| Directory > Science > Math > Chaos and Fractals The 3x + 1 Fractal
A paper that generalizes the famous 3x + 1 (or Collatz) problem to complex numbers, and in the
process, introduces a striking new fractal.
http://www.geocities.com/windmill96/collatz/cfractal.html
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The Fractal Foundation
Inspiring and educating people about Fractals, Chaos Theory and the interconnectedness of complex
systems. Our Fractal Balloons are a highly visible fusion of art and technology.
http://www.fractalfoundation.org
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Chaos, Fractals And Attractors In Science
Chaos theory is a popular name for the theory of Dynamical Systems (DS), mainly for non-linear
systems. The theory covers many aspects of the life of DS, all of them have the same
characteristics, they were born, they lived and they died.
http://www.geocities.com/ecometry
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Fractals and Chaos
Provides images, quotes and information on the different types of fractals.
http://astronomy.swin.edu.au/~pbourke/fractals/
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Fractal Geometry at Yale University
Course homepage for the Fractal Geometry course at Yale University.
http://classes.yale.edu/fractals/Welcome.html
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Interactive 3D Fractals
Shows how to create fractal mountains, 3D Mandelbrot and Julia sets, convex, stellated and
polyhedra. Uses tiny Java1.1 applets and VRML worlds.
http://www.people.nnov.ru/fractal/3Dapp/Mount.htm
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The Mandelbrot and Julia Sets Anatomy
A virtual investigation with interactive, animated fractals, articles and fractal math equations.
http://www.people.nnov.ru/fractal/MSet/Contents.htm
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Iterations and the Mandelbrot Set
Discusses how differently the iterations behave depending on which portions the coefficients are
plucked from.
http://www.cut-the-knot.com/blue/Mandel.html
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Technocosm
Focuses on the visualization of three dimensional strange attractors. Includes formula derivations
and image galleries.
http://technocosm.org/chaos/
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An Introduction To Fractals
Gives definition and explains the different types of formulas used. Includes illustrations and
bibliography.
http://www.swin.edu.au/astronomy/pbourke/fractals/fracintro/
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Sean Reed's Fractal Resource Page
Includes images, information and resource links.
http://wind.prohosting.com/sreed1/fractal.html
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Climate Dynamics
Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather
patterns.
http://www.geocities.com/CapeCanaveral/Lab/5833/
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Fractals and Scale
Discusses original concepts behind fractals and applications of their scales.
http://life.csu.edu.au/complex/tutorials/tutorial3.html
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Fractal Archipelago
Shows how fractals describe the shape of coastlines, and presents an "atlas" of fractal
islands.
http://www.swiss.ai.mit.edu/~rauch/islands
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Chaos Theory Resources - Fractals - Directories - Links
A Directory of Internet resources on chaos theory and fractals.
http://www.academicinfo.net/mathchaos.html
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IFS Attractors
Index to Named Fractals.
http://www.meden.demon.co.uk/Fractals/fractals.html
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Fractal Pages of Paul N. Lee
Computer Generated Fractal Images -- plus an exhaustive list of fractal generators, galleries
featuring fractals, and other fractal related information, such as the "Fractal Census".
http://home.att.net/~Paul.N.Lee/PNL_Fractals.html
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Fractals by Paul Bourke
Images of several attractors, some Newton Raphson method fractals, and L systems. Includes programs
and explanations how to write such programs.
http://www.swin.edu.au/astronomy/pbourke/fractals/
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3D Fractals using Bicomplex Dynamics
The Tetrabrot is the bicomplex generalization of the Mandelbrot set as realized by Dominic
'Ramdam' Rochon. Articles, pictures, news and other downloads.
http://www.3dfractals.com/
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Groupe Fractales
Research group at INRIA Rocquencourt. Research details, publications and software: FRACLAB, Algon,
Xalpha, EASEA.
http://www-rocq.inria.fr/fractales/
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Fractalized!
