See also:

• Science: Math: Applications: Complex Systems  (96)
• Science: Math: Differential Equations: Dynamical Systems  (70)

Fractal Geometry:  .

- 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.:  .

- Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.

Bitshifters: - Images generated by different commercial applications. Includes FAQs and tutorial.

Chaos, Fractals, and Arcadia: - Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.

3D Fractals Bicomplex Dynamics: - Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.

3D Mountains: - Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.

Dan Freeland: - Explains the basics. Includes gallery and free software for exploring different sets and singularities.

The Dynamical Systems and Technology Project: - Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.

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.




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.

Fractal Brownian Archipelago: - Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.

Fractal Dimensions: - Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Includes didactic examples and illustrations.

Fractal Explorer: - Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.

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.

Fractal Map: - Interactive online Mandelbrot and Julia generator.

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.

Fractals Unleashed: - Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian.

Homepage of Kristian Gustavsson: - Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.




IFS Attractors: - Index and definition of different attractors. Includes images, plots and glossary.

Images From Chaos: - Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.

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

An Introduction to Julia and Mandelbrot Sets: - Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian.

Introduction to Lacunarity: - Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.

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.

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.

Kleinian Groups Pictures: - Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.

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.




Mathematical Figures Using Mathematica: - Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.

Mathematics: Stilldreamer: - Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.

The Modular Group and Fractals: - Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.

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.

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.

Project Fractales: - Research group at the INRIA national research center, France. Includes research details, publications and software.

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.

The Spanky Fractal Database: - Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.

Technocosm: - Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.




Tetrabrot Fractal Videos: - Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.

What are Fractals?: - Explains the basics, addressing definitions, dimensions and uses. Includes gallery and resources.

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

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

A Fractal Christmas: - Short Article from Inside Science News Service describing the basics. Includes illustrations and links. (December 1, 2003)