21. The Geometry Junkyard: Fractals Apollonian Gasket, a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles. From MathWorld. http://www.ics.uci.edu/~eppstein/junkyard/fractal.html

Fractals Allegria fractal and mathematically inspired jewelry. Apollonian Gasket , a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles. From MathWorld. Area of the Mandelbrot set . One can upper bound this area by filling the area around the set by disks, or lower bound it by counting pixels; strangely, Stan Isaacs notes, these two methods do not seem to give the same answer. Balanced ternary reptiles Cantor's hourglass reptile spiral reptile stretchtiles ... trisection of India , the three Bodhi problem , and other Fractal tilings by R. W. Gosper Circle fractal based on repeated placement of two equal tangent circles within each circle of the figure. One could also get something like this by inversion, starting with three mutually tangent circles, but then the circles at each level of the recursion wouldn't all stay the same size as each other. The Curlicue Fractal , Fergus C. Murray. The Dynamic Systems and Technology Project at Boston Univ. offers several Java applets and animations of fractals and iterated function systems. Expansions geometric pattern creation techniques by John S. Stokes III.

22. Fractals Galore! fractals by songweaver.com. fractals are images which integrate real and imaginary numbers, producing vivid and fascinating works of art. http://songweaver.com/art/fractals/ring.html

To join the fractals webring you merely need to have a site which is about fractals in some form or another. If you don't know what fractals are, then this probably isn't the right webring for you. This fractals site is owned by Previous 5 Sites Skip Previous Previous Next ... List Sites Submit site to the Fractals webring Site Title: Site URL: Name: E-mail: Password: Please choose a password. (Don't forget it!!) Keywords: Enter up to 20 keywords to describe your site. Description: Enter a short description of your site. To join the ring you'll need sample code on your site somewhere similar to the code that follows: Once the code has been added, you're eligible to be added to the fractals webring. E-mail fractals@songweaver.com with any questions. If you want to include a graphic with your webring code, feel free to use the one at the top of this page, which you can access directly by clicking here , or the one on the right, which is available here . I only ask that instead of referencing an image at my site, you make a copy of it for yourself, so as not to overwhelm my server.

23. Chaos, Fractals, And Arcadia Article on the mathematical ideas lurking in the background of Tom Stoppard s play Arcadia. Includes examples, illustrations and references. http://math.bu.edu/DYSYS/arcadia/index.html

Chaos, Fractals, and Arcadia Robert L. Devaney Department of Mathematics Boston University Boston, MA 02215 Below you will find an animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia . For access to some of the mathematical software that generates some of the images contained herein, visit the Dynamical Systems and Technology Project at Boston University. To purchase a video involving some of the mathematical ideas in Arcadia, together with a taped discussion by Tom Stoppard, visit the Mathematical Sciences Research Institute at the University of California, Berkeley. Introduction Thomasina's Geometry of Irregular Forms The Chaos Game The Sierpinski Hexagon ... Some pictures from Arcadia We welcome your feedback on this material. Please send any comments or suggestions to Robert L. Devaney at bob@bu.edu Introduction (Next Section) (Return to Dynamical Systems and Technology Home Page

24. Fractals Of Change Tom Evslin blog about new technologies, especially in Web 2.0, VoIP, and transportation. http://blog.tomevslin.com/

Fractals of Change nothing great has ever been accomplished without irrational exuberance About Tom Evslin subscribe: via email via RSS via Kindle Reader Lijit Search Recent Posts Ben Bernanke’s Blunder: How NOT to Solve the Mortgage Crisis One Nation And Those Who Harbor Them What I Did on Town Meeting Day ... Danger: Biofuels Cause Global Warming Categories Advisory Capital afib Blocknot Blooks ... June 2007 var site="s13fractals" Powered by TypePad Member since 01/2005 technorati Ben Bernanke’s Blunder: How NOT to Solve the Mortgage Crisis Yesterday the US Federal Reserve took a big step towards prolonging the mortgage crisis. Its short-term reward was a big one-day run up in stock prices; Today prices were down again. I hope Fed Chairman Ben Bernanke isn’t making the mistake that was so hard for so many of us CEOs of public companies to avoid: navigating with one eye on the stock ticker. From the New York Times “In an action that sent stock prices soaring, the central bank offered to let the biggest investment banks on Wall Street borrow up to $200 billion in Treasury securities in exchange for hard-to-sell mortgage-backed securities as collateral. And the Fed made clear that it was prepared to do more as needed.” What the Fed did is get squarely in the way of unraveling the mortgage mess. Accepting these unsellable loans at face value as collateral is exactly the same as offering home equity loans to people whose mortgages are underwater based on the equity they used to have before prices fell.

