21. Basics Of Julia & Mandelbrot With Code -- MN Karthik Julia and mandelbrot fractals. This page has 4 sections containing code for Mandelbrot in Java C and Julia in Java C. You http://www.metlin.org/pgms/gfrac.html

" ....I said Innovate, not imitate! " Home Graphics Programming Downloads ... About Julia and Mandelbrot Fractals realtime java fractals And oh, by the way the code is far from clean or being optimised. So please do mail me if you find any errors or have any interesting suggestions. You can contact me at mnkarthik@yahoo.com Mandelbrot (Java) Mandelbrot (C) Julia (Java) Julia (C) Whew! That's about it!!! Do not hesitate to mail me if you have any questions or comments or a cool idea(umm!!!!) to share. You can contact me at mnkarthik@yahoo.com mnkarthik@yahoo.com

22. MANDELBROT mandelbrot. Home Page. Links. Books. Info. Explanation. Map. Fractalus. MB fractals. Fractal Arts. Fractal Domains. Fractal Music Lab. FractalArt. MuSoft. Fractal Modeling Tools. Fractal Wisdom. Fantastic fractals http://www.mandelbrot.com/

MANDELBROT Home Page Links Books Info About-Us ... z' = a*F(z) + c A Study by Richard Dickerson of UCLA Mandelbrot.com Since 1996 Catrepreneur@Hotmail.com

23. Mandelbrot Set And Fractals mandelbrot. Water. Rockets. SIRDS. Weird. TrueType. Fonts. FS98. UFO. Recipes. Hamster. WebCam. Computer. Security. Public. Key. Site Map. Links. EMail. fractals fractals. fractals have always http://ourworld.compuserve.com/homepages/pagrosse/mandelb.htm

Index Mah Jong Mandelbrot Water Rockets SIRDS Weird ... E-Mail Fractals Fractals have always been interesting to people who like to explore but getting your hands on a program that will let you do that has always been a problem. The link at the bottom of this page allows you to download a copy of my mandelbrot program which is postcardware (you send me a post card to license it) Technical Mumbo Jumbo:- ) as well as a number of more esoteric fractals. Exploration is not limited to the x : i plane but extends to the y : z plane as well giving you Julia sets and Fatou Dusts reflecting the earlier work of the mathematicians Gaston Julia and Pierre Fatou whilst extending it into higher order mappings. Background Mumbo Jumbo:- E xisting between the -1 and +1 in four dimensions, the ginger bread man fractal figures of the Mandelbrot set (based on two of the planes, the x plane and the imaginary plane) have become familiar to us all. M andelbrot's work was a result of trying to unify the work of Gaston Julia and Pierre Fatou during the First World War. The mathematics is based upon repetitive mapping of points in the imaginary plane. T he imaginary plane was invented to explain away problems in expressing time in relativity as imaginary numbers were the only solution to the four dimensional Pythagorean solution.

24. Dynamical Systems And Technology Project topics in mathematics (chaos, fractals, dynamics) into the classroom, and as iteration, fractals, iterated function systems (the chaos game), and the mandelbrot and Julia http://math.bu.edu/DYSYS

Dancing Triangles The Dynamical Systems and Technology Project at Boston University Zooming Sierpinski This project is a National Science 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 are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iteration, fractals, iterated function systems (the chaos game), and the Mandelbrot and Julia sets. Available at this site: JAVA Applets for chaos and fractals Play the chaos game; explore iterated function systems; and make fractal movies, like the Dancing Triangles and Zooming Sierpinski above, all at your own computer. These applets are now up and running! The Mandelbrot Set Explorer This is an interactive site designed to teach the mathematics behind the Mandelbrot and Julia sets. It consists of a series of tours in which you will discover some of the incredibly interesting and beautiful mathematics behind these images. The site is designed to be used by readers of

25. Efg's Fractals And Chaos Page Several Fractal and Chaos projects, including Evolution of mandelbrot Set, Fractal Discovery Lab, IFS images, Lorenz and other Strange Attractors. http://www.efg2.com/Lab/FractalsAndChaos

Contents Fractals Chaos Glynn Function Gallery Also see the Fractals and Chaos Section of the Math Reference Library in look for Mathematics Fractals / Chaos Note: If you have a fast machine (233 MHz Pentium II or faster), you'll likely need a patch to run TP 7 programs on this page. See this fix for "Runtime Error 200." Fractals Program Description Files Keywords Tutorial about Mandelbrot and Julia sets. Mandelbrot Set, Julia Set Evolution of the MandelbrotSet Mandelbrot Set Fractal Discovery Lab Art Gallery, Microscope, Movies, Tools, Library Fractals Show 2 Fractals, Chaos, Mandelbrot Set, Julia Set, Biomorph, Rainbow, WavelengthToRGB, pf32bit, Delphi Sierpinski Triangle Gasket Sierpinski triangle, Sierpinski gasket, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion von Koch Snowflake von Koch curve, von Koch snowflake, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion Chaos Program Description Files Keywords Iterated Function System to create four ferns (Also see, Mathematical Recreations

