41. Mandelbrot Explorer to see it. More fractals can be found at the mandelbrot Exhibition,part of the Virtual Museum of Computing Panagiotis Christias http://www.ntua.gr/mandel/mandel.html

Selected images created by *you* using Mandelbrot Explorer are available at the Mandelbrot Explorer Gallery Page. Zoom Factor : ZoomIn x16 ZoomIn x8 ZoomIn x4 ZoomIn x2 None ZoomOut x2 ZoomOut x4 ZoomOut x8 ZoomOut x16 Set the Zoom Factor as desired and then click at the point you like to zoom in (or out) in the image area above. Drawing Area : X Min : X Max : Y Min : Y Max : Commands : Alternatively, you can set the desired Drawing Area and press the ``Draw New Area'' button to see it. More Fractals can be found at the Mandelbrot Exhibition , part of the Virtual Museum of Computing Panagiotis Christias NTUA/SoftLab Home Page

42. Fractal Explorer Program that can generate polynomial and iteration sets as mandelbrot, Julia, Newton like fractals and orbital fractals. http://skyscraper.fortunecity.com/binary/34/

web hosting domain names email addresses related sites Dear friends, Fractal Explorer site has been moved to the new location: http://www.angelfire.com/art/fe/index.html Please, update your bookmarks. Now you will redirected to the new Fractal Explorer Homepage ! web hosting domain names Powered by Ampira

43. Fractal Explorer: Mandelbrot And Julia Sets (by Fabio Cesari) A fractal tutorial for beginners. Covers mandelbrot and Julia sets, as well as 4D fractals. Also features an interactive fractal generator. http://www.geocities.com/fabioc

Keywords: fractals, mandelbrot set, fractal, julia sets, quaternion, quaternion julia sets, Mandelbrot, Julia Your browser doesn't support frames. This site is best viewed with , or an equivalent browser that supports JavaScript and frames You can always access this no-frames version of this site. If you have troubles accessing it, please let me know Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms, how the Mandelbrot set and Julia sets are generated. This document provides an informal introduction to these subjects, and is only intended to be a starting point to learn more about fractals and fractal geometry. You can contribute to the future development of this site by filling out the feedback form Comments and suggestions are very appreciated. Have fun! About complex numbers Mandelbrot set Julia sets Images gallery ... Quaternion Julia sets images gallery" Other pages: About the author Links Feedback form Sign my guestbook ... View my guestbook This page hosted by Get your own Free Home Page

44. Kosmoi: Fractals The theory of fractals developed from Benoit mandelbrot's study ofcomplexity and chaos. mandelbrot, who is often called the father http://kosmoi.com/Science/Mathematics/Fractals/

Encyclo Gallery of Fractals Mathematics Science ... Mandelbrot applet Fractals Nature Agriculture Animals Biology ... Fractals, Googols and Other Mathematical Tales Theoni Pappas The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation Gary William Flake Fractal Geometry of Nature Benoit B. Mandelbrot Indra's Pearls: The Vision of Felix Klein David Mumford, Caroline Series, David Wright Fractals and Scaling in Finance Benoit B. Mandelbrot Opening Minds: A Journey of Extraordinary Encounters, Crop Circles, and Resonance Simeon Hein, Ira Liss Trading Chaos : Applying Expert Techniques to Maximize Your Profits Bill Williams The Fractal Murders Mark Cohen Chaos and Fractals: New Frontiers of Science Heinz-Otto Peitgen, Dietmar Saupe, H. Jurgens, L. Yunker Introducing Fractal Geometry Nigel Lesmoir-Gordon, Will Rood, Ralph Edney, Richard Appignanesi, William B. Rood In mathematics , a class of complex geometric shapes that commonly exhibit the property of self-similarity, such that a small portion of it can be viewed as a reduced scale replica of the whole. The term fractal is derived from the Latin word fractus ("fragmented," or "broken"). Fractals are distinct from the simple figures of classical, or

45. The Math Forum: Mathematical Figures By Robert M. Dickau Robert M. Dickau's page. The fractals and Chaos section has figures of attractors, Lsystems in 2 and 3 dimensions, Sierpinski gaskets, bifurcation, and Julia and mandelbrot sets. Includes Mathematica code. http://mathforum.org/advanced/robertd/index.html

Mathematical Figures Using Mathematica by Robert M. Dickau Back to Math by Subject Fractals and chaos Cantor dust (about 5K) Julia sets Another Julia set Mandelbrot (and similar) sets Randelbrot set ... Lozi attractor Combinatorial figures Catalan number diagrams (around 70K, and worth every bit) Permutation diagrams Derangements 2D shortest-path diagrams 2D shortest-path diagrams, text version ... Search http://mathforum.org/

