Fractals/Links

See also: Fractal software pages khan academy: pixar. Pixar in a Box is a behind-the-scenes look at how Pixar artists do their jobs. bridges math art complexity explorer from SANTA FE INSTITUTE scholarpedia: Dynamical systems fractal rendering by Raimond Tunnel from the University of Tartu Pictures of Julia and Mandelbrot Sets FF old fractal forums new FF Basic bulletin board codes guidelines mathjax-cheat-sheet blog of Claude Heiland-Allen mandelbrot-book mandelbrot-book/book : one file c programs , images and description fork of the mandelbrot-book and book in pdf format Fractal Geometry from Yale University by Michael Frame, Benoit Mandelbrot (1924-2010), and Nial NegerFebruary 2, 2013 Math 215 - Lecture notes by Professor Douglas C. Ravenel The Mandelbrot and Julia sets Anatomy by Evgeny Demidov : Java version and JavaScript version Mu-Ency - The Encyclopedia of the Mandelbrot Set by Robert Munafo Linas' Art Gallery fractalogy “Fractals don’t have to be scary.” Mandelbrot Maps: Creating a real-time Mandelbrot/Julia fractal explorer Iain Parris Paul Bourke : fractals Exploding the Dark Heart of Chaos by Chris King March 2009 Last Revised Jul 2016, Mathematics Department University of Auckland the Dynamical Systems Web The Mandelbrot set - lecture by Dr. Petra Bonfert-Taylor Wesleyan University different drawing techniques and algorithms by Arnaud Cheritat Mandelbrot set and example C programs ( not by A Cheritat) Tools for Outstanding Research and Investigation = TORI tetration forum Nature of Code Chapter 8: Fractals Complex Analysis Project - java applets, pdf files Complexity Explorer provides online courses and other educational materials related to complex systems science. Complexity Explorer is an education project of the Santa Fe Institute Sekino fractals fractal wiki by William Unsworth Chaos and FractalsA computational approach by Marc McClure Julia and Fatou sets by Michael Becker, 1/2004. Last modification: 8/2006. Computer Graphics from the University of Tartu Fractal rendering from the University of Tartu Form and Formula (Built with Jekyll on Cayman.) © B. L. Badger. 2023 real time rendering papers The Universal Mandelbrot Set: Beginning of the Story by Dolotin, V. Morozov, A. D Algebraic Geometry of Discrete Dynamics The case of one variable V.Dolotin and A.Morozov Guckenheimer, J., and McGehee, R., "a proof of the mandelbrot n2 conjecture," institut mittag-leffler, report 15, 1984. Jussi Harkonen : On Fractal Coloring Techniques Adrien Douady et John H. Hubbard Itération des polynômes quadratiques complexes C.R. de l’Académie des Sciences, t. 294, ser. 1 (1982) p. 123-126. Systemes dynamices holomorphices arxiv papers by Luna Lomonaco arxiv : Cheraghi_D arxiv: Deniz Asli Gerardo_Pastor contributions the Journal ofComputer Graphics Technique Arxiv - dynamical systems Arxiv : Mandelbrot set HAUSDORFF LIMITS OF EXTERNAL RAYS: THE TOPOLOGICAL PICTURE by CARSTEN LUNDE PETERSEN AND SAEED ZAKERI Pastor Papers M. Romera, G. Pastor, A. B. Orue, A. Martín, M-F Danca and F. Montoya, " A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set ", Mathematical Problems in Engineering, vol. 2013, Article ID 105283, 9 pages, 2013. http://dx.doi.org/10.1155/2013/105283. (PDF) G. Pastor, M. Romera, A. B. Orue, A. Martin, M-F. Danca and F. Montoya, " Harmonic Analysis in Discrete Dynamical Systems ", International Journal of Modern Nonlinear Theory and Application, vol. 1, Nº 1, March 2012;, pp. 14-31, doi:10.4236/ijmnta.2012.11003. (PDF) M-F. Danca, M. Romera, G. Pastor and F. Montoya, " Finding attractors of continuous-time systems by parameter switching ", Nonlinear Dynamics, Published on line: 28 September 2011. Doi 10.1007/s11071-011-0172-6. (PDF) G. Pastor, M. Romera, A. B. Orue, A. Martin, M-F. Danca and F. Montoya, "Calculation of the Structure of a Shrub in the Mandelbrot Set", Discrete Dynamics in Nature and