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= =people=
 * ComputerGraphics playlist by Jyothi Mandala
 * 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