Gourt > Science > Math > Chaos and Fractals (7)
The word fractal has two related meanings. In colloquial usage, it denotes a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification and is therefore often referred to as "infinitely complex." In mathematics a fractal is a geometric object that satisfies a specific technical condition, namely having a Hausdorff dimension greater than its topological dimension. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured."
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Complex Systems :: Applications
Dynamical Systems :: Differential Equations
@yaserhelmy I have read 2 of the seven (chaos and fractals)...not the one on misbehavior of markets...would like to :-)
CreatvEmergence (Michelle James) Wed, 16 Dec 2009 15:00:26 -0000
@yaserhelmy I have read 2 of the seven (chaos and fractals)...not the one on misbehavior of markets...would like to :-)
RT @fractalharry: 7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays: Mandelbulb by Dan... ...
KathyLoh (Kathy Loh) Wed, 16 Dec 2009 05:30:36 -0000
RT @fractalharry: 7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays: Mandelbulb by Dan... ...
RT @fractalharry: 7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays: Mandelbulb by Dan... ...
CreatvEmergence (Michelle James) Wed, 16 Dec 2009 05:17:17 -0000
RT @fractalharry: 7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays: Mandelbulb by Dan... ...
Raise awareness for fractals, during the holiday season, offer books about fractals and chaos http://bit.ly/5cezVl (via @fractalharry)
complexified (Bruce Waltuck) Tue, 15 Dec 2009 22:35:37 -0000
Raise awareness for fractals, during the holiday season, offer books about fractals and chaos http://bit.ly/5cezVl (via @fractalharry)
7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays http://bit.ly/5cezVl
fractalharry (Harry Seldon) Mon, 14 Dec 2009 23:19:54 -0000
7 lifechanging books about fractals, chaos, nature, philosophy and even finance for the holidays http://bit.ly/5cezVl
Hates fractals, hates chaos theory, and hates don zwiers.... ok, I don't hate don. But I do hate math......
TheOnSpring (Charlie) Thu, 10 Dec 2009 19:44:20 -0000
Hates fractals, hates chaos theory, and hates don zwiers.... ok, I don't hate don. But I do hate math......
Fractal Geometry - 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.
Mandelbrot, Benoit B. - Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.
Meta Description: [ Official Biography site. Benoit B. Mandelbrot is the world's foremost impetus for the advancement of Fractal Geometry. Learn about his life and work. ]
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.
A Fractal Christmas - Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
Bitshifters - Images generated by different commercial applications. Includes FAQs and tutorial.
Meta Description: [ These images are of the Mandelbrot set, a fractal generated from a simple mathematical formula.
They were produced by DRAWING Librarian Professional (DP). ]
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Chaos and Fractals: A Short Trip in Fractional Dimensions - Addresses the chaotic behavior of different attractors and their mathematical expressions. Includes plots, images and program source codes.
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Chaos Theory and Fractals - Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets.
Chaos, Fractals, and Arcadia - Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
Dan Freeland - Explains the basics. Includes gallery and free software for exploring different sets and singularities.
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.
Meta Description: [ A fractal tutorial for beginners by Fabio Cesari ]
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.
Meta Description: [ The Fractal Foundation is a nonprofit organization whose mission
is to educate and inspire people about the joy of math, art, science and technology. ]
Fractal Map - Interactive online Mandelbrot and Julia generator.
Meta Description: [ Fractal Map - A fun and addictive online fractal viewer. No Java required ]
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 and Scale - Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
Fractals Unleashed - Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
Fractals, Chaos - Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles.
Homepage of Kristian Gustavsson - Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
Meta Description: [ Project about fractals and chaos. The fractal generator FracZoom. Project in genetic computation: A selfprogramming Nintendo player. ]
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.
Meta Description: [ Chaotic, Complex & Critical Systems. Numerical Experiments, Mathematical Models, Fractals ]
Introduction to Lacunarity - Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
Introduction: Chaos, Fractals And Attractors - Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
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.
Mandelbrot Fractals Generator - Applet to explore the Mandelbrot set in real time.
Mathematical Figures Using Mathematica - Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.
Meta Description: [ Fractals and combinatorics diagrams created using Mathematica. ]
Mathematics: Stilldreamer - Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
Meta Description: [ Articles which pertain mostly to mathematics, often with sample programs. ]
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.
Meta Description: [ Quantum Jumps, EEQT and the Five Platonic Fractals ]
Sierpinski Gasket - Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references.
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.
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The 3x+1 Fractal - Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references.
The Dynamical Systems and Technology Project - Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
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.
The Modular Group and Fractals - Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
Meta Description: [ An exposition of the relationship
between fractals, the Riemann Zeta,
the Modular Group Gamma and the Farey Fractions ]
The Spanky Fractal Database - Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
What are Fractals? - Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
Meta Description: [ Ahh, the beauty of non-interger self-similar dimensions. An explanation of fractals and some cool picts. ]
Wikipedia: Fractals - Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
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