46. Mandelbrot Exhibition This exhibition provides some hyperlinks to material on mandelbrot sets, and related fractals. Explore the mandelbrot set interactively using an "active map" image. Less colourful and with fewer options, but still good. http://www.comlab.ox.ac.uk/archive/other/museums/computing/mandelbrot.html

Virtual Museum of Computing Mandelbrot Exhibition Please contact J.P.Bowen@reading.ac.uk if you wish to submit further Mandelbrot URL s for possible inclusion. This exhibition provides some hyperlinks to material on Mandelbrot sets, and related fractals. For historical background, see short biographies of Benoit Mandelbrot (largely responsible for the present interest in Fractal Geometry) and Gaston Julia (of Julia set fame) in the MacTutor History of Mathematics archive An introduction to Julia and Mandelbrot Sets is available. A large colourful Mandelbrot set image is available locally. Many beautiful Mandelbrot pictures and other fractal pictures and animations are available from France. Try the recommended Mandelbrot and Julia Set Explorer , an interactive and colourful utility using a form with plenty of options and an "active map" image. See also a generator using forms, an index of images . From Clark University, USA. Explore the Mandelbrot set interactively using an "active map" image. Less colourful and with fewer options, but still good. Especially recommended for European visitors. See also the Mandelbrot Gallery of Mandelbrot set images selected by visitors. Provided at TU Delft, The Netherlands.

47. The Fractal Microscope blue. But we can appreciate the beauty of the fractals encompassed inthe mandelbrot set without the specific mathematics behind it. http://archive.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html

The Fractal Microscope A Distributed Computing Approach to Mathematics in Education The Fractal Microscope is an interactive tool designed by the Education Group at the National Center for Supercomputing Applications (NCSA) for exploring the Mandelbrot set and other fractal patterns. By combining supercomputing and networks with the simple interface of a Macintosh or X-Windows workstation, students and teachers from all grade levels can engage in discovery-based exploration. The program is designed to run in conjunction with NCSA imaging tools such as DataScope and Collage. With this program students can enjoy the art of mathematics as they master the science of mathematics . This focus can help one address a wide variety of topics in the K-12 curriculum including scientific notation, coordinate systems and graphing, number systems, convergence, divergence, and self-similarity. Why Fractals? Many people are immediately drawn to the bizarrely beautiful images known as fractals . Extending beyond the typical perception of mathematics as a body of sterile formulas, fractal geometry mixes art with mathematics to demonstrate that equations are more than just a collection of numbers. With fractal geometry we can visually model much of what we witness in nature, the most recognized being coastlines and mountains. Fractals are used to model soil erosion and to analyze seismic patterns as well. But beyond potential applications for describing complex natural patterns, with their visual beauty fractals can help alter students' beliefs that mathematics is dry and inaccessible and may help to motivate mathematical discovery in the classroom.

48. Fractalized! Java animations of different fractals, including the mandelbrot and Julia sets. http://www-unix.oit.umass.edu/~dtillber/

Fractalized! DLA Builder DLA Mandelbrot/Julia Interactive Small Medium Large Very Large Animations Mandelbrot Zoom Julia Zoom Another Julia Zoom Home var test=0; document.write("<");document.write("! "); document.write(" ");document.write(">"); I'm currently a Sophomore Physics major at the University of Massachussetts at Amherst. The mainstay of this website is currently the Mandelbrot and Julia applets which you can find in the navigation bar to the left. Hopefully, I will find some time in the future to enhance the DLA applet I built a long time ago. Thanks for visiting! Join the search for ET. Vistors since September 4, 2001: Dan Tillberg

49. Don Archer Digital Art Traditional fractals, music, fractals combined with verse. Photo of Benoit mandelbrot taken April 6, 2001. http://www.donarcher.com/

Wednesday, 4/9/2003 , 12:23:16 PM (EST), Brooklyn and Prattsville, NY Updated April 4, 2003 This site is an exercise in love, vanity and art. It includes my current images, vintage fractals, animations, fractal music, ceramic tiles, digital photographs, digital postcards, and more... There are 2 viewers online now. Enjoy! There's nothing for sale here. Thanks for visiting! YEAR 2003 FRACTALS Gallery April 2003 Gallery March 2003 ... January 2003 YEAR 2002 FRACTALS Gallery December 2002 Gallery November 2002 ... January 2002 YEAR 2001 FRACTALS Gallery December 2001 Gallery November 2001 ... ANIMATIONS Don Archer, director CREDITS Online ABS gallery 2001-2003 hails Don Archer as "fractal guru" and publishes comprehensive exhibit of his art. Print art included in the collection of Ball State University Art Museum, Muncie, IN. Some 180 fractals included in a CD-ROM, Fractal Frenzy II, Postcards from the Edge of Space, published 1995 by Walnut Creek. Images included in Wirehead's CD-ROM, Virtual Media Gallery by Quantum Access, 1995. Several one-man and group shows, NYC and internationally, 1994-2003.