25. Chaffey's Fractal Links On The Web Welcome to the original Chaffey High School s Fractal Links of the Web. These pages where started as a hobby/extra curricular activity back in 1993, http://www.chaffey.org/fractals/

Chaffey High School's FRACTALS on the Web http://www.chaffey.org/fractals/ Last Updated February 28, 2003 This site should be renovated soon, please excuse the webmaster's lack of construction. Welcome to the original Chaffey High School's Fractal Links of the Web. These pages where started as a hobby/extra curricular activity back in 1993, and have grown to be a pretty large website for alumni of Chaffey High School, as well as general links resource for schools. Fractals are very interesting and mathematical occurrences. Chances are, if you have opened your eyes, you've seen Fractals. This site, Chaffey's Fractal Links, is meant as a resource for everybody to use as a tool in search of fractal information, programs, articles and other fractal related pages on the Internet. This page has been up since 1993 and is continuing to grow in content. More will be coming soon... CHS Home Fractals Home About Fractals Awards ... Theory

26. Fractals This relatively new word in mathematics was first coined by Benoit B. Mandelbrot and introduced to mathematicians and computer scientists in The Fractal http://curvebank.calstatela.edu/fractal/fractal.htm

Back to . . . Curve Bank Home Classic Curves Index The Mandelbrot Set weds the graphing of complex numbers to the recursive power of modern computers. MandelZoom takes approximately 15 seconds to load. Be patient. MandelZoom (C) Louis P. Santillan 2001-2002 Instructions: Click to zoom IN. O to zoom OUT. R to reset to the original screen. C to CHANGE COLORS. For source code, email Louis here. More fractals . . . The points of a Mandelbrot Set are bounded as follows: x: -2 x y i i x i Size: radius or distance from (0,0) The full Mandelbrot Set is plotted within the inscribed circle of radius . Other views showing the fractal edge are displayed by zooming in on only a portion of the bounded area. Sample calculation: Mathematicians in the early 20th century investigated curves that had highly intricate and detailed shapes. Moreover, they realized that while a region might be bounded and thus the area finite, the perimeter or border might seem to be infinite. These curves - the Koch Snowflake for example - with finite area and infinite perimeter, were given the name of "pathological." This particular area of research in mathematics has generated colorful names: Cantor's dust, Polya's sweeps, Peano's dragons, Sierpinski's carpet and others. When the edge of a curve under many iterations is broken, repeated, scaled down, and then scaled down again as the iterations progress, the curve has now become known as a fractal. This relatively new word in mathematics was first coined by Benoit B. Mandelbrot and introduced to mathematicians and computer scientists in

27. The Fractal Bargain Bin - Wallpapers / Eye Candy / Pretty Stuff Fractal and algorithmic art, free to use for any purpose. Print it, share it, create with it. http://www.sgeier.net/fractals/indexe.php

The infinite fractal loop: Help Next 5 Random ... Penguin Galleries: [Current] [flame-fractals] [all yearly galleries] Writing about Artistic issues Technical stuff The author/artist Welcome The thumbnails on this page are linked to much larger (1280x1024 or 1600x1200) JPG images and you can trust me that the large versions look a lot better than these tiny stamps. Please feel free to check them out. Copyleft X I created these because it pleases me to create them . Go ahead and download them, save them, give them to your friends, print them and hang them on a wall, whatever you want. "Property" is simply not a productive paradigm for art. If you like these images and you do something special with them, I'd be glad if you could drop me an e-mail , though, as I like getting feedback. And of course you're allowed to donate , if you'd like. NEW Fractal T-shirts Everything X This page has links to everything that can be found on this web site except my flam3 playground . If you'd like to read a few background words about the pieces feel free to have a look at the individual annual galleries which feature a little more by way of explanation. paying the bills...

28. Fractal World Gallery Thumbnails : Cosmic Recursive Fractal Flames Or Flame Frac Fractal World Gallery Home. Fractal World Gallery contains a collection of Pure flame fractals, Thanks for viewing the Fractal World Gallery. http://www.enchgallery.com/fractals/fracthumbs.htm

Fractal World Gallery contains a collection of Pure flame fractals, fractal flame composites, fractals, etc: established 1998 Flame Fractals date from 1998 to the Present by Cory Enc h I mages from this gallery may only be used with artist 's permission Fractal software includes Frax Flame and Apophysis for cosmic recursive fractal flames. FAQ I CONTACT I PRINTS More art work by Cory Ench at www.enchgallery.com images in room 6 click on the thumbnails for full view fractal image images in room 6 images in room 5 images in room 4 images in room 3 images in room 2 120 images in room Other non fractal art by Cory Ench at home Thanks for viewing the Fractal World Gallery. Please go to next gallery room for more cosmic recursive flame fractals. Don't forget to sign our guestbook and give some feedback. Sign Guestbook

