41. Arcane Fractals Home Page Take a journey into the fascinating and beautiful world of fractals. http://www.arcanefractals.com/

Home Galleries The Final Frontier Fantasy Mythology The Spirit Apophysis Tutorial Creating The Forms Colouring the Flames Saving and Rendering Some FAQ's Apophysis Resources Tutorials Scripts Plugins Gradients ... Links Arcane Fractals is currently undergoing an upgrade and as a result, there may be some broken links or glitches. Please bear with me and things should be back to normal within the next couple of days. Fran, 16th January 2008 LATEST IMAGES OF MY IMAGINATION Fractals are graphic representations of mathematical equations. Without the aid of a computer to generate the graphics from the equations, these mathematical objects would remain invisible. Traditionally flame fractals have always been particularly beautiful because of their ethereal quality. But in recent times, with the advent of many new marvellous scripts, new previously unimagined forms are now available. Many of my images are actually collages of individual flame fractals. Most of these flames are made in Apophysis, though a few of the earliest ones were made in the Gimp using it's flame plugin. Therefore, all the elements that you see, for example, the trees, plants, stars, etc. are flame fractals. These are opened in my graphics programme and then arranged to make the final picture. On a rare occassion I may sharpen a flame if it is warranted, but I don't add any extra effects as I like their purity.

42. Chaos, Solitons Fractals - Elsevier Journal which includes applications in science and engineering. Tables of contents and abstracts; full text to subscribers. http://www.elsevier.com/locate/chaos

Home Site map Elsevier websites Alerts ... Products Journal information Product description Editorial board Audience Abstracting/indexing Subscription information Bibliographic and ordering information Conditions of sale Dispatch dates Journal-related information Contact the publisher Impact factor Most downloaded articles Other journals in same subject area ... Select your view Applications in science and engineering Editor-in-Chief: M.S. El Naschie See editorial board for all editors information Description ISSN: 0960-0779 Imprint: PERGAMON Commenced publication 1991 Subscriptions for the year 2008, Volumes 35-38, 20 issues Institutional online access: ScienceDirect eSelect For purchase of online access to this journal on ScienceDirect. Order access for 2008 now and get the rest of 2007 for FREE! Institutional price: Order form EUR 3,804 for European countries and Iran JPY 505,100 for Japan USD 4,254 for all countries except Europe, Japan and Iran , and links to our regional sales offices For an overview of recently-dispatched issues, see the Journal issue dispatch dates Audience Engineers, physicists and mathematicians involved in nonlinear sciences, chaos and fractal research.

43. Douglas Cootey's AtomicFractal Artwork I treat fractal images as a photographer would treat a landscape, incorporating design and color composition into each piece. http://www.cootey.com/fractals/index.html

@import url(css/all.css); @import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=17764805"); Home Prints Achievements Gallery: Goods Fractal Art Parade Downloads What do you think about it? Name URL or Email Messages( smilies I treat fractal images as a photographer would treat a landscape, incorporating design and color composition into each piece. I call the process "Fractography". The process of my art differs from photography, however, in that I can alter the subject matter. I utilize happy accidents when I tweak and fiddle with the intial images and parameters. Then I pursue the image with focus and intensity though complex fractals require an investment in time and patience while they render. Allowing for serendipity makes fractography an art process more akin to watercolor painting and just as exciting for me. It is a process of discovery that uses layers of data like glazing and double glazing on canvas. As I adjust parameters and alter palettes I am betting that the resultant image is an improvement over the previous one. I do not stop until I love the results. Most images were created on a PC with Fractal eXtreme and, most recently

44. Fractal Grower (home) Fractal Grower is Java software for growing Lindenmayer substitution (Lsystems) fractals. In its default mode, the software displays an interface for http://www.cs.unm.edu/~joel/PaperFoldingFractal/

Fractal Grower Fractal Grower is Java software for growing Lindenmayer substitution (L-systems) fractals. In its default mode, the software displays an interface for simple L-Systems which can be modeled by paper folding. This interface is appropriate for teaching fractals to elementary and middle school students. The full L-System interface (selectable by menu) is more appropriate for high school and university students. An L-system is a formal grammar (a set of rules and symbols) most famously used to model the growth processes of plants. Changes to the library of preset parameters will quickly yield beautiful fractal images of such variety that it is unlikely that what you create has ever been seen before. By Joel Castellanos Department of Computer Science, University of New Mexico The paper folding system is based on a lecture given by Heinz-Otto Peitgen of the CeVis Research Center at the University of Bremen, Germany. Click here to run the Fractal Grower software in Java WebStart Some systems might take a few minutes to start the software.