50. Mandelbrot Pictures More fractals can be found at the mandelbrot Exhibition, part of the Virtual Museum of Computing http://graffiti.u-bordeaux.fr/MAPBX/roussel/fractals/mandel.html

Mandelbrot pictures Since they're lots of this kind of images, i've decided to put them in 14 directories. Their size (width x height) is 1140 x 940 pixels. They have been computed and colored using mandtool, an interactive program running under SunView at the University of Karlsruhe, Department of Computer Science, Operating Systems Research Group, D-7500 Karlsruhe / Germany E-mail address of their author, Uwe Krueger: ukrueger@ira.uka.de Make a journey into the depth of the mandelbrot set at the The Beauty of Chaos page (set up by Uwe Krueger) Mandelbrot (01-10) Mandelbrot (11-20) Mandelbrot (21-30) Mandelbrot (31-40) ... Mandelbrot (131-138) Previous page

51. Members.home.net/zzsolt/mandelbrot/mandel.html Similar pages Fractal Explorer mandelbrot and Julia sets (by Fabio Cesari)Keywords fractals, mandelbrot set, fractal, julia sets, quaternion, quaternionjulia sets, mandelbrot, Julia Your browser doesn't support frames. http://members.home.net/zzsolt/mandelbrot/mandel.html

52. Welcome To The Fractal EXtreme Web Site Win32 shareware program for exploration of the mandelbrot set and other fractals. http://www.cygnus-software.com/

Fractal eXtreme News: February 2002 a bug fix version of Fractal eXtreme was released. November 2001 a brand new version of Fractal eXtreme was released. This new version has many new features, including antialiased fractals and zoom movies, and an improved way of purchasing Fractal eXtreme January 1, 2001 Improved zoom movie player now has OpenGL support for vastly improved animation quality and much higher frame rates. Download the new zoom movie player here or download all of Fractal eXtreme here Sep 11, 1999 Improved zoom movie player now has colour cycling and .avi frame rate specification. Download the new zoom movie player here or download all of Fractal eXtreme here March 19, 1998 Improved fractal plugins for Fractal eXtreme are released, for faster exploration of the Mandelbrot set and other fractals. January 29, 1998 Fractal eXtreme Zoom Movie Plug-in 1.11 is released, allowing the playing of unique animated zooms into fractals on web pages. Now with bilinear scaling. September 30, 1997

53. Mandelbrot Biography of Benoit mandelbrot (19240BC) Benoit mandelbrot was largely responsible for the present interest in fractal geometry. He showed how fractals can http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html

54. Ted'z Turn Mandelbrot, Fractals, And Chaos! II. fractals, Chaos, and the Fourth dimension. C. Used computers to calculate z z 2 + c (mandelbrot Set) GREATEST discovery in 20th century mathematics? http://www.geocities.com/CollegePark/Dorm/6179/mandel.html

55. Benoit Mandelbrot, Fractals And Astronomy (Part 1) Benoit mandelbrot, fractals and Astronomy (Part 1). by Dave SnyderPrinted in Reflections November, 1998. fractals are mathematical http://www.umich.edu/~lowbrows/reflections/1998/dsnyder.3.html

Benoit Mandelbrot, Fractals and Astronomy (Part 1) by Dave Snyder Printed in Reflections: November, 1998. Fractals are mathematical objects with strange properties. They have been known for many years, but had been relegated to an obscure corner of mathematics. In the beginning fractals were curiosities, very few people thought they had any real applications (Ludwig Boltzmann and Jean Perrin were among the exceptions). All that changed when Benoit Mandelbrot began his career. Mandelbrot discovered that complex phenomenon in a variety of sciences, including astronomy, could be understood in terms of fractals. Fractal geometry along with several other sciences were motivated by examining human senses. For example, the sense of sight led to the study of electromagnetic radiation and the sense of hearing led to the study of acoustics. However until recently, there had never been any science of roughness. Starting in the late 1800's and into the early 1900's, a number of strange mathematical objects were developed by Georg Cantor, Helge von Koch, David Hilbert, Giuseppe Peano, Carl Ludwig Sierpinski and others. They were called "monster curves" as if they were unruly beasts who needed to be locked up before they did some real damage (the word fractal would come later). Unlike other objects like circles and sine curves which are smooth, these objects are rough and this roughness persists even as the object is magnified. As the object is magnified more and more, the same amount of roughness is present. They are created using a simple process known as aggregate replacement. By repeating this process indefinitely images of these objects form, showing that a complex object can result from a simple procedure.