26. Introduction To The Mandelbrot Set cover If you re interested in learning more about the mandelbrot set, fractals, and chaos theory I highly recommend reading James Gleick s classic book Chaos http://www.olympus.net/personal/dewey/mandelbrot.html

This page has been moved to http://www.ddewey.net/mandelbrot/ . The version here will no longer be maintained or updated. Please update your links. Introduction to the Mandelbrot Set A guide for people with little math experience. By David Dewey According to Web-Counter you are visitor number since November 02, 1996. The Mandelbrot set, named after Benoit Mandelbrot, is a fractal . Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers. Understanding complex numbers The Mandelbrot set is a mathematical set, a collection of numbers. These numbers are different than the real numbers that you use in everyday life. They are complex numbers . Complex numbers have a real part plus an imaginary part . The real part is an ordinary number, for example, -2. The imaginary part is a real number times a special number called

27. 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: December 2003 a bug fix version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. November 2003 a bug fix version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. October 2003 a new version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. 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

28. Math Forum - Fractals - Mandelbrot Set fractals naturally have a dimension that is not an integer not 1 or 2, but of all possible Julia sets for quadratic functions is called the mandelbrot set a http://mathforum.org/~sarah/mandelbrot.all.html

What is a Fractal? The Mandelbrot Set For the following information (paraphrased from Chapter 1, "A Mathematical and Historical Tour") and much more, see Robert Devaney, A First Course in Chaotic Dynamic Systems. Chaos occurs in objects like quadratic equations when they are regarded as dynamical systems by treating simple mathematical operations like taking the square root, squaring, or cubing and repeating the same procedure over and over, using the output of the previous operation as the input for the next (iteration). This procedure generates a list of real or complex numbers that are changing as you proceed - a dynamic system. For some types of functions, the set of numbers that yield chaotic or unpredictable behavior in the plane is called the Julia set after the French mathematician Gaston Julia, who first formulated many of the properties of these sets in the 1920s. These Julia sets are complicated even for quadratic equations. They are examples of fractals - sets which, when magnified over and over, always resemble the original image. The closer you look at a fractal, the more you see exactly the same object. Fractals naturally have a dimension that is not an integer - not 1 or 2, but often somewhere in between. The black points in graphic representations of these sets are the non-chaotic points, representing values that under iteration eventually tend to cycle between three different points in the plane so that their dynamical behavior is predictable. Other points are points that "escape," tending to infinity under iteration. The boundary between these two points of behavior - the interface between the escaping and the cycling points - is the Julia set.

29. 3D Fractals And Bicomplex Dynamics - Home Of The Tetrabrot The Tetrabrot is the bicomplex generalization of the mandelbrot set as realized by Dominic 'Ramdam' Rochon. Articles, pictures, news and other downloads. http://www.3dfractals.com/

Home DMI Contact us Home DMI Contact us

30. Fractal Explorer Program that can generate polynomial and iteration sets as mandelbrot, Julia, Newton like fractals and orbital fractals. http://www.eclectasy.com/Fractal-Explorer/index.html

Fractal Explorer Fractal Explorer Fractal Explorer Fractal Explorer Home License What's new Download ... Caricatures since Dec 24, 1998 Fractal Explorer is a freeware fractal generator that can produce mysterious and beautiful mathematically-based images. Not just a tool for professionals, FE can provide hours of entertainment for beginners and experts alike ! Fractal Explorer can render the classical polinomial fractal sets (like the Mandelbrot-set, the Julia-set, the Newton-set and theirs variations), 4D-complex fractals (called «quaternions»), 3D «strange» attractors, and IFS. Also, FE has many features for creation of special effects and improvement of the pictures. We are sorry because of absence of the Help file, but simple user-friendly interface should not cause difficulties. Thanks for your interest in this software, we hope you enjoy it ! Site news: February 23, 2004 The forum , devoted to the Fractal Explorer was created by Barbara "Bubblybabs" and ... Working with FE, image creation and post-processing, bug reports and future wishes are discussed here. You can ask any questions here and quickly receive the answers. December 26, 2003

31. Fractals Screensaver And Classic Pong Game For Windows Windows screensaver featuring 3D images, and fractals using mandelbrot and Julia Set. Download demo version. http://m3dsaver.netfirms.com/

Welcome! Please select the program of your interest

32. Fractal Explorer Fractal explorer This World Wide Web (WWW) site illustrates the infinite complexity and beauty of fractals with its interactive introduction to two fractals, the mandelbrot set and Julia sets. http://rdre1.inktomi.com/click?u=http://www.geocities.com/CapeCanaveral/2854/&am

33. Mandelbrot Explorer see it. More fractals can be found at the mandelbrot Exhibition, part of the Virtual Museum of Computing. Panagiotis Christias christia 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

