Chaos and Fractals

Media publications

• A Fractal Christmas - Short Article from Inside Science News Service describing the basics. Includes illustrations and links. (Published 2003.12.01)
• The 3x+1 Fractal - Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references. (Published 2004.06.01)

	Fractal Geometry URL: http://classes.yale.edu/fractals/ ODP description: 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.
	Mandelbrot, Benoit B. URL: http://www.math.yale.edu/mandelbrot/ ODP description: Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews. Page title: Benoit B. Mandelbrot Page description: Official Biography site. Benoit B. Mandelbrot is the world's foremost impetus for the advancement of Fractal Geometry. Learn about his life and work.
	The Spanky Fractal Database URL: http://spanky.triumf.ca/ ODP description: Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links. Page title: Spanky Welcome
	Julia and Mandelbrot Set Explorer URL: http://aleph0.clarku.edu/~djoyce/julia/explorer.html ODP description: Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers. Page title: Mandelbrot and Julia Set Explorer
	Wikipedia: Fractals URL: http://en.wikipedia.org/wiki/Fractals ODP description: Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets. Page title: Fractal - Wikipedia, the free encyclopedia
	3D Fractals Bicomplex Dynamics URL: http://www.3dfractals.com/ ODP description: Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads. Page title: 3D Fractals
	The Dynamical Systems and Technology Project URL: http://math.bu.edu/DYSYS/dysys.html ODP description: Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
	The Mandelbrot and Julia Sets Anatomy URL: http://www.ibiblio.org/e-notes/MSet/Contents.htm ODP description: Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations. Page title: The Mandelbrot set Anatomy: Contents
	Fractal Explorer URL: http://www.geocities.com/fabioc/ ODP description: Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery. Page title: Fractal Explorer: Mandelbrot and Julia sets (by Fabio Cesari) Page description: A fractal tutorial for beginners by Fabio Cesari
	Chaos, Fractals, and Arcadia URL: http://math.bu.edu/DYSYS/arcadia/ ODP description: Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
	Newton Basins URL: http://aleph0.clarku.edu/~djoyce/newton/newton.html ODP description: 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.
	Fractals Unleashed URL: http://library.thinkquest.org/26242/ ODP description: Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian] Page title: Fractals Unleashed - Team 26242
	Fractal Map URL: http://frac.samurajdata.se/ ODP description: Interactive online Mandelbrot and Julia generator. Page description: Fractal Map - A fun and addictive online fractal viewer. No Java required
	Introduction: Chaos, Fractals And Attractors URL: http://www.ecometry.biz/ ODP description: Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references. Page title: Ecometry
	Kleinian Groups Pictures URL: http://klein.math.okstate.edu/kleinian/ ODP description: Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
	Fractal Brownian Archipelago URL: http://swiss.csail.mit.edu/~rauch/islands/ ODP description: Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set. Page title: Fractal Brownian Islands exhibit - Fractional Brownian Motion - fractals and coastline
	Fractal Dimensions URL: http://math.rice.edu/~lanius/fractals/dim.html ODP description: Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations. Page title: Cynthia Lanius' Fractals Unit: Fractal Dimension
	NASA: Fractal Clouds URL: http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html ODP description: Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications. Page title:
	Images From Chaos URL: http://www.cps.unizar.es/~jlsubias/ ODP description: Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain. Page title: Mandelbrot set, Poincare section & Lorenz attractor as orbitals Page description: Chaotic, Complex & Critical Systems. Numerical Experiments, Mathematical Models, Fractals
	IFS Attractors URL: http://www.meden.demon.co.uk/Fractals/fractals.html ODP description: Index and definition of different attractors. Includes images, plots and glossary.
	3D Mountains URL: http://www.ibiblio.org/e-notes/3Dapp/Mount.htm ODP description: Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
	The Modular Group and Fractals URL: http://www.linas.org/math/sl2z.html ODP description: Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications. Page description: An exposition of the relationship between fractals, the Riemann Zeta, the Modular Group Gamma and the Farey Fractions
	Project Fractales URL: http://complex.inria.fr/ ODP description: Research group at the INRIA national research center, France. Includes research details, publications and software. Page title: The Complex Project at INRIA Rocquencourt
	Technocosm URL: http://technocosm.org/chaos/ ODP description: Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries. Page title: technocosm.org - Math, Chaos, and Fractals
	Mathematics: Stilldreamer URL: http://www.stilldreamer.com/mathematics/ ODP description: Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code. Page description: Articles which pertain mostly to mathematics, often with sample programs.
	Fractal Foundation URL: http://www.fractalfoundation.org ODP description: Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact. Page title: Welcome to the Fractal Foundation Page description: The Fractal Foundation is a nonprofit organization whose mission is to educate and inspire people about the joy of math, art, science and technology.
	Efg's Computer Lab: Fractals and Chaos URL: http://www.efg2.com/Lab/FractalsAndChaos ODP description: Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds. Page title: efg's Fractals and Chaos Page
	Fractals and Multi Layer Coloring Algorithms URL: http://www.mi.sanu.ac.yu/vismath/javier1 ODP description: Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references. Page title: Fractals and multi layer coloring algorithms
	Dan Freeland URL: http://homepage.ntlworld.com/daniel.freeland/ ODP description: Explains the basics. Includes gallery and free software for exploring different sets and singularities.
	Tetrabrot Fractal Videos URL: http://www.javaspider.com/jfract ODP description: Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions. Page title: page1
	The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models URL: http://www.geocities.com/CapeCanaveral/Lab/5833/ ODP description: Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references. Page title: Climate Dynamics,Chaos and Quantum Mechanics
	Mathematical Figures Using Mathematica URL: http://mathforum.org/advanced/robertd/ ODP description: Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations. Page title: The Math Forum: Mathematical Figures by Robert M. Dickau Page description: Fractals and combinatorics diagrams created using Mathematica.
	Iterations and the Mandelbrot Set URL: http://www.cut-the-knot.com/blue/Mandel.html ODP description: Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references. Page description: Demonstration of how the iterations behave starting inside and outside Mandelbrot set
	Quantum Jumps, EEQT and the Five Platonic Fractals URL: http://quantumfuture.net/quantum_future/papers/qfract/ ODP description: Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography. Page description: Quantum Jumps, EEQT and the Five Platonic Fractals
	An Introduction to Julia and Mandelbrot Sets URL: http://www.geocities.com/leibowitz.geo/fract_en.html ODP description: Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian] Page title: Introduction to Julia and Mandelbrot Fractal Set Page description: A detailed introduction on the principles of complex set fractals, with a particular emphasis on Julia and Mandelbrot set
	Bitshifters URL: http://bitshifters.com/fractal.html ODP description: Images generated by different commercial applications. Includes FAQs and tutorial. Page title: BitShifters SoftSource Factals Page description: These images are of the Mandelbrot set, a fractal generated from a simple mathematical formula. They were produced by DRAWING Librarian Professional (DP).
	Homepage of Kristian Gustavsson URL: http://www.dd.chalmers.se/~f99krgu/main/index.html ODP description: Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery. Page description: Project about fractals and chaos. The fractal generator FracZoom. Project in genetic computation: A selfprogramming Nintendo player.
	Introduction to Lacunarity URL: http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html ODP description: Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications. Page title: An Introduction to Lacunarity