29. Fractals For Mac OS X Program that generates fractal images. Several options for producing striking variations of fractal images, and includes advanced features for producing http://www.fractaldomains.com/

Fractal Domains Exploring fractals with your Macintosh Home Info Gallery Download ... Tutorial Fractal Domains 2.0.5 (Universal) is here! Get version 2.0.5 at download page ! See the news page for details. FD images at Zazzle! Over the years I have received requests for prints of the images in my gallery. Now you can purchase prints of a wide variety of high resolution images created with Fractal Domains. Choose from these featured images or go to the Fractal Domains Zazzle Gallery to see the full selection. Fractal Domains is a shareware program that generates fractal images. With Fractal Domains you can generate color images of the most popular fractal, the Mandelbrot set, and also generate images of the associated Julia sets. You can also generate an unlimited variety of fractal types based on rational functions, including fractals based on Newton's method and Halley's method. Fractal Domains has many options for producing striking variations of fractal images, and includes advanced features for producing high-quality images. Fractal Domains features include: Generation of Mandelbrot and Julia sets Generation of fractals based on iterating rational functions. The user may input expressions for any rational function (ratio of two polynomials).

30. Welcome To The Fractal EXtreme Web Site Home Page for Fractal eXtreme, a Win32 shareware program for fast 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

31. Module/fractal/index.html What essential information should you communicate to the representatives about fractals? During your presentation, you will want to appear relaxed and http://www.bcpl.net/~sullivan/modules/fractals/index.html

32. Fractal Frequently Asked Questions And Answers The Usenet newsgroup sci.fractals and the listserv forum fracl are devoted to discussions on fractals. This FAQ (Frequently Asked Questions) is an http://www.faqs.org/faqs/fractal-faq/

MultiPage Fractal Frequently Asked Questions and Answers There are reader questions on this topic! Help others by sharing your knowledge From: stepp@muvms6.mu.wvnet.edu (Ermel Stepp) Newsgroups: sci.fractals stepp@marshall.edu mail-server@rtfm.mit.edu with the message: send usenet/news.answers/fractal-faq The hypertext version of the Fractal FAQ has hyperlinks to sources on the World Wide Web. It can be accessed with a browser such as xmosaic at http://www.cis.ohio-state.edu/hypertext/faq/usenet/fractal-faq/faq.html . Also, the hypertext version is online for review and comment at: http://www.marshall.edu/~stepp/fractal-faq/faq.html . Please suggest other links to add to the Fractal FAQ. For your information, the World Wide Web FAQ is available via: The WWW: http://sunsite.unc.edu/boutell/faq/www_faq.html alt.binaries.pictures.fractals http://www.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html Fractal Microscope http://is.dal.ca:3400/~adiggins/fractal/ Dalhousie University Fractal Gallery http://acat.anu.edu.au/contours.html

33. Fractal Curves And Dimension fractals burst into the open in early 1970s. Their breathtaking beauty captivated many a layman and a professional alike. Striking fractal images can often http://www.cut-the-knot.org/do_you_know/dimension.shtml

var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Fractal Curves and Dimension Fractals burst into the open in early 1970s. Their breathtaking beauty captivated many a layman and a professional alike. Striking fractal images can often be obtained with very elementary means. However, the definition of fractals is far from being trivial and depends on a formal definition of dimension. It takes a few chapters of an Advanced Analysis book to rigorously define a notion of dimension. The important thing is that the notion is not unique and even more importantly, for a given set, various definitions may lead to different numerical results. When the results differ the set is called fractal. Or in the words of Benoit Mandelbrot [Ref 2], the father of fractals: A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension. The topological dimension of a smooth curve is, as one would expect, one and that of a sphere is two which may seem very intuitive. However, the formal definition was only given in 1913 by the Dutch mathematician L. Brouwer (1881-1966). A (solid) cube has the topological dimension of three because in any decomposition of the cube into smaller bricks there always are points that belong to at least

