Contents  > Science  > Math  > Chaos and Fractals

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• Science: Math: Applications: Complex Systems  (88)
• Science: Math: Differential Equations: Dynamical Systems  (71)

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• Fractal Geometry - 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 software.
• Mandelbrot, Benoit B. - Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.

  Bitshifters Images generated by different commercial applications. Includes FAQs and tutorial. http://bitshifters.com/fractal.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/

  3D Fractals Bicomplex Dynamics Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads. http://www.3dfractals.com/

  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

  Dan Freeland Explains the basics. Includes gallery and free software for exploring different sets and singularities. http://homepage.ntlworld.com/daniel.freeland/

  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

  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/

  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

  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

  Fractal Map Interactive online Mandelbrot and Julia generator. http://frac.samurajdata.se/

  Fractals: The Beautiful Complex Patterns Generated by Simple Iterative Computations Outlines a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references. http://amselvam.webs.com/

  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/

  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

  IFS Attractors Index and definition of different attractors. Includes images, plots and glossary. http://www.meden.demon.co.uk/Fractals/fractals.html

  Images From Chaos Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain. http://www.cps.unizar.es/~jlsubias/

  Introduction: Chaos, Fractals And Attractors Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references. http://www.ecometry.biz/

  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

  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

  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

  Kleinian Groups Pictures Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code. http://klein.math.okstate.edu/kleinian/

  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

  Mathematical Figures Using Mathematica Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations. http://mathforum.org/advanced/robertd/

  Mathematics: Stilldreamer Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code. http://www.stilldreamer.com/mathematics/

  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

  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

  Project Fractales Research group at the INRIA national research center, France. Includes research details, publications and software. http://complex.inria.fr/

  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/

  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/

  Technocosm Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries. http://technocosm.org/chaos/

  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

  Wikipedia: Fractals Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets. http://en.wikipedia.org/wiki/Fractals

  The 3x+1 Fractal Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. (June 1, 2004) 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