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Chaos and Fractals

Science > Math > Chaos and Fractals

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Chaos (42)
Fractal Art (136)
Software (67)

Related Categories:
Science > Math > Applications > Complex Systems (102)
Science > Math > Differential Equations > Dynamical Systems (75)

Web Pages

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

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.

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.

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]

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

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.

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

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.

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.

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.

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 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.

Fractal Geometry - http://classes.yale.edu/fractals/
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.

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

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.

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]

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.

IFS Attractors - http://www.meden.demon.co.uk/Fractals/fractals.html
Index and definition of different attractors. Includes images, plots and glossary.

Images From Chaos - http://www.cps.unizar.es/~jlsubias/
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.

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.

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

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.

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.

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

Mandelbrot, Benoit B. - http://www.math.yale.edu/mandelbrot/
Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.

Mathematical Figures Using Mathematica - http://mathforum.org/advanced/robertd/
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and illustrations.

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

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.

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.

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

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.

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

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.

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 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 Dynamics of Deterministic Chaos in Numerical Weather Prediction Models - http://www.geocities.com/CapeCanaveral/Lab/5833/
Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.

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.

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.

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.

Wikipedia: Fractals - http://en.wikipedia.org/wiki/Fractals
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.

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