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  Chaos and Fractals (276)

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Featured Websites in this category
http://www.math.yale.edu/mandelbrot/
Featured Site Mandelbrot, Benoit B. Open in a new browser windowLink Details
- Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.
- http://www.math.yale.edu/mandelbrot/

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http://classes.yale.edu/fractals/
Featured Site Fractal Geometry Open in a new browser windowLink Details
- Comprehensive 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.
- http://classes.yale.edu/fractals/

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Regular Websites in this category

Project Fractales Open in a new windowLink Details
- Research group at the INRIA national research center, France. Includes research details, publications and software.
- http://complex.inria.fr/

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The Modular Group and Fractals Open in a new windowLink Details
- 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

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The 3x+1 Fractal Open in a new windowLink Details
- Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references.
- 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&_u

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Quantum Jumps, EEQT and the Five Platonic Fractals Open in a new windowLink Details
- 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/

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Fractals and Scale Open in a new windowLink Details
- Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
- http://parallel.hpc.unsw.edu.au/complex/tutorials/tutorial3.html

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Fractal Brownian Archipelago Open in a new windowLink Details
- 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/

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Introduction: Chaos, Fractals And Attractors Open in a new windowLink Details
- Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
- http://www.ecometry.biz/

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Homepage of Kristian Gustavsson Open in a new windowLink Details
- 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

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Tetrabrot Fractal Videos Open in a new windowLink Details
- 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

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Images From Chaos Open in a new windowLink Details
- Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
- http://www.cps.unizar.es/~jlsubias/

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Bitshifters Open in a new windowLink Details
- Images generated by different commercial applications. Includes FAQs and tutorial.
- http://bitshifters.com/fractal.html

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Dan Freeland Open in a new windowLink Details
- Explains the basics. Includes gallery and free software for exploring different sets and singularities.
- http://homepage.ntlworld.com/daniel.freeland/

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Mathematics: Stilldreamer Open in a new windowLink Details
- Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
- http://www.stilldreamer.com/mathematics/

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Fractals and Multi Layer Coloring Algorithms Open in a new windowLink Details
- 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

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Wikipedia: Fractals Open in a new windowLink Details
- Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
- http://en.wikipedia.org/wiki/Fractals

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Chaos, Fractals, and Arcadia Open in a new windowLink Details
- 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/

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NASA: Fractal Clouds Open in a new windowLink Details
- 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

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Fractals Unleashed Open in a new windowLink Details
- 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/

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3D Mountains Open in a new windowLink Details
- 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

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The Mandelbrot and Julia Sets Anatomy Open in a new windowLink Details
- 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

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A Fractal Christmas Open in a new windowLink Details
- Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
- http://www.aip.org/isns/reports/2003/086.html

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Fractal Foundation Open in a new windowLink Details
- 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

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Iterations and the Mandelbrot Set Open in a new windowLink Details
- 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

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Technocosm Open in a new windowLink Details
- Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
- http://technocosm.org/chaos/

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IFS Attractors Open in a new windowLink Details
- Index and definition of different attractors. Includes images, plots and glossary.
- http://www.meden.demon.co.uk/Fractals/fractals.html

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

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Julia and Mandelbrot Set Explorer Open in a new windowLink Details
- 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

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Fractal Map Open in a new windowLink Details
- Interactive online Mandelbrot and Julia generator.
- http://frac.samurajdata.se/

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Mathematical Figures Using Mathematica Open in a new windowLink Details
- Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
- http://mathforum.org/advanced/robertd/index.html

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What are Fractals? Open in a new windowLink Details
- Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
- http://www.jracademy.com/~jtucek/math/fractals.html

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Efg's Computer Lab: Fractals and Chaos Open in a new windowLink Details
- Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
- http://www.efg2.com/Lab/FractalsAndChaos

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Introduction to Lacunarity Open in a new windowLink Details
- 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

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Fractal Dimensions Open in a new windowLink Details
- 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

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The Spanky Fractal Database Open in a new windowLink Details
- Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
- http://spanky.triumf.ca/

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The Dynamical Systems and Technology Project Open in a new windowLink Details
- Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
- http://math.bu.edu/DYSYS/dysys.html

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Kleinian Groups Pictures Open in a new windowLink Details
- Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
- http://klein.math.okstate.edu/kleinian/

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Newton Basins Open in a new windowLink Details
- 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

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