45. Alice Kelley's Fractals Alice Kelley, Cheshire Cat fractals. Send me feedback. The new Fractal Cosmos calendar All images Copyright 2002 Alice Kelley Terms of Use. http://www.alicekelly.com/

This gallery displays about 100 of my best images from 1997-2002 See my complete collection of over 500 images here, in my main gallery The new Fractal Cosmos calendar

46. Math.com Wonders Of Math Learn about fractals and create your own beautiful fractal images by Make your own fractals, take the fractal challenge and see fractal movies. http://www.math.com/students/wonders/fractals.html

Home Teacher Parents Glossary ... Email this page to a friend More Wonders Fractals Spirograph Conway's Game of Life Roman Numeral Calculator ... Lissajous Lab Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search Enter your search terms Web Math.com Submit search form Play Sudoku Fall Into Fractals The word FRACTAL was invented by Benoit Mandelbrot Fractals are interesting because as you zoom in closer, the pattern is just as beautiful and complex as when you start. Learn about fractals and create your own beautiful fractal images by following the links below. Interactive Fractal Sites Mandelbrot Set Zoom into a fractal in your browser window. Mandelbrot Explorer Make and post your own images. The Fractory A site built by students for the Thinkquest contest. Build your own fractals and learn about the math behind the images. Mandelbrot and Julia Set Explorer Zoom into fractals. Fractal Galleries Fractalus The fractal from an artist's point of view.

47. Fractals & The Fractal Dimension It could be a fraction, as it is in fractal geometry. This generalized treatment of dimension is named after the German mathematician, Felix Hausdorff. http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

Fractals and the Fractal Dimension Mandelbrot and Nature "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."(Mandelbrot, 1983). The Concept of Dimension So far we have used "dimension" in two senses: The three dimensions of Euclidean space (D=1,2,3) The number of variables in a dynamic system Fractals, which are irregular geometric objects, require a third meaning: The Hausdorff Dimension If we take an object residing in Euclidean dimension D and reduce its linear size by 1/r in each spatial direction, its measure (length, area, or volume) would increase to N=r D times the original. This is pictured in the next figure. We consider N=r D , take the log of both sides, and get log(N) = D log(r). If we solve for D. D = log(N)/log(r) The point: examined this way, D need not be an integer, as it is in Euclidean geometry. It could be a fraction, as it is in fractal geometry. This generalized treatment of dimension is named after the German mathematician, Felix Hausdorff. It has proved useful for describing natural objects and for evaluating trajectories of dynamic systems. The length of a coastline Mandelbrot began his treatise on fractal geometry by considering the question: "How long is the coast of Britain?" The coastline is irregular, so a measure with a straight ruler, as in the next figure, provides an estimate. The estimated length, L, equals the length of the ruler, s, multiplied by the N, the number of such rulers needed to cover the measured object. In the next figure we measure a part of the coastline twice, the ruler on the

48. Dynamical Systems And Fractals Lecture Notes Lecture Notes by David J. Wright in HTML. http://www.math.okstate.edu/mathdept/dynamics/lecnotes/lecnotes.html

Next: Contents Up: Dynamical Systems and Fractals Dynamical Systems and Fractals Lecture Notes David J. Wright Contents Introduction to Dynamical Systems Symbolic dynamical systems Discrete-time systems ... About this document ... David J. Wright Mon Aug 19 17:21:15 CDT 1996

49. Fantastic Fractals But it turns out that fractals are an excellent tool for math teachers. At least that s the opinion of fractal fan Cynthia Lanius, a math teacher at Milby http://whyfiles.org/046sci_project/fractal.html

Fractals aren't just cool they're comely. Fun with fractals If you think mathematics ricochets between the ancient and the mystical, never halting at the useful or comprehensible, if you think half of math was perfected by Euclid and Newton, and the other half can't be comprehended without a Ph.D., meet fractals. These geometric shapes are formed by repetition: Take a shape, do something to it, then do it again for as long as you want. Fractals generally start simple enough, but they can get hideously complicated. But it turns out that fractals are an excellent tool for math teachers. At least that's the opinion of fractal fan Cynthia Lanius , a math teacher at Milby High School, Houston, Texas. For one thing, she says, fractals make the shapes seen in nature. "You don't see a lot of triangles, squares or rectangles in the woods," but fractals show up in everything from cumulus clouds to fern fronds. For another, they are a field of modern math research that students can grasp. "Kids think that all mathematics was learned 500 years ago, that math is a dead study like Latin is a 'dead' language. I want them to understand that there are people living, breathing, and making a living as math researchers." Ten years ago, Lanius became captivated by fractals. When she consulted the web, she found the sites were either way too technical for her high-school students, or they were just pretty pictures with no explanations. So in June, 1996, Lanius created her own set of

