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Julia and Mandelbrot Set Explorer -
Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
http://aleph0.clarku.edu/~djoyce/julia/explorer.html Fractals Unleashed -
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
http://library.thinkquest.org/26242/ Quantum Jumps, EEQT and the Five Platonic Fractals -
Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
http://quantumfuture.net/quantum_future/papers/qfract/ Mathematics: Stilldreamer -
Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
http://www.stilldreamer.com/mathematics/ Kleinian Groups Pictures -
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
http://klein.math.okstate.edu/kleinian/ An Introduction to Julia and Mandelbrot Sets -
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
http://www.geocities.com/leibowitz.geo/fract_en.html 3D Mountains -
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
http://www.ibiblio.org/e-notes/3Dapp/Mount.htm The Mandelbrot and Julia Sets Anatomy -
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.
http://www.ibiblio.org/e-notes/MSet/Contents.htm The 3x+1 Fractal -
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. <small>(June 1, 2004)</small>
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYG-4C47CDM-5&_coverDate=06%2F30%2F2004&_alid=262438467&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5618&_sort=d&view=c&_acct=C000043379&_version=1&_urlVersion=0&_userid=791130&md5=92c370a59ff53edd249c27a91b0ed72e Introduction: Chaos, Fractals And Attractors -
Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
http://www.ecometry.biz/ The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models -
Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.
http://www.geocities.com/CapeCanaveral/Lab/5833/ Technocosm -
Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
http://technocosm.org/chaos/ Fractal Explorer -
Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
http://www.geocities.com/fabioc/ Images From Chaos -
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
http://www.cps.unizar.es/~jlsubias/ Project Fractales -
Research group at the INRIA national research center, France. Includes research details, publications and software.
http://complex.inria.fr/ The Modular Group and Fractals -
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
http://www.linas.org/math/sl2z.html Mathematical Figures Using Mathematica -
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
http://mathforum.org/advanced/robertd/ Fractal Map -
Interactive online Mandelbrot and Julia generator.
http://frac.samurajdata.se/ The Spanky Fractal Database -
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
http://spanky.triumf.ca/ Fractals and Multi Layer Coloring Algorithms -
Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
http://www.mi.sanu.ac.yu/vismath/javier1 Wikipedia: Fractals -
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
http://en.wikipedia.org/wiki/Fractals Efg's Computer Lab: Fractals and Chaos -
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
http://www.efg2.com/Lab/FractalsAndChaos Fractal Brownian Archipelago -
Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
http://swiss.csail.mit.edu/~rauch/islands/ Newton Basins -
Article about the basins of attraction for the Newton's method for finding roots of equations and their resulting representation in the complex plane. Includes mathematical framework and examples.
http://aleph0.clarku.edu/~djoyce/newton/newton.html 3D Fractals Bicomplex Dynamics -
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
http://www.3dfractals.com/ NASA: Fractal Clouds -
Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.
http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html Fractal Foundation -
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact.
http://www.fractalfoundation.org Dan Freeland -
Explains the basics. Includes gallery and free software for exploring different sets and singularities.
http://homepage.ntlworld.com/daniel.freeland/ Tetrabrot Fractal Videos -
Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.
http://www.javaspider.com/jfract The Dynamical Systems and Technology Project -
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
http://math.bu.edu/DYSYS/dysys.html Homepage of Kristian Gustavsson -
Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
http://www.dd.chalmers.se/~f99krgu/main/index.html Chaos, Fractals, and Arcadia -
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
http://math.bu.edu/DYSYS/arcadia/ A Fractal Christmas -
Short Article from Inside Science News Service describing the basics. Includes illustrations and links. <small>(December 1, 2003)</small>
http://www.aip.org/isns/reports/2003/086.html Fractal Dimensions -
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.
http://math.rice.edu/~lanius/fractals/dim.html IFS Attractors -
Index and definition of different attractors. Includes images, plots and glossary.
http://www.meden.demon.co.uk/Fractals/fractals.html Iterations and the Mandelbrot Set -
Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references.
http://www.cut-the-knot.com/blue/Mandel.html Introduction to Lacunarity -
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html Bitshifters -
Images generated by different commercial applications. Includes FAQs and tutorial.
http://bitshifters.com/fractal.html
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