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Newton Basins
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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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Kleinian Groups Pictures
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Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
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The Dynamical Systems and Technology Project
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Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
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The Spanky Fractal Database
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Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
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Fractal Explorer
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Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
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Fractal Dimensions
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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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Introduction to Lacunarity
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Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
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Chaos Theory and Fractals
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Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets.
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Efg's Computer Lab: Fractals and Chaos
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Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
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What are Fractals?
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Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
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Mathematical Figures Using Mathematica
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Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
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Fractal Map
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Interactive online Mandelbrot and Julia generator.
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Julia and Mandelbrot Set Explorer
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Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
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3D Fractals Bicomplex Dynamics
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Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
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IFS Attractors
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Index and definition of different attractors. Includes images, plots and glossary.
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The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models
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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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Technocosm
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Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
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Iterations and the Mandelbrot Set
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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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Fractals, Chaos
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Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles.
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Fractal Foundation
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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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A Fractal Christmas
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Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
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The Mandelbrot and Julia Sets Anatomy
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Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.
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3D Mountains
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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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Fractals Unleashed
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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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NASA: Fractal Clouds
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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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Chaos, Fractals, and Arcadia
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Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
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Fractal Geometry
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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.
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Chaos and Fractals: A Short Trip in Fractional Dimensions
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Addresses the chaotic behavior of different attractors and their mathematical expressions. Includes plots, images and program source codes.
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Wikipedia: Fractals
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Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
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Fractals and Multi Layer Coloring Algorithms
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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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An Introduction to Julia and Mandelbrot Sets
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Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
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Sierpinski Gasket
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Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references.
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Mathematics: Stilldreamer
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Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
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Dan Freeland
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Explains the basics. Includes gallery and free software for exploring different sets and singularities.
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Bitshifters
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Images generated by different commercial applications. Includes FAQs and tutorial.
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Mandelbrot Fractals Generator
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Applet to explore the Mandelbrot set in real time.
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Images From Chaos
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Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
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Tetrabrot Fractal Videos
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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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Homepage of Kristian Gustavsson
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Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
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Introduction: Chaos, Fractals And Attractors
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Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
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Fractal Brownian Archipelago
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Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
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Fractals and Scale
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Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
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Quantum Jumps, EEQT and the Five Platonic Fractals
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Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
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The Modular Group and Fractals
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Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
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Project Fractales
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Research group at the INRIA national research center, France. Includes research details, publications and software.
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Mandelbrot, Benoit B.
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Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.
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Mathematical Figures
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Illustrations of 2D and 3D L-Systems created with Mathematica.
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The Fractal Foundation
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Inspiring and educating people about Fractals, Chaos Theory and the interconnectedness of complex systems.
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Cynthia Lanius' Fractals Unit
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Explains the unusual concept of partial dimensions and shows comparisons to a dot, line, plane and cube.
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