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Relevant bibliographies by topics / Julia set and Geogebra

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Academic literature on the topic 'Julia set and Geogebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Julia set and Geogebra"

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KOZMA, ROBERT T., and ROBERT L. DEVANEY. "Julia sets converging to filled quadratic Julia sets." Ergodic Theory and Dynamical Systems 34, no. 1 (2012): 171–84. http://dx.doi.org/10.1017/etds.2012.115.

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AbstractIn this paper we consider singular perturbations of the quadratic polynomial $F(z) = z^2 + c$ where $c$ is the center of a hyperbolic component of the Mandelbrot set, i.e., rational maps of the form $z^2 + c + \lambda /z^2$. We show that, as $\lambda \rightarrow 0$, the Julia sets of these maps converge in the Hausdorff topology to the filled Julia set of the quadratic map $z^2 + c$. When $c$ lies in a hyperbolic component of the Mandelbrot set but not at its center, the situation is much simpler and the Julia sets do not converge to the filled Julia set of $z^2 + c$.

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Kim, Theodore. "Quaternion Julia Set Shape Optimization." Computer Graphics Forum 34, no. 5 (2015): 167–76. http://dx.doi.org/10.1111/cgf.12705.

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Dremov, V. A. "On ap-adic Julia set." Russian Mathematical Surveys 58, no. 6 (2003): 1194–95. http://dx.doi.org/10.1070/rm2003v058n06abeh000682.

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Hammood Altameemi, Ali yasir. "Computing the Filled Julia Set." IOP Conference Series: Materials Science and Engineering 928 (November 19, 2020): 042007. http://dx.doi.org/10.1088/1757-899x/928/4/042007.

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Levin, G. M. "Symmetries on the Julia set." Mathematical Notes of the Academy of Sciences of the USSR 48, no. 5 (1990): 1126–31. http://dx.doi.org/10.1007/bf01236299.

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Rohmah, Azizah Fattu. "ITERASI FUNGSI KUADRAT KOMPLEKS DAN KONSTRUKSI HIMPUNAN JULIA." EDUPEDIA 4, no. 1 (2020): 55. http://dx.doi.org/10.24269/ed.v4i1.429.

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This research aims to: (1) study and explain the definition of the Julia set, (2) study and explain the characteristics of the Julia set, (3) construct and visualize the Julia set in computer. This research is a qualitative descriptive research in the form of literature study. The method used in this research is examine various scientific literatures such as books and scientific journals about the definition, characteristics, and the method of constructing and visualizing Julia's set. The main reference of this research is the book Fractal Geometry Mathematical Foundations and Applications edi

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Negi, Ashish, Ankit Garg, and Akshat Agrawal. "Construction of 3D Mandelbrot Set and Julia Set." International Journal of Computer Applications 85, no. 15 (2014): 32–36. http://dx.doi.org/10.5120/14920-3514.

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Titaley, Jullia, Tohap Manurung, and Henriette D. Titaley. "CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTION." JURNAL ILMIAH SAINS 18, no. 2 (2018): 103. http://dx.doi.org/10.35799/jis.18.2.2018.21555.

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CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavi

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ATELA, PAU, and JUN HU. "COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET." International Journal of Bifurcation and Chaos 06, no. 12a (1996): 2427–32. http://dx.doi.org/10.1142/s0218127496001570.

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It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Julia set and commuting pairs.

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Beardon, A. F. "The components of a Julia set." Annales Academiae Scientiarum Fennicae Series A I Mathematica 16 (1991): 173–77. http://dx.doi.org/10.5186/aasfm.1991.1603.

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Dissertations / Theses on the topic "Julia set and Geogebra"

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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 a

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Haas, Stephen. "The Hausdorff Dimension of the Julia Set of Polynomials of the Form zd + c." Scholarship @ Claremont, 2003. https://scholarship.claremont.edu/hmc_theses/148.