56. Mandelbrot Benoit mandelbrot was largely responsible for the present interest in fractalgeometry. He showed how fractals can occur in many different places in both http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html

57. Background Information About Mandelbrot's Fractals How are these nice pictures arising altogether? The whole calculationis based on the behaviour of recursive formulas with complex http://www.hofen.ch/~andreas/Englisch/Fraktalgalerie/Hintergrundinformation.html

How are these nice pictures arising altogether? The whole calculation is based on the behaviour of recursive formulas with complex numbers (numbers in the form a + bj where j=sqrt(-1) i.e. defined square root of -1). Similar the number straight line of real numbers (our normal, ordinary numbers like 1, 2, 3, 4.766, 3.1415926... etc.), all complex numbers form a plane, the Gauss's number plane called from the famous mathematician Carl-Friederich Gauss (1777-1855). Each one of these picture are resulted from the simple formula where z(0) (start value) is the picture constant, c the point of the plane. The number of iterations will counted until the condition depth of computation xmax [e.g. 1000] to avoid an endless loop during the computing process). This procedure will be taken on each point (screen pixel on the computer), so they form these pictures at the finish of computation. This chaotic behaviour was already discovered from the French mathematician Gaston Julia but his knowledge's found only a further interest since the age of graphic computers. Go back to the first picture

58. Fractal Journeys - Explorations Into The Mandelbrot Set This page is devoted to the beauty of the mandelbrot set. Three New Journeys!Sea Life, Pinwheels, Garlands. Spring Flowers, Night Sky, Flaming fractals. http://www.deepleaf.com/fractal/

Fractal Journeys This page is devoted to the beauty of the Mandelbrot set. Three New Journeys! Sea Life Pinwheels Garlands Spring Flowers Night Sky Flaming Fractals Blue Leaves Silk Ribbon Chinese Plates Click on a thumbnail to see its series. Each of the icons above leads to a series of sixteen images that explore a single area of the Mandelbrot set. The images in these sets are arranged in order from the most superficial to the deepest (although I have sometimes gone back up to an earlier image to take a look at a different part of it and then back down from there). They are accompanied by a key that will allow you to see clearly how each image comes from a detail of the previous image. Click on any small image in a series to bring up a 640x480 version. There's also a non-technical explanation of where these images come from and what they mean. And if you'd like to see what the Mandelbrot set looks like whole, click here. This is how Conrad Aiken and Wallace Stevens look at chaos.

59. Mandelbrot Pictures mandelbrot pictures. Since they're lots of this kind of images, i've decided toput them in 14 directories. Their size (width x height) is 1140 x 940 pixels. http://graffiti.cribx1.u-bordeaux.fr/MAPBX/roussel/fractals/mandel.html

Mandelbrot pictures Since they're lots of this kind of images, i've decided to put them in 14 directories. Their size (width x height) is 1140 x 940 pixels. They have been computed and colored using mandtool, an interactive program running under SunView at the University of Karlsruhe, Department of Computer Science, Operating Systems Research Group, D-7500 Karlsruhe / Germany E-mail address of their author, Uwe Krueger: ukrueger@ira.uka.de Make a journey into the depth of the mandelbrot set at the The Beauty of Chaos page (set up by Uwe Krueger) Mandelbrot (01-10) Mandelbrot (11-20) Mandelbrot (21-30) Mandelbrot (31-40) ... Mandelbrot (131-138) Previous page

60. Mathematics Archives - Topics In Mathematics - Fractals KEYWORDS mandelbrot Set, Quaternionic fractals, Iterated Function Systems, SelfsimilarStructures, Lyapunov Exponents, Period Doubling, Reaction-Diffusion; http://archives.math.utk.edu/topics/fractals.html

Topics in Mathematics Fractals Chaos, Fractals, and Arcadia ADD. KEYWORDS: The Chaos Game, The Sierpinski Hexagon, Iterated Function Systems Chaos in the Classroom, Boston University ADD. KEYWORDS: The Chaos Game, Self-similarity, Fractal Dimension, Iterated Function Systems Clifford A. Pickover's Homepage ADD. KEYWORDS: Cellular Automata, Carotid-Kundalini Functions, Books, Puzzles, JAVA Geometry Explorer The Dance of Chance ADD. KEYWORDS: Random Processes, Branching Structures, Patterns in Nature, Student Activities, Laboratory Experiments, Visualization, Software, Fractal Dimension, Fractal Coastlines Diffusion-limited Aggregation Exploring Fractals ADD. KEYWORDS: Lesson Plan, Tutorial, Bibliography Fantastic Fractals ADD. KEYWORDS: Tutorials, Gallery, Fractal Music, Bibliography, Software, Newsgroups Fract-ED ADD. KEYWORDS: Iteration, Attractor, Software, Tutorial, Bifurcation, Self-similarity, Strange attractor Fractal Clouds The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

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