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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.
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Newton Basins References in books and on the web Newton's method for finding solutions to equations leads to some fantastic images when it's applied to complex functions. You start with an initial guess for the solution which may be any number, and...Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism and program source code.
http://klein.math.okstate.edu/kleinian/
Educational resource from the Boston University. Includes mathematical framework and formulation, animated illustrations and calculation spreadsheets.
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Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there...Collection of sets, attractors and related material for free distribution. Includes large categorized index of software, information and links.
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Spanky Welcome This is a collection of fractals and fractal related material for free distribution on the net. Most of the software was gathered from various ftp sites on the internet and it is generally freeware or shareware. Please abide by the...Tutorial for beginners covering the Mandelbrot and Julia sets, as well as four-dimensional sets. Includes interactive generators and gallery.
http://www.geocities.com/fabioc
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and publications.
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An Introduction to Lacunarity Lacunarity is a counterpart to the fractal dimension that describes the texture of a fractal. It has to do with the size distribution of the holes. Roughly speaking, if a fractal has large gaps or holes, it has high lacunarity;...Glossary and terms directory. Includes mathematical formulations and illustrations of the most common sets.
http://www.mathjmendl.org/chaos/
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
http://www.efg2.com/Lab/FractalsAndChaos
Explains the basics, adressing definitions, dimensions and uses. Includes gallery and resources.
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What are fractals? Fractals have come up as an important question two times before the invention of computers. The first time was when British map makers discovered the problem with measuring the length of Britain's coast. On a zoomed out map, the coastline...Interactive online Mandelbrot and Julia generator.
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Fractal Map No new tiles will be rendered while I sort out a platform switch. Cached tiles still work fine. Fractal Map Click to zoom in Zoom out Tiles in que: 78965 Iterations: 75 150 300 Color map: B/W Royal Volcano Blues...Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
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Mandelbrot and Julia Set Explorer There is detailed help available for using this form. For more information on complex numbers, see Dave's Short Course on Complex Numbers. Also, check out the Applet to explore the Mandelbrot set. Mandelbrot Set:x in 1.0,2.0];y in 1.5,1.5 Parameters Clicks...Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, illustrations, news and downloads.
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3D Fractals 3D Fractals...Index and definition of different attractors. Includes images, plots and glossary.
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IFS Attractors Pisot number with complex conjugates. 15th October 2002: added gallery of 3-element tiles associated with the 4th unit cubic Pisot number with complex conjugates. 14th May 2005: corrected sign error on page for 8rd unit cubic Pisot number with complex...Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.
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Climate Dynamics,Chaos and Quantum Mechanics Flows who are the visitors? View Page StatsSee who's visiting this page. Updated on 7 June 2005 Sign Guestbook View Guestbook Fractals: The beautiful complex patterns generated by simple iterative computations: Some examples A hierarchy of selfsimilar structures: The large...Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
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technocosm.org Math, Chaos, and Fractals Before contemplating chaos theory, I recommend having a cup of tea. In fact, I love green tea, and have many kinds. My favorite supplier for tea via internet is Adagio Teas. Head on over, and pick up some Dragonwell Green...Discusses how differently the iterations behave depending on which portions the coefficients are plucked from. Includes basics, concept, formulations and references.
http://www.cut-the-knot.com/blue/Mandel.html
Quotes and information on different types of sets and attractors. Includes image gallery, plots, mathematical formulation and articles.
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Fractals The contents of this web site are Copyright Paul Bourke or a third party contributer where indicated. You may print or save an electronic copy of parts of this web site for your own personal use. Permission must be sought...Short Article from Inside Science News Service describing the basics. Includes illustrations and links.
http://www.aip.org/isns/reports/2003/086.html
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Includes animated samples, articles and mathematical formulations.
http://www.ibiblio.org/e-notes/MSet/Contents.htm
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. Includes pictures, plots and mathematical formulations.
http://www.ibiblio.org/e-notes/3Dapp/Mount.htm
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, applets, programs, gallery and an art contest. [English, Russian, Ukrainian]
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Fractals Unleashed Team 26242 ENGLISH RUSSIAN UKRAINIAN TEXT ONLY KIDS ZONE ©1999 Fractals Unleashed Created by Team 26242 for ThinkQuest...Information on the modeling aspects of cloud forms and structures, and their implications for climate. Including descriptions of cloud types, movies, glossary and publications.
http://climate.gsfc.nasa.gov/~ca...FractalClouds/FractalClouds.html
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
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Below you will find an animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. For access to some of the mathematical software that generates some of the images contained herein, visit the...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.
http://classes.yale.edu/fractals/
Addresses the chaotic behavior of different attractors and their mathematical expressions. Includes plots, images and program source codes.