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Complex dynamics is the study of iteration of functions which map the complex plane onto itself. In general, their dynamics are quite complicated and hard to explain but for some simple classes of functions many interesting results can be proved. For example, one often studies the class of rational functions (i.e. quotients of polynomials) or, even more specifically, polynomials. Each such function f partitions the extended complex plane C into two regions, one where iteration of the function is chaotic and one where it is not. The nonchaotic region, called the Fatou Set, is the set of all poi

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Joyner, Sheldon T. "On non-archimedean dynamical systems." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51861.

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Thesis (MSc) -- University of Stellenbosch, 2000.<br>ENGLISH ABSTRACT: A discrete dynamical system is a pair (X, cf;) comprising a non-empty set X and a map cf; : X ---+ X. A study is made of the effect of repeated application of cf; on X, whereby points and subsets of X are classified according to their behaviour under iteration. These subsets include the JULIA and FATOU sets of the map and the sets of periodic and preperiodic points, and many interesting questions arise in the study of their properties. Such questions have been extensively studied in the case of complex dynamics, but m

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Lima, Carlos Alberto Siqueira. "Dinâmica complexa e formalismo termodinâmico." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06062011-152648/.

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Estudaremos sistemas dinâmicos complexos da esfera de Riemann, e empregaremos técnicas do Formalismo Termodinâmico incluindo a fórmula de Bowen para provar que a dimensão de Hausdorff \'dim IND. H\' J( \'f IND. lâmbda\' ) do conjunto de Julia J( \'f IND. lâmbda\' ) de uma família holomorfa de funções racionais hiperbólicas f \'lambda\' define uma função real analítica do parâmetro \'lambda\' . Este resultado foi provado por Ruelle [44] em 1981. Daremos uma prova alternativa usando movimentos holomorfos. Trata-se de uma técnica inovadora, originalmente desenvolvida por Mañé, Sad e Sullivan

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Marchioli, Andresa Baldam. "Dinâmica de endomorfismos do plano complexo e conjuntos de Julia na esfera de Rieman /." São José do Rio Preto : [s.n.], 2009. http://hdl.handle.net/11449/94261.

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Orientador: Ali Messaoudi<br>Banca: Eduardo Garibaldi<br>Banca: Maria Gorete Carreira Andrade<br>Resumo: Neste trabalho, estudaremos as propriedades dinâmicas de endomorfismos do plano complexo C. Provaremos e o teorema de Montel e mostraremos algumas propriedades topológicas do conjunto de Julia J(f), onde f : C "seta" C é uma aplicação racional de grau > ou = 2<br>Abstract: In this work, we will study the dynamical properties of endomorfisms of complex plane C. We will also prove Montel's theorem and show some topological properties of Julia set J(f), where f : C 'seta' C is a rational map o

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Taixés, i. Ventosa Jordi. "Connectivity of Julia sets of transcendental meromorphic functions." Doctoral thesis, Universitat de Barcelona, 2011. http://hdl.handle.net/10803/50391.

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Newton's method associated to a complex holomorphic function f is defined by the dynamical system Nf(z) = z – f(z) / f'(z). As a root-finding algorithm, a natural question is to understand the dynamics of Nf about its fixed points, as they correspond to the roots of the function f. In other words, we would like to understand the basins of attraction of Nf, i.e., the sets of points that converge to a root of f under the iteration of Nf. Basins of attraction are actually just one type of stable component or component of the Fatou set, defined as the set of points for which the family of itera

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Bianchi, Fabrizio. "Motions of Julia sets and dynamical stability in several complex variables." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30099/document.