50. Ivars Peterson's MathTrek Pascal s fractals. Fascinating patterns can arise out of arrays of numbers defined by . It s a neat way to explore the fractal side of Pascal s triangle. http://www.maa.org/mathland/mathland_2_10.html

Ivars Peterson's MathTrek February 10, 1997 Pascal's Fractals Fascinating patterns can arise out of arrays of numbers defined by simple rules. For example, start with the number 1, and make it the apex of what will become a triangle of numbers. In the second row, write two 1s. For each subsequent line, add together adjacent numbers of the previous row and write the sums in the new row, then place 1s at both ends of the line. Here's what one gets for the first eight rows: This set of numbers is now widely known as Pascal's triangle, named for French philosopher and mathematician Blaise Pascal (1623-1662), who studied it intensively. Pascal, however, was not the first to identify the pattern. The mathematician, astronomer, and poet Omar Khayyam (1048-1122) described this number triangle in his writings. It was also well-known to the Chinese. A nine-row version was featured prominently in the introduction to the book "Precious Mirror of the Four Elements," which appeared in 1303. The book's author refers to the triangle as a "diagram of the old method for finding eighth and lower powers." Indeed, the triangle represents a simple way to determine, for example, that (

51. Evil Mad Scientist Laboratories - Iterative Algorithmic Plastic Sculpture: Fimo Iterative Algorithmic Plastic Sculpture Fimo fractals . Fimo fractals and fancy nbsp;fiber from The Daily Photon Evilmadscientist has a welldocumented http://www.evilmadscientist.com/article.php/fimofractals

Evil Mad Scientist Laboratories Making the World a Better Place, One Evil Mad Scientist at a Time About EvilMadScientist Buy Stuff Contact Forums ... Welcome to Evil Mad Scientist Laboratories New projects posted every Wednesday. What's New STORIES 2 new Stories in the last 7 days COMMENTS last 7 days One Hundred Perce... [+3] Computing the vol... Cat bed made usin... [+3] Linkdump: January... ... Halloween link ro... TRACKBACKS last 7 days Vintage Software ... Make A Cylon Jack... Bristlebot: A tin... [+4] Five Minute Proje... ... One Hundred Perce... Topics Home Field Trips Everything Else EMSL Projects ... General News User Functions Username Password A no-hassle account lets you post non-anonymously. Sign up Lost your password Help Request Interactive Art (for sale) Interactive LED Coffee Tables from Evil Mad Scientist Laboratories in collaboration with Because We Can LED Mini Menorah Kits Popular Articles How to make the simplest electric motor Solid freeform fabrication: DIY, on the cheap, and made of pure sugar One Hundred Percent EDIBLE Googly Eyes! Make A Cylon Jack-O-Lantern ... Lego Abominations Bookmark EMSL Evil Mad Scientist RSS Feed feedburner feed Feed on Google Reader Livejournal feed del.icio.us

52. African Fractals African fractals book (Rutger s University Press) Interactive software simulate African Reviews of African fractals in newspapers and journals http://www.rpi.edu/~eglash/eglash.dir/afractal/afractal.htm

African Fractals by Ron Eglash African Fractals book (Rutger's University Press) Interactive software: simulate African designs, create your own patterns, and learn about fractal mathematics African fractals: the TED talk ... Reviews of African Fractals in newspapers and journals Related web sites International Study Group on Ethnomathematics Back to Ron Eglash home page

53. Mathematical Imagery By Jos Leys. Numerous Ultra Fractal rendered images, some animated using Java. http://www.josleys.com/

@import "http://www.josleys.com/style.css"; Home Galleries Articles References ... About Latest Galleries : The shape of Planet Earth Could the Earth have been flat after all? How about cigar shaped? Or do you prefer pear shaped? It seems it is all possible. Just a question of enough spin.. Knots and dynamics A collaboration with Prof. Etienne Ghys of the Ecole Normale Supérieure de Lyon, containing material presented at the International Congress of Mathematicians (Madrid, August 2006) Knots and dynamics animations. A collection of animations where one can see what a matrix looks like in four dimensions, how to make spaghetti using a 'horocycle', and more.. . The Droste effect A collection of images and animations, made with a "Droste effect" image transformation. Escher tilings A collection of tilings, based on the work of M.C.Escher. View all galleries YouTube Video Posted on 2008-01-03 19:18 Steve Turnidge made this video with a selection of my work: Featurecolumn at the American Mathematical Society Posted on 2006-11-01 20:49 The American Mathematical Society this month publishes an article on their website entitled "Lorenz and modular flows: a visual introduction.

