- Newton Basins - http://aleph0.clarku.edu/~djoyce/newton/newton.html
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.
- Kleinian Groups Pictures - http://klein.math.okstate.edu/kleinian/
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
- The Dynamical Systems and Technology Project - http://math.bu.edu/DYSYS/dysys.html
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
- The Spanky Fractal Database - http://spanky.triumf.ca/
Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
- Fractal Explorer - http://www.geocities.com/fabioc
Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
- Fractal Dimensions - http://math.rice.edu/~lanius/fractals/dim.html
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.
- Introduction to Lacunarity - http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
- Chaos Theory and Fractals - http://www.mathjmendl.org/chaos/
Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets.
- Efg's Computer Lab: Fractals and Chaos - http://www.efg2.com/Lab/FractalsAndChaos
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
- What are Fractals? - http://www.jracademy.com/~jtucek/math/fractals.html
Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
- Mathematical Figures Using Mathematica - http://mathforum.org/advanced/robertd/index.html
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
- Fractal Map - http://frac.samurajdata.se/
Interactive online Mandelbrot and Julia generator.
- Julia and Mandelbrot Set Explorer - http://aleph0.clarku.edu/~djoyce/julia/explorer.html
Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
- 3D Fractals Bicomplex Dynamics - http://www.3dfractals.com/
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
- IFS Attractors - http://www.meden.demon.co.uk/Fractals/fractals.html
Index and definition of different attractors. Includes images, plots and glossary.
- Technocosm - http://technocosm.org/chaos/
Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
- Iterations and the Mandelbrot Set - http://www.cut-the-knot.com/blue/Mandel.html
Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references.
- Fractals, Chaos - http://astronomy.swin.edu.au/~pbourke/fractals/
Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles.
- Fractal Foundation - http://www.fractalfoundation.org
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact.
- A Fractal Christmas - http://www.aip.org/isns/reports/2003/086.html
Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
- The Mandelbrot and Julia Sets Anatomy - http://www.ibiblio.org/e-notes/MSet/Contents.htm
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.
- 3D Mountains - http://www.ibiblio.org/e-notes/3Dapp/Mount.htm
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
- Fractals Unleashed - http://library.thinkquest.org/26242/
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
- NASA: Fractal Clouds - http://climate.gsfc.nasa.gov/~cahalan/FractalClouds/FractalClouds.html
Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.
- Chaos, Fractals, and Arcadia - http://math.bu.edu/DYSYS/arcadia/
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
- Fractal Geometry - http://classes.yale.edu/fractals/
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.
- Wikipedia: Fractals - http://en.wikipedia.org/wiki/Fractals
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
- Fractals and Multi Layer Coloring Algorithms - http://www.mi.sanu.ac.yu/vismath/javier1
Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
- An Introduction to Julia and Mandelbrot Sets - http://www.geocities.com/leibowitz.geo/fract_en.html
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
- Sierpinski Gasket - http://astronomy.swin.edu.au/~pbourke/fractals/gasket/
Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references.
- Mathematics: Stilldreamer - http://www.stilldreamer.com/mathematics/
Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
- Dan Freeland - http://homepage.ntlworld.com/daniel.freeland/
Explains the basics. Includes gallery and free software for exploring different sets and singularities.
- Bitshifters - http://bitshifters.com/fractal.html
Images generated by different commercial applications. Includes FAQs and tutorial.
- J.Sprott Fractals in 3D. - http://www.geocities.com/mischa_griesman/index.html
Gallery and program with source. Includes animated three-dimensional sets and attractors.
- Images From Chaos - http://www.cps.unizar.es/~jlsubias/
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
- Tetrabrot Fractal Videos - http://www.javaspider.com/jfract
Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.
- Homepage of Kristian Gustavsson - http://www.dd.chalmers.se/~f99krgu/main/index.html
Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
- Fractal Brownian Archipelago - http://swiss.csail.mit.edu/~rauch/islands/
Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
- Fractals and Scale - http://parallel.hpc.unsw.edu.au/complex/tutorials/tutorial3.html
Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
- Quantum Jumps, EEQT and the Five Platonic Fractals - http://quantumfuture.net/quantum_future/papers/qfract/
Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
- The 3x+1 Fractal - 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&_urlVersion=0&_userid=791130&md5=92c370a59ff53edd249c27a91b0ed72e
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references.
- The Modular Group and Fractals - http://www.linas.org/math/sl2z.html
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
- Project Fractales - http://complex.inria.fr/
Research group at the INRIA national research center, France. Includes research details, publications and software.
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