 Fractals on the Web  Chaffey High School
An extensive searchable collection of sites dealing with fractals, in the following categories: programs, galleries, fractal music, fractal compression, fractal theory, and fractal newsgroups.
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 Fractals  ThinkQuest 1997
Information (definition, applications, fractal mountains), data sets (Mandelbrot and Julia), and animations with source code.
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 Fractals Unleashed  Aronov, Radomyselskiy, Ming; ThinkQuest 1999
A tutorial on fractals, including types of fractals, famous fractals, applications, programs and downloads, links, references, and a Kids Zone. With Java applets and CGI programs, a gallery, and a fractal art contest. In English, Russian, and Ukrainian.
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 Fractals with Mathematica  Robert M. Dickau; Math Forum
Some simple fractal images and Mathematica code for Cantor dust; Julia sets; Mandelbrot (and related) sets; Randelbrot set; Menger sponge; Sierpinski tetrahedron; Newton's method; variation on Newton's method; Sierpinski carpet; 2D and 3D Lsystems (also
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 Fractalus Entrance  Damien Jones et al.
Galleries: a site designed to display the best in fractal art.
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 Fractal Video Art Gallery  Eric Shol
Fractals generated using Fractint, free for copying and distribution on a noncommercial basis. Recent Acquisitions; Room Two (Bluedive I & II  image/animation); Room Three (Zoom  image/animation); Room Four (Twist); Room Five (Rose, Dome, Joy).
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 Fractal Wallpaper  Ian Anderson Design
A gallery of fractal wallpaper images.
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 FractaSketch  Peter Van Roy
FractaSketch is a drawing tool for Macintosh based on linear fractal geometry. The program allows, by direct manipulation (no equations), full control over the shape, complexity, and colorization of the fractal. Downloadable freeware, flyer, user manual,
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 FractEd: The FractEd Information Pages  Douglas Martin; EALSoft
FractED is an introductory fractal tutorial for high school and college students that discusses elements of fractal geometry and chaos theory. It includes interactive programs which demonstrate the techniques of fractal generation and provides links
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 FractImage  David Rose
Preview jigsaw puzzle images that exhibit selfsimilarity, and purchase the puzzles online. Visit the fractal gallery; read about fractals and FractImage; and download fractal wallpaper for your desktop.
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 The Fractint Wishlist  The Stone Soup Group
A forum for collecting ideas about what needs to be done to keep Fractint in its place as "(probably) the best fractal generator," with a link to download the source code and the executable, directions for joining the fractint mailing list, and archived
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 The Fractory: An Interactive Tool for Creating and Exploring Fractals  Green, Kulesza, Bergstresser; ThinkQuest 1996
Learn about fractals  what they are and how to design them  and discover more on your own. Fractals show an order in seemingly random things, and give us tools with which we can predict the weather, render natural looking objects, and help understand
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 FracZoom Explorer, FracZoom Navigator  SoftOrange Interactive
FracZoom Explorer is a fractal program that lets you explore a 3D world to find a lost damsel, then examine fractals for yourself. FracZoom Navigator allows you to create films of your fractal zooms at very fast rates, plus up to 24bit fractal images.
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 Frattali  Isawi
Disegni a mano libera elaborati con Autocad e Photoshop per creare immagini di tipo frattali.
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 From Chaos: Beauty  Kitara
Fractal galleries created using UltraFractal.
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 The FUNKtion  Appreciating Math through Art  ThinkQuest 1996
How to do really hard graphic stuff. Tilings, Fractals, Sierpinski Gaskets, animations, pictures, links. Math "crash courses" on Complex Numbers; Magnitude and the Pythagorean Theorum; Functions; and 3D.
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 Fun with Fractals and the Platonic Solids  Gayla Chandler
A site rich with photographs and drawings of Sierpinski triangles and Platonic solids, made by hand, to inspire children of all ages to construct their own mathematical structures. See photographs, many set in marine environments, of dodecahedra, hexahedra
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 Fun with Fractals  Keith Gabryelski
Click in the fractal image to select the area of the fractal you would like to examine; select a location and style for the fractal image by modifing the values in the form.
