In Chaos. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-85869-7_3.

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Peitgen, Heinz-Otto, and Peter H. Richter. "The Mandelbrot Set." In The Beauty of Fractals. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61717-1_4.

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Weitz, Edmund. "Die Mandelbrot-Menge." In Konkrete Mathematik (nicht nur) für Informatiker. Springer Fachmedien Wiesbaden, 2018. http://dx.doi.org/10.1007/978-3-658-21565-1_40.

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Peitgen, Heinz-Otto, Evan Maletsky, Hartmut Jürgens, Terry Perciante, Dietmar Saupe, and Lee Yunker. "The Mandelbrot Set." In Fractals for the Classroom: Strategic Activities Volume Two. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-5276-2_3.

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Schappacher, Norbert. "Mandelbrot, Benoît B." In Kindlers Literatur Lexikon (KLL). J.B. Metzler, 2020. http://dx.doi.org/10.1007/978-3-476-05728-0_15429-1.

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Vince, John. "The Mandelbrot Set." In Imaginary Mathematics for Computer Science. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94637-5_13.

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Weitz, Edmund. "Die Mandelbrot-Menge." In Konkrete Mathematik (nicht nur) für Informatiker. Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62618-4_40.

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Keller, Karsten. "The Abstract Mandelbrot set." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/bfb0104002.

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Mandelbrot, Benoit B. "Mandelbrot on price variation." In Fractals and Scaling in Finance. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2763-0_16.

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Korsch, H. J., and H. J. Jodl. "Mandelbrot and Julia Sets." In Chaos. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-662-02991-6_11.

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Conference papers on the topic "Mandelbrot"

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Ashlock, Daniel, and Joseph Alexander Brown. "Fitness functions for searching the Mandelbrot set." In 2011 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2011. http://dx.doi.org/10.1109/cec.2011.5949741.

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Sui Tao, Hong-Yan Liu, Zhang Ze-yang, and Tian Ming-hao. "Research on Misiurewiz points in Mandelbrot set." In 2011 International Conference on Computer Science and Network Technology (ICCSNT). IEEE, 2011. http://dx.doi.org/10.1109/iccsnt.2011.6182410.

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Sun, Yuan-yuan, Rui-qing Kong, Xing-yuan Wang, and Lian-cheng Bi. "An Image Encryption Algorithm Utilizing Mandelbrot Set." In 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2010. http://dx.doi.org/10.1109/iwcfta.2010.70.

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Kumar, Suthikshn. "Public Key Cryptographic System Using Mandelbrot Sets." In MILCOM 2006. IEEE, 2006. http://dx.doi.org/10.1109/milcom.2006.302396.

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Rama, Bulusu, and Jibitesh Mishra. "Generation of 3D fractal images for Mandelbrot set." In the 2011 International Conference. ACM Press, 2011. http://dx.doi.org/10.1145/1947940.1947990.

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DRAKOPOULOS, V. "COMPARING SEQUENTIAL VISUALISATION METHODS FOR THE MANDELBROT SET." In Proceedings of the International Conference (ICCMSE 2003). WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704658_0033.

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Huseinovic, Alvin, and Samir Ribic. "Benchmark comparison of computing the Mandelbrot set in OpenCL." In 2015 23rd Telecommunications Forum Telfor (TELFOR). IEEE, 2015. http://dx.doi.org/10.1109/telfor.2015.7377632.

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Sui Tao, Tian Ming-hao, and Zhang Ze-yang. "Research on high-periodic attracting points in Mandelbrot set." In 2011 International Conference on Computer Science and Network Technology (ICCSNT). IEEE, 2011. http://dx.doi.org/10.1109/iccsnt.2011.6182371.

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Koichi Ito, Ayako Suzuki, Sei Nagashima, and Takafumi Aoki. "Performance evaluation using Mandelbrot images for image registration algorithms." In 2009 16th IEEE International Conference on Image Processing ICIP 2009. IEEE, 2009. http://dx.doi.org/10.1109/icip.2009.5413618.

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Sun, Ningping, Ryo Miyazaki, and Naoki Yoshida. "Complex mapping with the interpolated Julia set and Mandelbrot set." In ACM SIGGRAPH ASIA 2010 Posters. ACM Press, 2010. http://dx.doi.org/10.1145/1900354.1900409.

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Reports on the topic "Mandelbrot"

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Rodríguez, Javier, Signed Prieto, Catalina Correa, et al. Aplicación de la ley de Zipf-Mandelbrot al diagnóstico de la dinámica cardíaca normal y aguda. Siicsalud.com, 2020. http://dx.doi.org/10.21840/siic/159579.

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