54. Fractals fractals are one of the most interesting puzzles of mathematics. They are made by a simple formula, yet they have such beautiful and complex designs. http://www.bugman123.com/Fractals/Fractals.html

Contents Home Physics Simulations Engineering ... Links Fractals are one of the most interesting puzzles of mathematics. They are made by a simple formula, yet they have such beautiful and complex designs. This page provides simple Mathematica code for many of the most interesting types of fractals. Some of this code may not be very efficient, but it should be enough to give you a basic understanding of the mathematics involved. Mandelbrot Set Zoom - original version: Java , 5/24/01; animated version: C++, 2/16/05 z n+1 = z n +z c This animation zooms in on the Mandelbrot set by a factor of 10 code for double-doubles . See also my Java program and C program . Here is some Mathematica code for this fractal: (* runtime: 1 minute *) < 2, z = z^2 + zc; i++]; i]; Here is a faster version: (* runtime: 7 seconds *) POV-Ray has a built-in function for this fractal: // runtime: 0.5 second Links Deep-zooming Fractint can zoom in by magnification factors of up to 10 1/50 of a Light Year - zooming animation by Damien Jones Kleinian Double Cusp Group - calculated in Mathematica 4.2

55. MathsNet Fractals In order to understand fractals you need to understand a little bit of mathematics concerning complex numbers and the process of iteration. http://www.mathsnet.net/fractals.html

home geometry curriculum puzzles ... MathsNet.com "Mathematics possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture." Betrand Russell Fractals What are fractals? The properties of fractals What else are fractals? Logo fractals ... 4D Magic Cube A brief summary of the mathematics of fractals. What are fractals? In order to understand fractals you need to understand a little bit of mathematics concerning complex numbers and the process of iteration. First you need to know about the special number known as i . You can do arithmetic with i . A complex numbe r is a number made up of two parts added together. These parts are called the "real" part and the "imaginary" part . Examples of complex numbers are: 4 - 6i, 2.1 + 4.7i, 1-i, and so on... In fact any number of the form a + bi, where a and b are real numbers, and i is as above, is a complex number. Addition and multiplication of these numbers is achieved using the conventional rules of algebra. Complex numbers have a size. It is usually called their

56. Makin' Magic Fractals Freeware Fractal 3d Program Programs, fractals, utilities, freeware, shareware, source code, algorithms, MMFrac from Makin Magic. (Dave Makin s homesite) http://skyscraper.fortunecity.com/terabyte/966/

web hosting domain names photo sharing Makin' Magic Programs, Fractals, Freeware, and Graphics This is the Makin' Magic main index page or, if you prefer, Dave Makin's index page. This site is best viewed at width 1024 or higher, the galleries should now view ok at width 640. Main site (or downloads) last updated 8th September 2002. This page last updated 14th January 2008. If you are interested in purchasing David Makin's fractal art prints or simply would like to view David's most recent artwork please visit our main website at fractalgallery.co.uk David produces fractal art in many styles which include impressionist, science fiction, abstract art and mineral art. Every print we supply is printed on good quality matte paper, we also produce larger prints such as Giclée on canvas or Durst Lambda. As fractals are generated using complex mathematical formulas we are also able to supply custom art prints using numerical data which you supply, this could be an anniversary for instance. David Makin's fractal art prints are available in size A4 through to A0 and licences to publish are available for a fee on request. For more information please visit fractalgallery.co.uk

57. Hidden Dimension Galleries Ron Barnett s fractal images, music, raytracing, Ultra Fractal formulas and links. http://www.hiddendimension.com/

Welcome to the wonderful world of algorithmic art. In your tour through this site you will be able to see algorithmic art created by a variety of programs and hear music created from mathematical algorithms. Come explore and learn more about fractals! Visit the art galleries and decide for yourself whether fractals can be art. Mouse over an image to see where it leads. Click on the image to visit the site. Email me Mathematics of Fractals: Visit this page for a description of the mathematics of various types of fractals - including Divergent, Convergent, Strange Attractors, IFS, Juliabrots, Quaternions, L-Systems, Kleinian Groups, Circle and Sphere Inversions and Hyperbolic Tessellations. Art Galleries: The main page for entrance to the various art galleries and animations. The memorial gallery for Red Williams is also here. Tutorials: The main page for UltraFractal tutorials for selected formulas. These are step-by-step how to instructions and a different from the help files available in the Downloads section below. Downloads: Some of my UltraFractal formulas are too large for inclusion the UltraFractal database and are available here. Windows style formula help files which can be used within UltraFractal are also available, along with a gradient editor designed for Fractint but which also works with UltraFractal.

