# Fractals/Links

See also:

# 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