21. > Java > Fractals Julia and mandelbrot fractals Java Mandelbrot and Julia set explorer byOla Andersson. Mandelbro Fractal - Java Mandelbro Fractal Example. http://www.mathtools.net/Java/Fractals/

Mathtools.net Java Fractals Add Link ... Other Mandelbrot-Set Java-Applet with Zoom-Function - A Mandelbrot-Set Java-Applet with zoom-function for download. An Introduction to Fractals - A lesson, including Java applets, that teaches very simple methods to construct fractals, to do and practice some math, and to appreciate the beauty of fractals. Fractal - MegageM Fractal Products - A Java Applet that creates an automatic Mandelbrot Set Zoom Sequence. We'll change this from time to time so stay tuned! This one is 20 images, with a total magnification of about one million. Fractal Explorer - Fractal Explorer is Java applet which can open to you the beautiful world of fractals. Its unique features make it quite different from other fractal viewers and generators. Fractal Filmer - Java Fractal Filmer that creates fractal animation using Fractint. Supports all fractint parameters, 'smart palette' color rotation and network CPU pooling. Fractal Fun - This applet draws the following fractals: The Fern , The Gingerbread Man , The Sirpinski Gasket , The Mandelbrot Set.

22. Fractals Display Chaos, Fractals and the Mandelbrot Set. Julia and Mandelbrot Set Explorer. DynamicalSystems and Fractals. mandelbrot fractals. Fractals and SpaceFilling Curves. http://www.math.ksu.edu/main/events/special/openhouse/oh01fractals.htm

KSU Math Home Events Special Events Open House : Fractals Display Printable Version K-State Open House - Department of Mathematics Fractals Display Saturday - April 6, 2002 - 9 a.m. to 3 p.m. Fractalus.com Math : Chaos and Fractals An Introduction to the Fractint Formula Parser A program for creating fractal animation ... Printable Version Last Modified Mar 11, 2003 1:58 pm

23. Fractal Desktop -- The Forge! (page 1) A leitmotiv in mandelbrot fractals BTW, all these images are mandelbrot fractals.The initial m of the file name stands, precisely, for Mandelbrot. http://fractaldesktop.virtualave.net/forge.htm

Refinance now homeowner even if you have bad credit. 185 loc The forge This is where you can learn how to draw a fractal. The lesson has a very practical approach, it's accessible to everyone. You'll see you don't need to juggle personally with complex math to create such artwork! 0. What is a fractal? If you need to get the idea of "fractal", I can give you two examples: first, think of a coast line. From a plane, the water border has a length; from the beach, for a man, it has a greater length, because he can walk along the border. Now imagine that instead of a man there is an ant walking along the border: the coast line has still a greater length. We could continue till the size of an electron. Next, think of a cauliflower. Each of its warts is made of little copies of itself. Fractals have this in common: they are images that are made of little copies of themselves, that, in their turn, are made of little copies of themselves and so on. A leitmotiv in Mandelbrot fractals [BTW, all these images are Mandelbrot fractals. The initial "m" of the file name stands, precisely, for Mandelbrot. Benoit Mandelbrot is the "father" of fractals; he also gave them this name.] is the "snowman". m1.jpg constitutes the basic "snowman". You will never believe that all the images from m2 to m100 are zoomings of m1, made in different areas. :-) But, how about a complete definition of fractal? Here is my personal one:

24. 3D Mandelbrot And Julia Fractals 3D Mandelbrot and Julia fractals. Instead of initializing z (0) =0 it sets z (0) =dwhere d is the Julia parameter. This creates distorted mandelbrot fractals. http://www.tcs.hut.fi/~msmakela/sw/Fractal/