58. Amazing Flame Fractals Take Your Breath Away | TechRepublic Photo Gallery Witness the beauty and elegance of mathematics with 50+ breathtaking fractals.) http://content.techrepublic.com.com/2346-10878_11-33277-1.html

@import url("http://i.techrepublic.com.com/css/tr_ws2006.css"); @import url("http://i.techrepublic.com.com/css/trPhotoGallery.css"); @import url("http://news.zdnet.com/css/z/ads/hs.css"); On BNET: 10 free apps for your flash drive BNET Business Network: BNET TechRepublic ZDNet My Workspace ... Store Amazing flame fractals take your breath away by Tags: off topic geekend fractal background ... Digg This Water Lilies Witness the beauty and elegance of mathematics with 50 breathtaking fractals. Webshots member rajah created these Fractal Flames with Apophysis a freeware Windows application with which you can design and render fractal flames. According to http://apophysis.wikispaces.com/ and http://www.flam3.com/ , Fractal Flames were created by Scott Draves in 1992 and are an "extension of the iterated function system class of fractals". Click on each image for a full-size version. rajahh Digg this Add to del.icio.us Print/View all Posts Comments on this gallery I can't help but notice.... Kinda the same idea Coral employ fractals... Small vacations ... RE: Monolith (Amazing flame fractals take your breath away) What do you think? Alert me when new posts are added Add Comment Cracking open the original Apple iBook G3 clamshell World of Warcraft: Celebrating the holidays in style On the road with an IT Pro: Sydney Australia Cracking Open The Xbox 360 Elite ... How do I... Create holiday cards in Microsoft Word?

59. Browsing Fractal Art On DeviantART Fractal Art. Categories Digital Art Fractal Art. Show 2460120 Newest Popular Way back. Time Range24 hours2 days3 days1 week1 monthAll Time http://browse.deviantart.com/digitalart/fractals/

GA_googleAddSlot("ca-pub-2005626271413567", "right_ws_browse_digitalart");GA_googleAddSlot("ca-pub-2005626271413567", "top_lb_browse_digitalart"); GA_googleAddAdSensePageAttr("google_ad_channel","6796827591"); // Country us Channel 6796827591 GA_googleAddAdSensePageAttr("google_kw_type","broad"); GA_googleAddAdSensePageAttr("google_hints","digitalart, fractals"); GA_googleAddAdSensePageAttr("google_color_border","D4E2DE"); GA_googleAddAdSensePageAttr("google_color_bg","D4E2DE"); GA_googleAddAdSensePageAttr("google_color_link","339933"); GA_googleAddAdSensePageAttr("google_color_text","000000"); GA_googleAddAdSensePageAttr("google_color_url","669900"); GA_googleAddAttr("LoggedIn", "No"); deviant ART Browse Shop Chat ... Forum Username: Password: login or Not a member? Become a Deviant! No items in Shopping Cart Lost Password? [x] ... Advertise Here Fractal Art Categories Digital Art Fractal Art Show Newest Popular Way back Time Range 24 hours 2 days 3 days 1 week ... RSS Previous Page Next Page see also Submit Here Digital Art Forum Random Deviation Random Deviant ... Services Our Partners [ back

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

Thursday, 1/24/2008 , 5:52:50 PM ET, Brooklyn and Prattsville, NY Updated December 31, 2007 This site is an exercise in love, vanity and art. It includes my current images, vintage fractals, animations, ceramic tiles, digital photographs, and more... There are 351 viewers online now. Enjoy! And thanks for visiting! COLLECTION 2004 Gallery I December 2004 Gallery II Oct-Nov 2004 ... January-June 2004 COLLECTION 2003 Gallery I January-June 2003 Gallery II July-December 2003 COLLECTION 2002 Gallery I January-June 2002 Gallery II July-December 2002 VINTAGE FRACTALS Fractal Zoo, Part 1 Fractal Zoo, Part 2 Fractal Camera Black and white ... Faultline fractals COLLECTION 2007 In Memoriam Sam Archer COLLECTION 2006 Part I Twenty images Part II Twenty images ... Phantasma Gallery COLLECTION 2005 Virtual Portraits I Virtual Portraits II Virtual Portraits III Flags of the Fractal Nations ... In Retrospect COLOR SHIFT ANIMATIONS Don Archer, director DIGITAL PHOTOGRAPHS FRACTAL MUSIC ... VERSE CREDITS One man show, Flag series, Phantasma Gallery, Windham, NY, July 2006

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