A fractal is a chaotic mathematic object which can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and are generally self-similar and independent of scale. In many cases a fractal can be generated by a repeating pattern, typically a recursive or iterative process. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken"-"fraction". Chaos theory, in mathematics and physics, deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions. Chaos and Fractals Math Science.
- Fractal Geometry www
An educational resource on the mathematical framework and formalism from the Yale University, Geometry, covering the concept of self similarity. Includes topical examples, images, algorithms and software.
- Mandelbrot, Benoit B. www
Founder of fractal geometry. Benoit B.. Includes biography, vita, publications, interviews, and reviews.
- Educational The Dynamical Systems and Technology Project www
Educational resource from the Boston University. Dynamical Systems and Technology Project. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets. The Dynamical Systems and Technology Project.
- Introduction Chaos, Economics and Stock Markets www
Introduction to chaos, Economics and Stock Markets, attractors and dynamic systems theory. Includes mathematical formulation, images and references. Chaos, Economics and Stock Markets.
- Software Efg's Computer Lab: Fractals and Chaos www
Software and information resource on the Mandelbrot set, Computer Lab: Fractals and Chaos, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds. Efg's Computer Lab: Fractals and Chaos.
- Images Bitshifters www
Images generated by different commercial applications. Bitshifters. Includes FAQs and tutorial. Bitshifters.
- Collection Tetrabrot Fractal Videos www
Collection of videos made by rotation, Fractal Videos, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions. Tetrabrot Fractal Videos.
- Online Julia and Mandelbrot Set Explorer www
Online navigator for various sets and attractors from the Clark University. and Mandelbrot Set Explorer. Includes background and a short course on complex numbers. Julia and Mandelbrot Set Explorer.
- Collection Wikipedia Category: Fractals www
Collection of encyclopedia articles about self-similar geometric objects with both aesthetical and scientific uses. Wikipedia Category: Fractals.
- Analysis Introduction to Lacunarity www
Analysis of the degree of gappiness of different sets. Lacunarity. Includes mathematical aspects, results and publications. Introduction to Lacunarity.
- Outlines Fractals: The Beautiful Complex Patterns Generated by Simple Iterative Computations www
Outlines a general systems theory for chaos, The Beautiful Complex Patterns Generated by Simple Iterative Computations, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references. Fractals: The Beautiful Complex Patterns Generated by Simple Iterative Computations.
- Free Wikipedia: Fractal www
Free encyclopedia article covering historical aspects and mathematical formulations. Fractal. Includes two and three dimensional illustration sets. Wikipedia: Fractal.
- Shows Fractal Brownian Archipelago www
Shows how brownian motion can model the shape of coastlines. Brownian Archipelago. Includes interactive demonstration and a collection of island set. Fractal Brownian Archipelago.
- Collection Mathematical Figures Using Mathematica www
Collection of sets and attractors. Figures Using Mathematica. Includes Mathematica source code, mathematical formulations and illustrations. Mathematical Figures Using Mathematica.
- Article Chaos, Fractals, and Arcadia www
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Fractals, and Arcadia. Includes examples, illustrations and references. Chaos, Fractals, and Arcadia.
- Foundation Fractal Foundation www
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Foundation. Includes mission statement, mathematical framework, gallery and contact. Fractal Foundation.
- Index IFS Attractors www
Index and definition of different attractors. Attractors. Includes images, plots and glossary. IFS Attractors.
- Explains The Modular Group and Fractals www
Explains the basics of fractals, Modular Group and Fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications. The Modular Group and Fractals.
- Interactive Fractal Map www
Interactive online Mandelbrot and Julia generator. Fractal Map.
- Article Newton Basins www
Article about the basins of attraction for the Newton's method for finding roots of equations and their resulting representation in the complex plane. Basins. Includes mathematical framework and examples. Newton Basins.
- Shows 3D Mountains www
Shows how to create fractal mountains, Mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations. 3D Mountains.
- Discusses Kleinian Groups Pictures www
Discusses the mathematical theory of Kleinian groups. Groups Pictures. Includes illustrations, examples, formalism and program source code. Kleinian Groups Pictures.
- Tutorial Fractals Unleashed www
Tutorial covering the different types of sets and attractors. Unleashed. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian] Fractals Unleashed.
- Scientific The Mandelbrot and Julia Sets Anatomy www
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Mandelbrot and Julia Sets Anatomy. Includes animated samples, articles and mathematical formulations. The Mandelbrot and Julia Sets Anatomy.