34. Mandelbrot graphics, mandelbrot who then worked at IBM s Watson Research Center, was able to show how Julia s work is a source of some of the most beautiful fractals http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html

Benoit Mandelbrot Born: 20 Nov 1924 in Warsaw, Poland Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Benoit Mandelbrot was largely responsible for the present interest in fractal geometry. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. Mandelbrot was born in Poland in 1924 into a family with a very academic tradition. His father, however, made his living buying and selling clothes while his mother was a doctor. As a young boy, Mandelbrot was introduced to mathematics by his two uncles. Hadamard in this post, took responsibility for his education. In fact the influence of Szolem Mandelbrojt was both positive and negative since he was a great admirer of Hardy and Hardy 's philosophy of mathematics. This brought a reaction from Mandelbrot against pure mathematics, although as Mandelbrot himself says, he now understands how Hardy 's deep felt pacifism made him fear that applied mathematics, in the wrong hands, might be used for evil in time of war. The war, the constant threat of poverty and the need to survive kept him away from school and college and despite what he recognises as "marvellous" secondary school teachers he was largely self taught.

35. 3D Mountains Shows how to create fractal mountains, 3D mandelbrot and Julia sets, convex, stellated and polyhedra. Uses tiny Java1.1 applets and VRML worlds. http://www.ibiblio.org/e-notes/3Dapp/Mount.htm

3D Mountains "Lorenz hat" "Lorenz hat" equation is y(x,z) ~ 1/(x + z See Hidden Surface Removal Algorithms for a couple of hints. Controls: Drag mouse to rotate mountain. Drag mouse with "Shift" to zoom it. Press mouse with "Alt"("Ctrl") to increase (decrease) two times number of points. 3D Mandelbrot and Julia sets More examples Fractal terrains Controls: Drag mouse to rotate mountain. Drag mouse with "Shift" to zoom it. Press mouse with "Ctrl" to get new terrain! Press mouse with "Alt"(+"Shift") to increase (decrease) two times number of points (you can see n value in the Status bar). Ice Terrains See also 3D random hills and 3D VRML mountains for explanations. E-notes Fractal polyhedra and Hidden Surface Removal Algorithms updated 11 Oct 2001

36. The Mandelbrot Set Anatomy: Contents A virtual investigation with interactive, animated fractals, articles and fractal math equations. http://www.ibiblio.org/e-notes/MSet/Contents.htm

A virtual investigation with interactive pictures Part 1. The Mandelbrot and Julia sets Anatomy Contents Introduction Quick tour Robert L. Devaney Rotation numbers and internal angles of the M-bulbs The primary M-bulbs counting The secondary and The third level M-bulbs Iterations of quadratic maps Iterations of real maps Bifurcation diagram for quadratic maps Iterations on the complex plane. The Mandelbrot, Julia and Fatou sets The Julia sets The Julia sets symmetry Iterations of inverse maps Critical points and Fatou theorem The Fundamental Dichotomy for J-sets Attractors The fixed points and periodic orbits Local dynamics at a fixed point Attracting fixed point and period-2 orbit Tangent bifurcations ... Period doubling and period trippling bifurcations Periodic and preperiodic points Periodic and preperiodic points in the M-set Misiurewicz points and the M-set self-similarity Douglas C. Ravenel The M and J-sets similarity. Lei's theorem Douglas C. Ravenel "More" Mandelbrot sets Polynomial maps "Growth" in complex exponential dynamics Renormalization "Linear" approximation. Midgets scaling

37. Fractals: Mandelbrot, Pictures The theory of fractals developed from Benoit mandelbrot s study of complexity and chaos. mandelbrot, who is often called the father http://kosmoi.com/Science/Mathematics/Fractals/

EncycloZine Astronomy Biology Chemistry ... Fractals, Googols and Other Mathematical Tales Theoni Pappas The Fractal Murders Mark Cohen Trading Chaos : Maximize Profits with Proven Technical Techniques Justine Gregory-Williams, Bill M. Williams, Marketplace Books Indra's Pearls: The Vision of Felix Klein David Mumford, Caroline Series, David Wright The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation Gary William Flake Trading Chaos : Applying Expert Techniques to Maximize Your Profits Bill M. Williams, Marketplace Books The Fractal Geometry of Nature Benoit B. Mandelbrot Fractal Geometry : Mathematical Foundations and Applications Kenneth Falconer Fractals John Briggs Heaven's Fractal Net: Retrieving Lost Visions in the Humanities William J. Jackson Fractals About Us A - Z Site Map Top Pages ... Cell Phones See also: Encyclo Gallery of Fractals Mathematics Science ... Pictures Sierpinski Triangle 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

38. 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

39. The Fractal Microscope NCSA) for exploring the mandelbrot set and other fractal patterns can appreciate the beauty of the fractals encompassed in the mandelbrot set without the specific mathematics behind http://www.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.

40. 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/

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