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CSE Fractals Explorer III A short trip in fractional dimensions [Strange Attractors|Fractional Dimensions|String Systems|Nature|Software] CSE, 2003-2004 Strange Attractors Chaos is an interesting behavior of systems that lies between the simplicity of stability or periodicity and the highest disorder of randomness. Such systems are unpredictable,...Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
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Fractal Wikipedia, the free encyclopedia A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be broken up in a radical way. Some of the best examples can be divided into parts, each of...Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
http://www.mi.sanu.ac.yu/vismath/javier1
Explains the mathematical basics of Julia and Mandelbrot sets. Addresses principles, and complex plane algorithms. [English, Italian]
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Introduction to Julia and Mandelbrot Fractal Set This page has been written to describe, but in a quite simple way, two of the fundamental families of fractals: the Julia and Mandelbrot sets. To read this document, it may be really useful to have a little knowledge on...Scientific article describing the mathematical background of the Sierpinski gasket. Includes formulation, models and references.
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Sierpinski Gasket The following is an attempt to acquaint the reader with a fractal object called the Sierpinski gasket. The gasket was originally described in two dimensions but represents a family of objects in other dimensions. This family of objects will be...Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
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Mathematics: Stilldreamer Articles which pertain mostly to mathematics, often with sample programs. Content from Mathematics, sorted by title: 1D Cellular Automaton One dimensional, or elementary, cellular automaton. Chaos Game Building Sierpinski’s triangle with the chaos game. Koch Island Fractal built from a...Explains the basics. Includes gallery and free software for exploring different sets and singularities.
http://homepage.ntlworld.com/daniel.freeland/
Images generated by different commercial applications. Includes FAQs and tutorial.
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BitShifters SoftSource Factals The numbers next to each image indicate the coordinates of the location of the picture the lower left corner in parentheses followed by the length of a side. If you pass these three numbers to DRAWING Librarian Professional's MAND script...Gallery and program with source. Includes animated three-dimensional sets and attractors.
http://www.geocities.com/mischa_griesman/index.html
Applet to explore the Mandelbrot set in real time.
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Realtime Mandelbrot Fractal Generation CGI This site is a program that allows everyone to explore the fashinating word of Fractals. Fractal is a term coined by Benoit Mandelbrot to refer to a structure bearing statistically similar details over a wide range of scales.Click on the...Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
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Mandelbrot set, Poincare section Lorenz attractor as orbitals Representing attractors by orbitals clik here to learn more) Numerical experiments, Mathematical models, Fractals Mandelbrot set Mandelbrot set Zoom of Mand. set Zoom of Mand. set Zoom of Mand. set Zoom of Mand. set Zoom of Mand. set Zoom of...Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot sets. Includes basics, mathematical formulations and descriptions.
http://www.javaspider.com/jfract
Weblog about the mathematical background of different sets and attractors in the complex plane. Includes downloadable generator and gallery.
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Homepage of Kristian Gustavsson Statistics over the visit of br.count+1 persons D bk 2.gif 20,5 A This visit bi y Page y Visits y Average visited time y Program file y Downloads y Outgoing link y Followed link h=0;a=0;for(e=0;e F top.ap(0 h 1 bd[h],be[h...Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references.
http://www.ecometry.biz/
Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
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Fractal Brownian Islands exhibit Fractional Brownian Motion fractals and coastline Some surprisingly simple processes can give rise to shapes that resemble natural features, such as coastlines. Brownian motion is a simple concept. A particle making random jumps traces out a trail which, if one steps back, has structure on all...Discussion about the original mathematical concepts and the applications of scales and dimensions. Includes formalisms, examples and illustrations.
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Fractals and scale This preprint may be copied and used provided that this notice and the authorship details remain attached. FRACTALS AND SCALE David G. Green, Environmental and Information Sciences, Charles Sturt University Introduction How long is the coast-line of Great Britain? At...Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
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Quantum Jumps, EEQT and the Five Platonic Fractals It is shown that symmetric configurations of fuzzy spin direction detectors generate, through quantum jumps, IFS fractals on the sphere OpenSource Java project accompanies the paper. 1. Introduction 2. EEQT Quantum Fractals 1. Geometry 2. The algorithm 1. The Hilbert...Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and references.
http://www.sciencedirect.com/sci...92c370a59ff53edd249c27a91b0ed72e
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski question mark. Includes publications.
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The Modular Group and Fractals An exposition of the relationship between Fractals, the Riemann Zeta, the Modular Group Gamma, the Farey Fractions and the Minkowski Question Mark. Linas Mathematical Art Gallery has been running for fifteen or twenty years while being silent about the underlying...Research group at the INRIA national research center, France. Includes research details, publications and software.
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Welcome to the COMPLEX team This page is currently under construction. Please forgive us for any inconsistency while we set up the new COMPLEX site Welcome to the COMPLEX team Evolution, Fractals and complex interactions The COMPLEX team follows up on the FRACTALES project. The...