Chaos and Fractals

Bitshifters - Images generated by different commercial applications. Includes FAQs and tutorial.
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.
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.
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.
www.ibiblio.org/e-notes/3Dapp/Mount.htm

Dan Freeland - Explains the basics. Includes gallery and free software for exploring different sets and singularities.
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.
math.bu.edu/DYSYS/dysys.html

The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models - Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.
www.geocities.com/CapeCanaveral/Lab/5833/

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.
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.
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.
math.rice.edu/~lanius/fractals/dim.html

Fractal Explorer - Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
www.geocities.com/fabioc/

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.
www.fractalfoundation.org

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

Fractals and Multi Layer Coloring Algorithms - Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
www.mi.sanu.ac.yu/vismath/javier1

Fractals Unleashed - Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
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.
www.dd.chalmers.se/~f99krgu/main/index.html

IFS Attractors - Index and definition of different attractors. Includes images, plots and glossary.
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.
www.cps.unizar.es/~jlsubias/

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

An Introduction to Julia and Mandelbrot Sets - Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
www.geocities.com/leibowitz.geo/fract_en.html

Introduction to Lacunarity - Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
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.
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.
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.
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.
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.
mathforum.org/advanced/robertd/

Mathematics: Stilldreamer - Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
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.
www.linas.org/math/sl2z.html

NASA: Fractal Clouds - Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.
climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.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.
aleph0.clarku.edu/~djoyce/newton/newton.html

Project Fractales - Research group at the INRIA national research center, France. Includes research details, publications and software.
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.
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.
spanky.triumf.ca/

Technocosm - Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
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.
www.javaspider.com/jfract

What are Fractals? - Explains the basics, addressing definitions, dimensions and uses. Includes gallery and resources.
www.jracademy.com/~jtucek/math/fractals.html

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

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

A Fractal Christmas - Short Article from Inside Science News Service describing the basics. Includes illustrations and links. <small>(December 1, 2003)</small>
www.aip.org/isns/reports/2003/086.html