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Wikipedia: Fractals - http://en.wikipedia.org/wiki/Fractals
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets. |
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The Spanky Fractal Database - http://spanky.triumf.ca/
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links. |
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Julia and Mandelbrot Set Explorer - http://aleph0.clarku.edu/~djoyce/julia/explorer.html
Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers. |
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Mandelbrot, Benoit B. - http://www.math.yale.edu/mandelbrot/
Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews. |
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Project Fractales - http://complex.inria.fr/
Research group at the INRIA national research center, France. Includes research details, publications and software. |
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The Mandelbrot and Julia Sets Anatomy - http://www.ibiblio.org/e-notes/MSet/Contents.htm
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations. |
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Fractal Foundation - http://www.fractalfoundation.org
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact. |
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Newton Basins - http://aleph0.clarku.edu/~djoyce/newton/newton.html
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. |
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The Dynamical Systems and Technology Project - http://math.bu.edu/DYSYS/dysys.html
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets. |
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Fractal Dimensions - http://math.rice.edu/~lanius/fractals/dim.html
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations. |
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3D Mountains - http://www.ibiblio.org/e-notes/3Dapp/Mount.htm
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations. |
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NASA: Fractal Clouds - http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html
Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications. |
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The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models - http://www.geocities.com/CapeCanaveral/Lab/5833/
Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references. |
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Fractal Geometry - http://classes.yale.edu/fractals/
An educational resource on the mathematical framework and formalism from the Yale University, covering the concept of self similarity. Includes topical examples, images, algorithms and softwares. |
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A Fractal Christmas - http://www.aip.org/isns/reports/2003/086.html
Short Article from Inside Science News Service describing the basics. Includes illustrations and links. |
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Fractals Unleashed - http://library.thinkquest.org/26242/
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian] |
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Fractal Map - http://frac.samurajdata.se/
Interactive online Mandelbrot and Julia generator. |
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Introduction: Chaos, Fractals And Attractors - http://www.ecometry.biz/
Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references. |
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Fractal Explorer - http://www.geocities.com/fabioc/
Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery. |
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Chaos, Fractals, and Arcadia - http://math.bu.edu/DYSYS/arcadia/
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references. |
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Iterations and the Mandelbrot Set - http://www.cut-the-knot.com/blue/Mandel.html
Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references. |
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Images From Chaos - http://www.cps.unizar.es/~jlsubias/
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain. |
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Bitshifters - http://bitshifters.com/fractal.html
Images generated by different commercial applications. Includes FAQs and tutorial. |
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3D Fractals Bicomplex Dynamics - http://www.3dfractals.com/
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads. |
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The Modular Group and Fractals - http://www.linas.org/math/sl2z.html
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications. |
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IFS Attractors - http://www.meden.demon.co.uk/Fractals/fractals.html
Index and definition of different attractors. Includes images, plots and glossary. |
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Kleinian Groups Pictures - http://klein.math.okstate.edu/kleinian/
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code. |
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Dan Freeland - http://homepage.ntlworld.com/daniel.freeland/
Explains the basics. Includes gallery and free software for exploring different sets and singularities. |
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Homepage of Kristian Gustavsson - http://www.dd.chalmers.se/~f99krgu/main/index.html
Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery. |
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An Introduction to Julia and Mandelbrot Sets - http://www.geocities.com/leibowitz.geo/fract_en.html
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian] |
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Fractals and Multi Layer Coloring Algorithms - http://www.mi.sanu.ac.yu/vismath/javier1
Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references. |
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Tetrabrot Fractal Videos - http://www.javaspider.com/jfract
Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions. |
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Efg's Computer Lab: Fractals and Chaos - http://www.efg2.com/Lab/FractalsAndChaos
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds. |
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Mathematical Figures Using Mathematica - http://mathforum.org/advanced/robertd/
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations. |
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The 3x+1 Fractal - 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
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. |