Society, volume 2011 (2011) Article ID 837262, 23 pages . (PDF) A.B. Orue, G. Alvarez, G. Pastor, M. Romera, D. Arroyo, F. Montoya and S. Li, "A new parameter determination method for some double-scroll 3 chaotic systems and its applications to chaotic cryptanalysis", Commun Nonlinear Sci Numer Simulat, volume 15 (2010) 3471-3483 . (PDF) M. Romera, G. Pastor, A. B. Orue, D. Arroyo and F. Montoya, "Coupling patterns of external arguments in the multiple-spiral medallions of the Mandelbrot set", Discrete Dynamics in Nature and Society, volume 2009 (2009) Article ID 135637, 14 pages . (PDF) M. F. Danca, M. Romera and G. Pastor, "Alternate Julia sets and connectivity properties", Int. J. of Bifurcations and Chaos, 19 (2009) 2123-2129. (PDF) G. Pastor, M. Romera, G. Álvarez, D. Arroyo, A. B. Orue, V. Fernández and F. Montoya, "A general view of pseudoharmonics and pseudoantiharmonics to calculate external arguments of Douady and Hubbard", Appl. Math. And Comput., 213 (2009) 484-497. (PDF) M. Romera, G. Álvarez, D. Arroyo, A.B. Orue, V. Fernándezand G. Pastor "Drawing and computing external rays in in the multiple-spiral medallions of the Mandelbrot set", Computers & Graphics, 32 (2008) 597-610. Preprint G. Pastor, M. Romera, G. Álvarez, D. Arroyo, A. B. Orue, V. Fernández and F. Montoya, "Algorithm for external arguments calculation of the nodes of a shrub in the Mandelbrot set", Fractals, vol. 16, Issue 2 (June 2008) 159-168 . Preprint G. Pastor, M. Romera, G. Alvarez, J. Nunez, D. Arroyo and F. Montoya, "Operating with external arguments of Douady and Hubbard", Discrete Dynamics in Nature and Society, volume 2007 (2007) Article ID 45920, 17 pages . (PDF) G. Pastor, M. Romera, G. Álvarez, D. Arroyo and F. Montoya, "On periodic and chaotic regions in the Mandelbrot set", Chaos, Solitons & Fractals, 32 (2007) 15-25. Preprint G. Pastor, M. Romera, G. Álvarez, D. Arroyo and F. Montoya, "Equivalence between subshrubs and chaotic bands in the Mandelbrot set", Discrete Dynamics in Nature and Society, volume 2006 (2006) Article ID 70471, 25 pages. (PDF) M. Romera, G. Pastor, G. Álvarez and F. Montoya, "External arguments in in the multiple-spiral medallions of the Mandelbrot set", Computers & Graphics, 30 (2006) 461-470. Preprint G. Pastor, M. Romera, G. Álvarez and F. Montoya, "External arguments for the chaotic bands calculation in the Mandelbrot set", Physica A, 353 (2005) 145-158. Preprint G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Chaotic bands in the Mandelbrot set", Computers & Graphics, 28 (2004), 779-784. Preprint M. Romera, G. Pastor, G. Álvarez and F. Montoya, "External arguments of Douady cauliflowers in the Mandelbrot set", Computers & Graphics, 28 (2004), 437-449. Preprint G. Pastor, M. Romera, G. Álvarez and F. Montoya,. "How to work with one-dimensional quadratic maps", Chaos, Solitons and Fractals, 18 (2003), 899-915. Preprint M. Romera, G. Pastor, G. Álvarez and F. Montoya, "Shrubs in Mandelbrot set ordering", Int. J. Bifurcation and Chaos, 13, 8 (2003), 2279-2300. Preprint G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Operating with external arguments in the Mandelbrot set antenna", Physica D, 171 (2002), 52-71. Preprint M. Romera, V. Bañuls, G. Pastor, G. Álvarez and F. Montoya, "Snail-like pattern generation with the Hénon family of maps", Computers and Graphics, 25 (2001), 529-537. Preprint G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Misiurewicz point patterns generation in one-dimensional quadratic maps", Physica A, 292 (2001), 207-230. Preprint Jesús Calvo, Miguel Romera, Gerardo Pastor, Gonzalo Álvarez y Fausto Montoya, "Argumentos externos del conjunto de Mandelbrot", Revista Española de Física, 15 (3) (2001), 29-33. Preprint M. Romera, G. Pastor, G. Álvarez, F. Montoya, "Growth in complex exponential dynamics", Computers & Graphics, 24 (2000), 115-131. Preprint M. Romera, G. Pastor, G. Álvarez and