3D Mandelbrot and Julia fractals Fractals became popular in the 1980s, when microcomputers started to become common. Everyone could produce the Mandelbrot set with their home computer. It is difficult to conceive how so simple mathematic formulae can create such beautiful images having such detailed and in some sense recursive structure. Some theory The underlying mathematics makes use of complex numbers. For each point c=t+j x in the complex plane, one associates a colour by using an iterative process: z z (i+1) =z (i) ²+c The colour of the point c is the smallest i for which (i) This is the process for the Mandelbrot set. The Julia set is similar, but it uses the formulae z =c z (i+1) =z (i) ²+d where d is an additional parameter, which is used for all points in the fractal. Programming languages usually do not directly support complex number arithmetics. Therefore, the iteration equations are usually split into real and imaginary components z (i) =t (i) +j x (i) c (i) =ct (i) +j cx (i) and the iteration step is as follows: t (i+1) =t (i) ²-x (i) ²+ct x (i+1) =2 t (i) x (i) +cx This can be generalized to 3 dimensions by adding another coordinate y , which is orthogonal to both the t and x axes: t (i+1) =t (i) ²-x (i) ²-y (i) ²+ct x (i+1) =2 t (i) x (i) +cx y (i+1) =2 t (i) y (i) +cy These formulae were originally found out by my friend Topi Kärki, who wanted to see how the Mandelbrot fractal behaves when using quarternions instead of complex numbers. It turned out that the 4th dimension was redundant.

25. WisFaq! Formule Von Koch fractaal. Julia fractals begrensd en mandelbrot fractals convergent?Wat betekenen die bolletjes? Bekijk alle vragen in de categorie 'Fractals'. http://www.wisfaq.nl/overzicht.asp?categorie=Fractals

26. Complex Fractals The exponent can be changed to produce different mandelbrot fractalsand so can the function, as long as it retains the Z=Z +C format. http://www.ga.k12.pa.us/academics/us/math/geometry/stwk98/ABIDEN/complex.html

Complex Fractals I The Mandelbrot set is one of the most commonly seen complex fractals, it applies a simple nonlinear algebraic equation Zn = Zn-1^2 + C which is called the recursion law. All fractals using this equation belong to the Mandelbrot set. The following graph displays the complex plane. Image obtained from Fractal Explorer The Mandelbrot set is built starting with a point C on the complex plane. Calculate the value of the expression: Z^2 + C using zero as the value of Z (the result would be C obviously). Assign the result to Z and repeat the calculation. It would then be C^2 + C. Assign this value to Z and repeat this process many times. This is called the iteration of the function Zn = Zn-1^2 + C.

27. Angell's Heaven Presents Fractals Julia and mandelbrot fractals. There are two main types of fractals, Mandelbrotand Julia- fractals, use the radio-buttons to switch between the two. http://www.angells.com/fun/games/tetris/index3.htm

Games Downloads Jigsaw Puzzles ... Search This page has not been converted to the new site format. Please be patient with us during this time of change. Home Smokey the Bear Wallpapers Subscribe to List ... Angell's Heaven Julia and Mandelbrot Fractals Press button to start. Drag on picture to zoom. The fractal viewer is not a game. It just looks good, and it came free with Tetris. Press the button to start the interactive fractal program. There are two main types of fractals, Mandelbrot- and Julia- fractals, use the radio-buttons to switch between the two. The Mandelbrot fractal always looks the same, but the Julia fractal can be altered by changing the two constants and pressing enter You can zoom in into the fractals by dragging with the mouse. Zoom back out by pressing the radio-button once again. Look at Fractals here with a java enabled browser. It takes a few seconds to load the applet. Please be patient.

28. LINK-MAIL: Mandelbrot And Julia - Fractal Image Art Galleries, Tools & Facts Mandelbrot Explains ( ..Benoit Mandelbrot discovered fractals 40 years ago. Juliaand Mandelbrot Set Explorer; Julia and mandelbrot fractals (Online Explorer); http://www.link-mail.com/43260.html

Submit-your-Links! Be a Volunteer Tell Your Friends Link-Mail commerce Bangkok's Family Escort Service Beautiful Asian Handicrafts ... or home decor Edition #43260-1 Updated regularly Fractal art images belong to truly beautiful artistic creations on the net and are based on a mathematical model developed by Benoit Mandelbrot and often included with Julia filters. We guide you to the best galleries, tools, sites and all mathematical facts. To receive your special link-mail letter and report from us just click the 'Get it now' button on the end of this page. Your privacy is of course respected and the link-mail letter below is absolute FREE New visitor? Please read our FAQ LETTER OF CONTENTS: I. In this section are all information regarding Mandelbrot and his mathematical model: Fractal What? Mandelbrot Explains ("..Benoit Mandelbrot discovered fractals 40 years ago. Born in Poland, he was raised in France and has done most of his work in the U.S...")