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Dans cette thèse, on s'intéresse aux systèmes dynamiques holomorphes dépendants de paramètres. Notre objectif est de contribuer à une théorie de la stabilité et des bifurcations en plusieurs variables complexes, généralisant celle des applications rationnelles fondées sur les travaux de Mané, Sad, Sullivan et Lyubich. Pour une famille d'applications d'allure polynomiale, on prouve l'équivalence de plusieurs notions de stabilité, entre autres une version asymptotique du mouvement holomorphe des cycles répulsifs et d'un sous-ensemble de l'ensemble de Julia de mesure pleine. Cela peut etre consid

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Marchioli, Andresa Baldam [UNESP]. "Dinâmica de endomorfismos do plano complexo e conjuntos de Julia na esfera de Rieman." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/94261.

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Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-08-10Bitstream added on 2014-06-13T18:07:02Z : No. of bitstreams: 1 marchioli_ab_me_sjrp.pdf: 317494 bytes, checksum: 518683b62d488d3433a0bee79ecd4f53 (MD5)<br>Neste trabalho, estudaremos as propriedades dinâmicas de endomorfismos do plano complexo C. Provaremos e o teorema de Montel e mostraremos algumas propriedades topológicas do conjunto de Julia J(f), onde f : C seta C é uma aplicação racional de grau > ou = 2<br>In this work, we will study the dynamical properties of endomorfisms of c

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Poirier, Schmitz Alfredo. "Invariant measures on polynomial quadratic Julia sets with no interior." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96022.

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We characterize invariant measures for quadratic polynomial Julia sets with no interior. We prove that besides the harmonic measure —the only one that is even and invariant—, all others are generated by a suitable odd measure.<br>En este artículo caracterizamos medidas invariantes sobre conjuntos de Julia sin interior asociados con polinomios cuadráticos. Probamos que más allá de la medida armónica —la única par e invariante—, el resto son generadas por su parte impar.

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Uceda, Rafael Asmat [UNESP]. "Máquina de somar, conjuntos de Julia e fractais de Rauzy." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/103050.

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Made available in DSpace on 2014-06-11T19:32:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-15Bitstream added on 2014-06-13T21:04:11Z : No. of bitstreams: 1 uceda_ra_dr_sjrp.pdf: 905373 bytes, checksum: c2f0ae66c1c9b9621f826e692c6d9b4c (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Em 2000, Killeen e Taylor definiram a máquina de somar estocástica em base 2. Eles mostraram que o espectro do op erador de transi cão (agindo em l∞( N)), associado a essa máquina, e igual ao conjunto de Julia cheio de uma função quadrática. Nesse trabalho, estudamos outras

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Books on the topic "Julia set and Geogebra"

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Keller, Karsten. Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/bfb0103999.

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Riedl, Johannes. Arcs in Multibrot sets, locally connected Julia sets and their construction by quasiconformal surgery. Techniche Universität München, Zentrum Mathematik, 2001.

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Milnor, John W. Dynamical systems (1984-2012). Edited by Bonifant Araceli 1963-. American Mathematical Society, 2014.

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Donnelly, Jean. The Julia Set. Edge Books, 1995.

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Donaldson, Julia. Julia Donaldson and Lydia Monks x 8 Book Set. Macmillan Children's Books, 2017.

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Keller, Karsten. Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set. Springer, 2000.

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Raybourn, Deanna. Lady Julia Grey Mystery Collection Volume 1: A Victorian Romance Box Set. Harlequin Enterprises, Limited, 2019.

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Quick, Amanda. Dancing at Midnight / To Catch an Heiress. Harpercollins (Short Disc), 2002.

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Hewson, David. Flood, The: A mystery set in Florence, Italy (Pino Fratelli and Julia Wellbeloved). Severn House Publishers, 2015.

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Strindberg, August. Five Plays, Set 2: There Are Crimes And Crimes; Miss Julia; The Stronger; Creditors; Pariah. Echo Library, 2006.

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Book chapters on the topic "Julia set and Geogebra"

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Beardon, Alan F. "Properties of the Julia Set." In Iteration of Rational Functions. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4422-6_4.

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Douady, Adrien. "Julia Sets and the Mandelbrot Set." In The Beauty of Fractals. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61717-1_13.