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 Gallery of Fractal Images  Paul Bourke
An experiment in a creating a virtual gallery based upon a minimal WWW environment that doesn't require Java, VRML, or server features such as a rendering engine or CGI programs. Upon entering the gallery, move forward by clicking near the upper center
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 Gallery of Mathematical Images  Dept. of Mathematical Sciences, Loughborough University, UK
The Mandelbrot Set (frames from an animation); Quaternionic Fractals (an extension of the complex numbers  Mandelbrot and Julia sets); Hyperspace (4dimensional structures projected into 3dimensional space); Molecular Dynamics (images from simulations,
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 Gamelan  The Official Java Directory  EarthWeb, Inc.
Gamelan's primary mission is to serve as a central registry and directory of Java resources. Much like Yahoo!, Gamelan collects links to resources stored on other sites across the Web. However, unlike Yahoo!, Gamelan's mission is specific  Gamelan collects
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 General Mathematics, AM (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on basic mathematics, including biographical information about mathematicians, from the abacus to Gaspard Monge.
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 Genuine Fractals Software  Altamira Group, Inc.
Genuine Fractals™ plugins for Adobe Photoshop and compatible image editing programs enable highquality digital photo enlargements and artwork at various sizes and resolutions from the same low to mediumresolution originals. Stepbystep instructions
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 The Geometer's Sketchpad  Key Curriculum Press
Geometry software for Euclidean, coordinate, transformational, analytic, and fractal geometry, recommended for students from grade 5 through college. Developed for geometry, students now also use Sketchpad's flexibility and reach to explore algebra, trigonometry,
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 The Geometer's Sketchpad Resource Center  Key Curriculum Press
Search collection of Sketchpad Classroom Activities for download or purchase, browse the Advanced Sketch Gallery, access Technical Support, explore some online JavaSketches created with Sketchpad, and find links to others' sketches and related resources.
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 GeomeTree  John Miller
Explore fractals with this treedrawing app for iPod, iPhone, and iPad. Choose the number of branches, angle between branches, and the common ratio of the levels in the tree. See, in particular, the exercises and open questions on GeomeTree for the
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 Geometria Fractal Geometry  Jaume Domenech
Fractal geometry basics, including links to biographies and software, plus a collection of articles, mostly in Spanish, some in English.
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 Geometric Models (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material describing physical objects corresponding to geometric constructions (and methods for creating such objects), particularly polytopes.
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 Geometry  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
More than 95 games or puzzles having to do with geometry, chaos, fractals, and topology with extensive discussions and solutions. Most require a browser capable of displaying JavaScript or Java.
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 The Geometry Junkyard  David Eppstein, Theory Group, ICS, Univ. of California at Irvine
A collection of usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry  some serious and much also entertaining. Junk sorted into piles (Topics):
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 Geometry of SelfContacting Binary Fractal Trees  Michael Frame; Union College, Schenectady, NY
Animations illustrating the constructions of binary fractal trees, with branch scaling chosen so some points of the left and right branches intersect, but only at the branch tips. The animations show how the geometry of the tree, and of the branch tips,
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 Geometry Out of Africa  Ivars Peterson (MathTrek)
Two recent books that introduce African geometry. Geometry from Africa, by Paulus Gerdes, shows how one can discover or derive the Pythagorean theorem from African designs, explores the role of symmetry (with suggestions for home and classroom crafts
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 The Geometry Section (Zona Land)  Edward A. Zobel
Fractals (fractal tree, VRML fractal monoliths), common shapes (circle, rhombus, trapezoid), areas and volume (box, cylinder, box with cylindrical hole), coordinate geometry (VRML (x, y, z) Axes and Planes Worlds), and points, lines, and planes (symbol
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 Giant Fractal Pecan Pie
The creators of this tutorial explain that they wanted to figure out how to design a large pie that still strikes a balance between the filling (area) and the crust (perimeter). View the steps they took to construct a very enormous pecan pie in the shape
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 GirlTECH  Cynthia Lanius; Center for Research on Parallel Computation (CRPC)
GirlTECH was a teacher training and student council program that encouraged young women to pursue careers in mathematics and science, offering intensive technology training to explore innovative teaching strategies for gender equity in the classroom through
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 Giuseppe Zito Pictures
A gallery of fractal images generated by chance from a database of around 50,000 planar dynamical systems by Zito's program, Ufattr, with some commentary.