Java animations of different fractals, including the Mandelbrot and Julia sets.
http://www-unix.oit.umass.edu/~dtillber/
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Fractal Text
Turn words into fractals.
http://b435-boas.stanford.edu/home/science/ftext/index.html
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Mandelbrot and Julia Set Explorer
Clark University hosts various graphic images and links to fractal and other mathematical methods
of imaging.
http://aleph0.clarku.edu/~djoyce/julia/explorer.html
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A Sketchbook on L-systems
Modeling and visualization of plants using parametric L systems.
http://coco.ccu.uniovi.es/malva/sketchbook/
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Fractal Map
A fun and addictive online Mandelbrot viewer.
http://frac.samurajdata.se/
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Mandelbrot Set Explorer
A Java applet for discovering interesting regions of the Mandelbrot Set.
http://www.users.nac.net/thegangof4/blackSaturn/mandelbrot/MandelbrotSetExplorer.htm
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Mathematical Figures Using Mathematica
Robert M. Dickau's page. The "Fractals and Chaos" section has figures of attractors,
L-systems in 2 and 3 dimensions, Sierpinski gaskets, bifurcation, and Julia and Mandelbrot sets.
Includes Mathematica code.
http://mathforum.org/advanced/robertd/index.html
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What are Fractals?
Explanation of fractals, along with fractal art and uses.
http://www.jracademy.com/~jtucek/math/fractals.html
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efg's Computer Lab: Fractals and Chaos Page
Several Fractal and Chaos projects, including "Evolution of Mandelbrot Set," Fractal
Discovery Lab, IFS images, Lorenz and other Strange Attractors.
http://www.efg2.com/Lab/FractalsAndChaos
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Chaos Theory and Fractals
History of chaos as well as extensive information on Chaos Theory and fractals. Contains several
pictures of fractals and links to other Chaos Theory and fractals pages.
http://www.mathjmendl.org/chaos/
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Fractal Pages at Thinks.com
Enter the wonderful world of fractals - where mathematics meets art and music.
http://thinks.com/fractals.htm
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Fractals Unleashed
The most comprehensive website about fractals on the net. Contains enourmous amounts of
information, including fractal applications, lots of Java applets and CGI programs, a
well-organized gallery, and a fractal art contest. Download software and learn how to program
fractal.
http://library.advanced.org/26242/
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Fractal Screensavers
A site with two free screensavers. Each is a fractal produced by a random number generator and a
set of transformations, based on Barnsley's Chaos Game.
http://www.geocities.com/ResearchTriangle/System/8956/mall/ssaver.htm
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Introduction to Fractal Lacunarity
Lacunarity is a counterpart to the fractal dimension, and describes the degree of gappiness of a
fractal. Uses in ecology, and image analysis.
http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html
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The Computational Beauty of Nature
Companion site for the book by Gary William Flake. Contains applets and source code for simulations
of fractals, chaos, complex systems, and adaptation.
http://mitpress.mit.edu/books/FLAOH/cbnhtml/
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Fractal Dimensions
An easy to comprehend mathematical approach to understanding the significance of the applied study
of fractals.
http://math.rice.edu/~lanius/fractals/dim.html
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Fractal Explorer
A fractal tutorial for beginners. Covers Mandelbrot and Julia sets, as well as 4D fractals.
Also features an interactive fractal generator.
http://www.geocities.com/fabioc
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Fractal Adventures
The purpose of this site is to help the beginner to create fractal images. An overview of
programs is provided along with a program-related fractal Gallery.
http://home.att.net/~Novak.S/
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Our Fractal Universe
A site devoted to covering many different aspects of fractals, such as mathematics, music,
applications, image compression, and advanced math.
http://library.advanced.org/25810/
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The Spanky Fractal Database
Large categorized index of software, information and links.
http://spanky.triumf.ca/
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Dynamical Systems and Technology Project
An educational site on chaos and fractals.
http://math.bu.edu/DYSYS/dysys.html
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Limit Sets of Kleinian Groups
Graphics, software.
http://klein.math.okstate.edu/kleinian/
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Newton Basins
Introduction to basins of attraction for Newton's method and the fractals they form.
http://aleph0.clarku.edu/~djoyce/newton/newton.html
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