29. Tech mandelbrot fractals are probably the most varied and complex of the fractals. Theformula for mandelbrot fractals is amazingly simple z(n+1) = z(n)^2 + C. http://www.goshen.edu/~kevin/tech.html

Technical Realities You may be interested in some technical aspects of how these fractal images were created and transferred to prints. If not, feel free to skip this section. Look at the fractals some more. The real reason I like fractals is because they are beautiful and emotionally evocative. Enjoy! Although I have been working with fractals on and off since April 1988, all the images in this exhibit were created since May 1990. That is when I found the fractal generating software FRACTINT . Fractint is the collaborative effort of dozens of individuals across North America under the name The Stone Soup Group . Their contribution policy "Don't want money. Got money. Want admiration." is something of a credo of hackers in the best sense. They take on a challenge, overcome it with style and spread the benefits around to anyone interested. FRACTINT with its many tools and features has allowed me to focus more on the fractals I am creating and less on the computational details. The Stone Soup Group definitely has my admiration and appreciation.

30. Ken Shirriff: Fractals Details here. I'm currently experimenting with techniques to use fractionalexponents in mandelbrot fractals. Details here. I have http://www.righto.com/fractals/

Ken Shirriff Fractals Here are pictures and algorithms of my Voronoi fractals, which have an interesting leaf-like structure. You probably know Mandelbrot's equation z -> z^2+c, but what happens if you want to use -2 for the exponent? Details here I'm currently experimenting with techniques to use fractional exponents in Mandelbrot fractals. Details here I have written papers on how to generate fractals from Voronoi diagrams, reciprocals , and polynomial composite functions , or with the xfractint program. See my bat fractal and Java Mandelbrot My fractals have appeared in The Pattern Book and Computers and the Imagination I also have some (non-fractal) patterns designed to appeal to babies. Ken Shirriff shirriff@eng.sun.com This page: http://www.righto.com/fractals/index.html

31. ÒµÓàÊýѧÌìµØ-ÍøÉÏ×ÊÔ´ more ; Studying mandelbrot fractals Suzanne Alejandre What is a fractal? Generalinformation about Mandelbrot, fractals, and their computer generation. http://extend.hk.hi.cn/~zzm/resource.htm

Amatuer Mathmatics World Abstract Algebra Algebra Analysis Applied Mathematics ... The Fractal Microscope - Education Group, National Center for Supercomputing Applications (NCSA) An interactive tool for exploring the Mandelbrot set and other fractal patterns. With the Fractal Microscope students can enjoy the art as they master the science of mathematics, and can address a variety of topics in the K-12 curriculum including scientific notation, coordinate systems and graphing, number systems, convergence, divergence, and self-similarity. The program is designed to run in conjunction with NCSA imaging tools such as DataScope and Collage. Fractals: A Visual Introduction - Erik Sudderth A final project for a course in Introduction to Image Engineering taught by Professor Ramesh Jain during 1997 at UC San Diego. Contents: Introduction: What are fractals?; The Mathematics of Fractals; Julia Sets and the Mandelbrot Set; VRML Terrain Generation with Fractals; Fractal Image Gallery; Image Processing Techniques; Sources and Bibliography. Fractals - Cynthia Lanius This lesson plan for exploring fractals is designed so 4th through 8th grade students can work independently and be assessed innovatively. Conforms to 1989 NCTM standards; links to other fractal sites. Contents: Why study fractals? Making fractals: Sierpinski Triangle, Sierpinski Meets Pascal, Jurassic Park Fractal, Koch Snowflake. Fractal Properties: Self-similarity, Fractional dimension, Formation by iteration. Teacher-to-Teacher notes; Fractals on the Web.