F. Montoya, "Heredity in one-dimensional quadratic maps", Physical Review E, 58 (1998), 7214-7219. Preprint G. Álvarez, M. Romera, G. Pastor, F. Montoya, "Determination of Mandelbrot set hyperbolic component centres", Chaos Solitons and Fractals, 9 (1998), 1997-2005. Preprint M. Romera, G. Pastor, G. Álvarez and F. Montoya, "Ordering of the Mandelbrot-like set of the exponential map", Chaos, 8, No. 4 (1998), 739-740. Preprint G. Pastor, M. Romera, J.C. Sanz-Martín, F. Montoya, "Simbolic sequences of one-dimensional quadratic map points", Physica A, 256 (1998), 369-382. Preprint M. Romera, G. Pastor, G. Álvarez and F. Montoya, "On the tufts of the Mandelbrot set", Fractalia, 7, n.º 25 (1998), 4-6. G. Álvarez, M. Romera, G. Pastor, F. Montoya, "Gray codes and 1D quadratic maps", Electronic Letters, 34 (1998), 1304-1306. Preprint M. Romera, G. Pastor and F. Montoya, "A Scaling Constant equal to Unity in 1-D Quadratic Maps", Computers & Graphics, 21 (1997), 849-857. Preprint G. Pastor, M. Romera and F. Montoya, "Harmonic structure of one-dimensional quadratic maps", Physical Review E, 56 (1997), 1476-1483. Preprint G. Pastor, M. Romera and F. Montoya, "A revision of the Lyapunov exponent in 1D quadratic maps", Physica D, 107 (1997), 17-22. Preprint M. Romera, G. Pastor, and F. Montoya, "Multifurcations in non hyperbolic fixed points of the Mandelbrot map", Fractalia, 6, n.º 21 (1997), 10-12. M. Romera, G. Pastor and F. Montoya, "On the cusp and the tip of a midget in the Mandelbrot set antenna", Physics Letters A, 221 (1996), 158-162. Preprint G. Pastor, M. Romera and F. Montoya, "On the calculation of Misiurewicz patterns in one-dimensional quadratic maps" Physica A, 232 (1996), 536-553. Preprint M. Romera, G. Pastor and F. Montoya, "Misiurewicz points in one-dimensional quadratic maps", Physica A, 232 (1996), 517-535. Preprint G. Pastor, M. Romera and F. Montoya, "An approach to the ordering of one-dimensional quadratic maps", Chaos, Solitons and Fractals, 7/4 (1996), 565-584. Preprint M. Romera, G. Pastor and F. Montoya, "Graphic Tools to Analyse One-Dimensional Quadratic Maps", Computers & Graphics, 20/2 (1996), 333-339. Preprint M. Romera, G. Pastor and F. Montoya, "Drawing the Mandelbrot set by the method of escape lines", Fractalia, 5, n.º 17 (1996), 11-13. books Max K. Agoston Computer Graphics and Geometric Modeling Implementation and Algorithms Introduction to Computer Graphics Version 1.3, August 2021 (Version 1.3.1, December 2021) Author: David J. Eck - WebGl, JavaScript, Java A First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka Tea Time Numerical Analysis Experiences in Mathematics complex-analysis by Juan Carlos Ponce Campuzano Basic complex dynamics. A computational approach by Mark McClure pdf ( old = not updated) interactive version (new = updated) First course in complex analysisbs by Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka Colours Of Infinity book 2011 Remaster PDF edition from Springer publisher's website Hyperbolic noneuclidean world by Tadao Ito Freely downloadable book Elementary Symbolic Dynamics and Chaos in Dissipative Systems by Bailin HAO, World Scientific, 1989, by kind permission of the publisher. Introduction to Computing with Geometry by Adrian Bowyer and John Woodwark Linear Algebra Done Right by Sheldon Axler (open access) videos ComputerGraphics playlist by Jyothi Mandala people Matthias Müller Matteo Basei Christopher Batty Paul Bourke Henk Bruin Complex dynamics Danny Calegari - Schottky, Kleinian Arnaud Chéritat Keenan Crane Evgeny Demidov Bob Devaney David J. Eck Bernat Espigulé Eric Haines Claude Heiland-Allen Wolf Jung  Tomoki Kawahira Chris King Sara W. Lapan Tan Lei (1963 - 2016) Juan Rivera-Letelier Ricardo PÉREZ-MARCO Mark McClure Robert Munafo  Kento Nakamura Roice Nelson - hiperbolic geometry Gerardo Pastor Amit Patel Emmanuel Risler Michael Sargent Karl Sims malin christersson