- Scientific Fractals and Multi Layer Coloring Algorithms www
Scientific paper of the University of the Basque Country, and Multi Layer Coloring Algorithms, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references. Fractals and Multi Layer Coloring Algorithms.
- Explains Quantum Jumps, EEQT and the Five Platonic Fractals www
Explains how quantum jumps generate new family of fractals on spherical canvas. Jumps, EEQT and the Five Platonic Fractals. Includes graphics in several formats, mathematical framework and bibliography. Quantum Jumps, EEQT and the Five Platonic Fractals.
- Easy Fractal Dimensions www
Easy to comprehend mathematical approach to understanding the significance of the applied study of fractals and attractors. Dimensions. Includes didactic examples and illustrations. Fractal Dimensions.
- Gallery Images From Chaos www
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, From Chaos, Spain. Images From Chaos.
- Weblog Homepage of Kristian Gustavsson www
Weblog about the mathematical background of different sets and attractors in the complex plane. Kristian Gustavsson. Includes downloadable generator and gallery. Homepage of Kristian Gustavsson.
- Focuses Technocosm www
Focuses on the visualization of three dimensional attractors. Technocosm. Includes formula derivations and image galleries. Technocosm.
- Explains Mathematics: Stilldreamer www
Explains the basics of Sierpinski systems and other sets. Stilldreamer. Includes interactive example programs with source code. Mathematics: Stilldreamer.
- Resource 3D Fractals Bicomplex Dynamics www
Resource on the bicomplex generalization of the Mandelbrot set. Fractals Bicomplex Dynamics. Includes scientific publications, illustrations, news and downloads. 3D Fractals Bicomplex Dynamics.
- Research Chaos at Maryland www
Research group at the University of Maryland. Maryland. Includes papers, gallery, database, abstracts, software, bibliography and contact. Chaos at Maryland.
- Covering The Chaos Hypertextbook www
Covering several aspects of the theory by topics, Chaos Hypertextbook, including nonlinear dynamics. Includes experiments for programmable calculators and definitions. The Chaos Hypertextbook.
- A The New Artificial Life (Alife) Database www
A searchable database of artificial life-related sites. New Artificial Life (Alife) Database. The New Artificial Life (Alife) Database.
- A Links on Complexity, Self-organization and Artificial Life www
A collection of annotated links. Links on Complexity, Self-organization and Artificial Life.
- A General Systems Theory of Everything www
A systems theory for chaos, Systems Theory of Everything, quantum mechanics and climate dynamics applicable to dynamical systems of all space-time scales. General Systems Theory of Everything.
- Maintained Bibliography on Nonlinear Dynamics and Chaos www
Maintained by Peter E. Nonlinear Dynamics and Chaos. Beckmann, Johannes Gutenberg Universität. Bibliography on Nonlinear Dynamics and Chaos.
- Art Sekino's Fractal Gallery www
Art from math professor Junpei Sekino, Fractal Gallery, blended with discussion of formula types and colouring methods. Sekino's Fractal Gallery.
- Ultra Mikko Vainiala's Fractal Gallery www
Ultra Fractal images in a textured, Vainiala's Fractal Gallery, geometric style. Mikko Vainiala's Fractal Gallery.
- Délocalisation Transformation chaotique d'un vecteur www
Délocalisation pseudo-aléatoire réversible des composantes d'un vecteur obtenue par un algorithme générant une suite chaotique et permettant la transformation inverse. chaotique d'un vecteur. Exemples Excel, applications et modélisation de stockage sur une structure en boucle. Transformation chaotique d'un vecteur.
- Proposes WebFractales www
Proposes des images provenant de différents auteurs, WebFractales, ainsi que des logiciels de création fractal. WebFractales.
- Offers Quintessential Sophistry www
Offers several Michael Sargent's QS-series DOS and Windows fractal generators. Quintessential Sophistry.
- Fast XaoS www
Fast portable realtime fractal zoomer. XaoS.
- Combined Mathematics Archives www
Combined archive and directory of math web sites, Archives, mailing lists, and teaching materials. Located at University of Tennessee. Mathematics Archives.
- Award Knot a Braid of Links www
Award and review service for math web sites, Braid of Links, offering a new selection each week. Knot a Braid of Links.
- Alexa: Chaos and Fractals Math
Alexa Directory Top Sites: Chaos and Fractals Math
- DMOZ: Chaos and Fractals Math
dmoz.org Directory: Chaos and Fractals Math