32. Zeal.com - United States - New - Computing - Multimedia - Graphics - Fractals - Check out a free downloadable software utility designed for creating and studyingmandelbrot fractals. Includes recommended properties and algorithms. http://www.zeal.com/category/preview.jhtml?cid=10021030

33. Spanky Whats-new display. Anton Feenstra anton@chem.rug.nl has a thumbnail thumbnailgallery of mandelbrot fractals created with FractInt. Stanley http://spanky.triumf.ca/www/whats-new.html

THE SPANKY FRACTAL DATABASE An interesting mandelbrot. What's New with Spanky It can get confusing browsing these fractal pages in their semi-organized state brought on by my random updating. All the links can be a little overwhelming so I'm going to make an attempt to filter all the new links through this page before moving them to their appropriate index page. If you're just looking for recent developments in the Fractal Community, then this is the page for you. I'll form a small set of links under each of the main information catagories I maintain and just keep pointers to recent additions here. I'll try and keep the number of links low and reasonably up-to-date. This page will have a very simple format, within each catagory, new things will be added to the bottom of the list, and moved to the related index page when they get to the top. This is also one page where the header image may change from time to time. I'll use this page to introduce any current favourite or recent image that I've created. New Fractal Images Other Images directory Les St Clair's les_stclair@compuserve.com

34. JAMS Julia mandelbrot fractals Written by Ken Gaal Julia and mandelbrot fractalsare beautiful patterns created by sets of complex numbers. http://www.oro.net/~kgaal/jams.htm

Written by Ken Gaal Julia and Mandelbrot Fractals are beautiful patterns created by sets of complex numbers. Set membership is based on a the simple recursive formula Z = Z*Z + C. This program allows the user to generate, view, and manipulate these fascinating fractal patterns. One can also view the orbit (trace) of the recursive complex number sequence. The program name JAMS stands for Julia And Mandelbrot Sets. jams.zip < Click here to Download After downloading this file jams.zip, run >PKUNZIP JAMS Then, to execute this fractal program run >JAMS If you have any problems/questions/comments, feel free to contact me at kgaal@oro.net Yuba College, 2088 N. Beale Rd., Marysville, CA, 95901

35. ENC: Curriculum Resources: Suzanne's Mathematic Lessons (ENC-011220, Full Record Also found at this site are interactive student lessons for investigating polyhedraand mandelbrot fractals with Java Applets and four interactive games that http://www.enc.org/resources/records/full/0,1240,011220,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. URL: http://mathforum.org/alejandre/index.html ENC#: ENC-011220 Publisher: Swarthmore College Date: Grades: Languages: English; Spanish Abstract: Reviews and Awards: ENC Digital Dozen, June 1998. ( http://enc.org/weblinks/dd/archive/0,,6-1998,00.shtm Additional information available at: http://enc.org/weblinks/dd/about/ User Comments: None currently available. Add a User Comment for this resource. Record Created: Last Modified: Contents: Web workshop ideas page Web units Magic squares (Math, history, geography) Tessellations (Tutorials, math, connections) Interactive lessons and classroom activities Studying polyhedra Studying Mandelbrot fractals Traffic jam Bricks Locker problem Dominoes Technology in the classroom ClarisWorks graphing Bar graphs Pie charts Pictograms Exponential functions Linear functions Polynomial functions Reference page information Functions Mathematicians and scientists Number systems Patterns Math 7 introduction Unit 7 Unit 8 Unit 9 Unit 10 Unit 11 Unit 12 Interdisciplinary activities Curriculum links Math 6 course Math 7 course Math 8 course Suggestion box Home The collection Help desk Quick reference Search Equipment:

