Fractals/Links

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pages[edit | edit source]

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

papers[edit | edit source]

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

Pastor[edit | edit source]

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.

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