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Milnor, John. "Using the Fatou Set to Study the Julia Set." In Dynamics in One Complex Variable. Vieweg+Teubner Verlag, 2000. http://dx.doi.org/10.1007/978-3-663-08092-3_6.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "The Mandelbrot Set: Ordering the Julia Sets." In Chaos and Fractals. Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21823-8_15.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "The Mandelbrot Set: Ordering the Julia Sets." In Chaos and Fractals. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4740-9_15.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "The Mandelbrot Set: Ordering the Julia Sets." In Fractals for the Classroom. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4406-6_8.

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Sreeja, K. U., P. B. Vinod Kumar, and P. B. Ramkumar. "Julia Set of Some Graphs Using Independence Polynomials." In Topological Dynamics and Topological Data Analysis. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0174-3_16.

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Zhou, Longfu, Sen Bai, Yuqiang Cao, and YingLong Wang. "Image Visually Meaningful Cryptography Based on Julia Set Generating and Information Hiding." In Digital Forensics and Watermarking. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43575-2_32.

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You, Fucheng, and Yingjie Liu. "The Research on Anti-counterfeiting of Fractal Graphics in Color Printing Based on Escape Time Algorithm of Julia-set." In Advanced Research on Computer Education, Simulation and Modeling. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21783-8_29.

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Devaney, Robert L. "The Julia Set." In A First Course in Chaotic Dynamical Systems. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780429280665-16.

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Conference papers on the topic "Julia set and Geogebra"

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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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Zhang, Xin, and Zhiqiang Xu. "Implementation of Mandelbrot set and Julia Set on SOPC platform." In 2011 International Conference on Electronics, Communications and Control (ICECC). IEEE, 2011. http://dx.doi.org/10.1109/icecc.2011.6066355.

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NAKAGAMI, FUKO, and NINGPING SUN. "Complex Mapping of 3DCG Models with Julia Set and Mandelbrot Set." In Sixth International Conference On Advances in Computing, Electronics and Electrical Technology - CEET 2016. Institute of Research Engineers and Doctors, 2016. http://dx.doi.org/10.15224/978-1-63248-109-2-25.

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Dong, Andrew, and Daniel Ashlock. "Clustering Julia Set Examples to Enhance Evolution of Fractal Parameters." In 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2020. http://dx.doi.org/10.1109/cec48606.2020.9185604.

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Mohammed, Nada Qasim, Qasim Mohammed Hussein, and Mohammed Sh Ahmed. "Suitability of Using Julia Set Images as a Cover for Hiding Information." In 2018 Al-Mansour International Conference on New Trends in Computing, Communication, and Information Technology (NTCCIT). IEEE, 2018. http://dx.doi.org/10.1109/ntccit.2018.8681185.

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Isnanto, R. Rizal, Achmad Hidayatno, and Ajub Ajulian Zahra. "Fractal Batik Motifs Generation Using Variations of Parameters in Julia Set Function." In 2020 8th International Conference on Information and Communication Technology (ICoICT). IEEE, 2020. http://dx.doi.org/10.1109/icoict49345.2020.9166282.

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Zhang Heng and Suyi Liu. "Pattern design of textile printing based on the transform of the Julia set." In 2009 IEEE International Conference on Virtual Environments, Human-Computer Interfaces and Measurements Systems (VECIMS). IEEE, 2009. http://dx.doi.org/10.1109/vecims.2009.5068886.

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Jovanovic, Vojin, and Kazem Kazerounian. "Optimal Design Using Chaotic Descent Method." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5853.

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Abstract This paper presents a novel method for locating global minima in design optimization problems. The method is applicable to any general nonlinear function. It is based on utilizing sensitive fractal areas to locate all of the solutions along one direction in variable space. The search begins from an arbitrary chosen point in the space and descends towards a better design along a randomly chosen direction. Descent depends on finding points that belong to Julia set from which all of the solutions along that direction can be located. The process is repeated until optimal design is obtaine

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