36. Cynthia Lanius' Lessons: A Fractals Lesson - Introduction Features a fascinating introduction the world of fractals to elementary and middleschool children. Includes notes to teachers. Pictured A Famous Fractal - The mandelbrot Set. A fractals Unit for Elementary and Middle School Students http://math.rice.edu/~lanius/frac

Cynthia Lanius Fractals Pictured: A Famous Fractal - The Mandelbrot Set A Fractals Unit for Elementary and Middle School Students That Adults are Free to Enjoy Table of Contents Introduction Why study fractals? What's so hot about fractals, anyway? Making fractals Sierpinski Triangle Using Java Math questions Sierpinski Meets Pascal ... Using Java Fractal Properties Self-similarity Fractional dimension Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received What are Fractals? They're everywhere, those bright, weird, beautiful shapes called fractals. But what are they, really? Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun! Teachers: Every lesson has a print version for classroom use.

37. Mandelbrot Set May 13, 1994. mandelbrot. This directory contains pictures of subranges of the mandelbrot set. The format is 1140x890 http://www.ugcs.caltech.edu/~werdna/pics/Fractals/Mandelbrot

Last Update: May 13, 1994 Mandelbrot This directory contains pictures of subranges of the mandelbrot set. The format is 1140x890 pixels. They are computed and colored using mandtool, an interactive program running under SunView at University of Karlsruhe Department of Computer Science Operating Systems Research Group D-7500 Karlsruhe / Germany This archive is a pseudo-mirror of . To make indexing easier, I've used an image map (click on the image you want to see). The advantage of doing things this way is obvious: it's faster. The disadvantages include: Can't get browsers like Mosaic to remember which pics you've selected Incompatibility with browsers that don't support image maps You never get to see the "true" URL's of the pics (so it's hard to make links to individual images) Somewhat uglier (that border around the edges, and limited to 256 colors) Because of these disadvantages, I keep around another file that uses the traditional way of doing this: 91 separate thumbnail pics. (Definitely try this if you've got more than 8-bit color, but it will take much longer to load.) Andrew Tong werdna@ugcs.caltech.edu

38. Mandelbrot And Julia Set Explorer Clark University hosts incredible graphic images and links to fractal and other mathematical methods Category Science Math Chaos and fractals......Julia and mandelbrot Set Explorer. David E. Joyce. For backgroundon Julia and mandelbrot sets, see the introduction. There http://aleph0.clarku.edu/~djoyce/julia/explorer.html

Julia and Mandelbrot Set Explorer David E. Joyce For background on Julia and Mandelbrot sets, see the introduction. 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 my page on Hyperbolic Tessellations Mandelbrot Set x in [-1.0,2.0]; y in [-1.5,1.5]. Parameters Clicks on the Mandelbrot set image will get a Julia set magnify the Mandelbrot set by a factor of Alternate Mandelbrot parameter plane mu lambda (mu = lambda^2/4-lambda/2) 1/mu 1/(mu+.25) 1/lambda 1/(lambda-1) 1/(mu-1.40115) Width= by Height= in pixels. Maximum number of iterations= Note that it may take a while if you set your parameters to ask for a big image or a lot of iterations. Image rendition Image colors Color images Grayscale images Wrap through the colors times. Escape shape: circular (standard) square half plane Level pattern: plain feathered binary Download the Mandelbrot set image for an external viewer or viewing on a separate page. Index of recently created images . Many interesting images are found by others. Click on html files for the full form; click on gif files for just the image.

39. 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

40. 3d Fractals! Advances In Bicomplex Dynamics - Images And Pictures - The Tetrabro 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/

z Prof. Dominic Rochon, Ph.D. (819) 376-5011 ext.:3805 Fax: (819) 376-5185 Dominic_Rochon@uqtr.uquebec.ca Web Site Design By rabrot is the bicomplex generalization of the Mandelbrot set realized by Domic "Ramdam" Rochon. Using 3 out of 4 possible dimensions, it renders 3d fractals the way not even quaternions can approach. With 3 dimensions it only represents a part of the entity. We can use the 4th parameter as time and see the 3d fractal morph in intricate shapes! -v2

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