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 Graphical Iteration  Mark Scheuern
This applet demonstrates graphical iteration, using the quadratic iterator xn+1 = fa(xn) , fa(x) = ax(1x), 0<=a<=4 and iterating for twenty steps. Try different values of x0 and a. Note that some values will produce a stable state and others result
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 Great Math Programs  Xah Lee
A listing about 40 excellent recreational math programs for Macintosh that do: polyhedra and Rubic cubes, curves and surfaces, fractals and Lsystems, tilings and symmetry, game of hex and game of life, chess and fiveinarow, peg solitare and polyominos,
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 Groupe Fractales (INRIA)  Benoît Leblanc and Frédéric Raynal
A group of researchers studying the application of fractal techniques to complex systems, especially signal processing. Introduction to the theoretical aspects of fractal analysis; genetic algorithms; introduction to timescale analysis, in French; applications,
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 Guide to the Mandelbrot Set  Paul Derbyshire
Explore the Mandelbrot set with a fractaldrawing program: images of wellknown portions of the set, their locations, comments on miniature images of the Mandelbrot set that arise from different formulas, and Julia sets.
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 The Hartman Fractal Hypotenuse Hypothesis  John "Dobe Doinat" Hartman
Proving the maximum fractal dimension of an infinitely squiggly staircase replacing a normal hypotenuse in a square or rectangle.
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 Henry Segerman's webpages  Henry Segerman
Mathematical and typographical art "of various kinds and dimensions." See, in particular, Segerman's 3D printed sculpture, book covers and posters, diamond Go, ambigrams, autologlyphs, autological words, Escher's Printgallery, and mathart tshirts available
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 Homepage & Papers  Dr. Peter Singer
Dr. Singer is associated with the MeVisCenter for Diagnostic Systems and Medical Visualization at the Univ. of Bremen, Germany. His interests and publications include: mathematics of finance; Fourier analysis; fractals; medical image processing; stochastic
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 Home Page  Tony Roberts; Dept. of Mathematics and Computing, University of Southern Queensland, Australia
Links to recent research papers (titles, abstracts and electronic copies of recent research documents); software (computer routines to do various taks such as estimate fractal dimensions, solve DAEs, etc,, mainly in Matlab); teaching and other material
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 Hopalong Image Generator  David Imai
This Java applet generates a unique fractal image before your eyes, based
on Martin's Hopalong algorithm. This mapping was described in an article by
A.K. Dewdney in the September 1986 issue of Scientific American magazine.
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 The house of Mathematics software  Akihiro Akitsu
Math '98 for Windows, free software to download. Topics include the Mandelbrot set; Complex numbers; Dragon curve; Tree curve; Koch curve; Peano curve; Pascal's triangle; and the Sierpinski gasket. In English and Japanese.
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 HoweTwo Software  Leslie Howe
Over 70 interactive Windows programs that target specific concepts in secondary mathematics, written by a classroom teacher/programmer. Many free sample downloads are available. The programs are written in Microsoft Visual Basic. Site includes HTML generators,
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 IFS Construction Kit  Larry Riddle
IFS Construction Kit is Windowsbased software that can be used to design and draw fractals based on iterated function systems. The program consists of three main windows. The IFS Window is where you can see and edit the code for the transformations that
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 IFS: Fractal Image Compression  Pulcini, Verrando, Meloni Rossi
Download IFS Application Framework, a freeware educational program for fractal image coding. Note: It needs 486DX2/66, 8MB RAM, Windows 3.1 with a 11MB swapfile and a 32000 SVGA driver (at least). Download IFSDOC, an introduction to IFS and IFSAF (in
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 IFS (Iterated Function Systems) for 2D and 3D Visualization  Craig M. Wittenbrink
Using fractal interpolation to graphically represent two and threedimensional scalar data: download article in PDF or PostScript format, and view related images.
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