ABC Directory : Science : Math : Chaos and Fractals :

$http://www.3dfractals.com/$

Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
http://www.3dfractals.com/

http://www.ibiblio.org/e-notes/3Dapp/Mount.htm

3D Mountains

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

http://www.aip.org/isns/reports/2003/086.html

A Fractal Christmas

Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
http://www.aip.org/isns/reports/2003/086.html

$http://bitshifters.com/fractal.html$

Bitshifters

Images generated by different commercial applications. Includes FAQs and tutorial.
http://bitshifters.com/fractal.html

$http://math.bu.edu/DYSYS/arcadia/$

Chaos, Fractals, and Arcadia

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/

http://homepage.ntlworld.com/daniel.freeland/

Dan Freeland

Explains the basics. Includes gallery and free software for exploring different sets and singularities.
http://homepage.ntlworld.com/daniel.freeland/

http://www.efg2.com/Lab/FractalsAndChaos

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.
http://www.efg2.com/Lab/FractalsAndChaos

http://swiss.csail.mit.edu/~rauch/islands/

Fractal Brownian Archipelago

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/

$http://math.rice.edu/~lanius/fractals/dim.html$

Fractal Dimensions

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

$http://www.fractalfoundation.org$

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.
http://www.fractalfoundation.org

$http://frac.samurajdata.se/$

Fractal Map

Interactive online Mandelbrot and Julia generator.
http://frac.samurajdata.se/

Fractals Unleashed

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/

http://www.mi.sanu.ac.yu/vismath/javier1

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.
http://www.mi.sanu.ac.yu/vismath/javier1

http://parallel.hpc.unsw.edu.au/complex/tutorials/tutorial3.html

Fractals and Scale

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

http://www.dd.chalmers.se/~f99krgu/main/index.html

Homepage of Kristian Gustavsson

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

$http://www.meden.demon.co.uk/Fractals/fractals.html$

IFS Attractors

Index and definition of different attractors. Includes images, plots and glossary.
http://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.
http://www.cps.unizar.es/~jlsubias/

http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html

Introduction to Lacunarity

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

Introduction: Chaos, Fractals And Attractors

Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
http://www.ecometry.biz/

http://www.cut-the-knot.com/blue/Mandel.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.
http://www.cut-the-knot.com/blue/Mandel.html

http://aleph0.clarku.edu/~djoyce/julia/explorer.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.
http://aleph0.clarku.edu/~djoyce/julia/explorer.html

$http://klein.math.okstate.edu/kleinian/$

Kleinian Groups Pictures

Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
http://klein.math.okstate.edu/kleinian/

http://mathforum.org/advanced/robertd/index.html

Mathematical Figures Using Mathematica

Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
http://mathforum.org/advanced/robertd/index.html

http://www.stilldreamer.com/mathematics/

Mathematics: Stilldreamer

Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
http://www.stilldreamer.com/mathematics/

http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.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.
http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html

http://aleph0.clarku.edu/~djoyce/newton/newton.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.
http://aleph0.clarku.edu/~djoyce/newton/newton.html

Project Fractales

Research group at the INRIA national research center, France. Includes research details, publications and software.
http://complex.inria.fr/

$http://quantumfuture.net/quantum_future/papers/qfract/$

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.
http://quantumfuture.net/quantum_future/papers/qfract/

Technocosm

Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
http://technocosm.org/chaos/

$http://www.javaspider.com/jfract$

Tetrabrot Fractal Videos

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

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

The 3x+1 Fractal

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

$http://math.bu.edu/DYSYS/dysys.html$

The Dynamical Systems and Technology Project

Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
http://math.bu.edu/DYSYS/dysys.html

http://www.ibiblio.org/e-notes/MSet/Contents.htm

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.
http://www.ibiblio.org/e-notes/MSet/Contents.htm

$http://www.linas.org/math/sl2z.html$

The Modular Group and Fractals

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

The Spanky Fractal Database

Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
http://spanky.triumf.ca/

$http://www.jracademy.com/~jtucek/math/fractals.html$

What are Fractals?

Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
http://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.
http://en.wikipedia.org/wiki/Fractals