34. Linda S Fractals Galleries of Ultra Fractal, Frax Flames, and collage. http://www.lindabucklin.com/fractals/

NEW! Gallery One Gallery Four Frax Flame Gallery Click on a picture to enter a gallery Three NEW Galleries added 6/24/04 NEW! GalleryTwo Gallery Five Frax Flame 2 NEW! Gallery Three Apophysis One Fractal Collage Visit ‘Linda’s Universe’ - My Main Page, with links to all of my sites, including ‘Cats! Cats! Cats! and ‘Linda’s World’. Visit Linda’s World to see my paintings, drawings and digital images. There are also two galleries that exhibit mental illness - related art. My photos, paintings, drawings and digital images of cats. Visit my Renderosity Gallery to see a wide selection of my artwork. Lots of links to some gorgeous fractal galleries! Contact Linda Bucklin Linda's Fractals Gallery One Frax Flame1 ... Frax Flame 2

35. Aros Fractals Aros fractals is a free, hires, truecolor fractal program for Windows95, NT and Macintosh. http://www.arosmagic.com/Fractals/

F i lle Download more cool software! Aros Magic Viewer Aros Magic Checkers Aros Magic Reversi Aros Magic Go-Moku/Ninuki-Renju/ Renju Aros Fractals W elcome to the world of Fractals! With Aros Fractals you can explore some classical fractal images at extremely high resolutions (physical size and color depths). For the current version of Aros Fractals and other information, you've reached the correct destination. We are constantly updating information here, so visit often and let us know if there is additional material you would like to see here. System Requirements Minimum All Platforms: Floating Point Unit (FPU). 8-bit video card (256 colors). Sufficient hard disk space to store large images. 486DX/25. 8M RAM. Windows NT: 486DX/25. 16M RAM. Macintosh: 68020. System 7.0. Thread Manager. 8M RAM. (Aros Fractals will let you know if it is missing any additional required components at startup time). Recommended All Platforms: 32-bit video card (True Color) Pentium. 24M RAM.

36. Pollock's Fractals | Math | DISCOVER Magazine That isn t just a lot of splattered paint on those canvases, it s good mathematics. Visit Discover Magazine to read this article and other exclusive science http://discovermagazine.com/2001/nov/featpollock

document.write(''); Log In Subscribe Give a Gift Archives ... Customer Service SEARCH Technology Space Human Origins Living World ... RSS Daily Dose March 14 : Resourceful sand dollars evade predation by cloning themselves. For NASA , this week’s missions didn’t go exactly as planned March 13 Sci-fi reality check: laser-guided bots, nano-brains , and the search for a new dimension Geneticists create manic mice —a possible blessing for the mouse art world Science News Mighty Electric Fields Found Inside Cells 15 million volts per meter? Ay, carumba. Science Says War Is Over Now (Given the Right Conditions) Given adequate food, fuel, and gender equality, mass conflict just might disappear. Keeping Up With The Picards The director of Jumper on putting teleportation on-screen. Mission to the Forgotten Planets Before the Pluto fiasco, two asteroids were stripped of planet status. Einstein Didn't Grok His Own Revolution He thought black holes and quantum mechanics were too weird to be true. The Incredibly Strong See-Through Bicycle Want a lighter bike? Poke holes in it—the more the better. The Borderline Whack-Jobs Who Pioneered Psychoanalysis Some were fanatical prudes, while one was dubbed “the Pied Piper of carnality.”

37. What Are Fractals? Well, the surface of a fractal has features on a large scale which are the same basic shape as smaller scale features, so when you look at a fractal and http://www.physlink.com/Education/AskExperts/ae458.cfm

Ask the Experts Physics Job Board ... eStore Local in California? Visit one of our retail stores. XUMP - Science Toys Question What are fractals? Asked by: Ryan Answer A fractal is a mathematical object that is self-similar irrespective of scale. So what does that mean? Well, the surface of a fractal has features on a large scale which are the same basic shape as smaller scale features, so when you look at a fractal and zoom in or out, it still basically looks the same. A classic example is the Koch curve. Imagine an equilateral triangle. Then in the center third of each edge, place a smaller equilateral triangle. If you have it right you should now have a symmetrical six pointed star. Now in the central third of each edge, again place an equilateral triangle. (these edges are 1/9th the length of the original). Repeat an infinite number of times. As you zoom in on an edge, the shape looks the same forever. And what is the perimeter of this polygon you have just constructed? Infinity, even though it fits inside a circle with finite radius. More information on fractals.

38. Fractals And Fractal Art fractals Your guide to the best web sites for fractals and fractal art. http://thinks.com/webguide/fractal.htm

Sponsored Links Electronic Sudoku Multiplayer Games Bingo Brain Games ... Home Fractals and Fractal Art AllisonArt's Cyberhome Great images by Linda Allison. Amazing Seattle Fractals! Doug Harrington's site has an online, step by step fractal tutorial, complete with screenshots to help people create their own fractal art. It also features fractal art galleries,fractal animations,free fractal software and a free fractal screensaver (rated by ZD Net as an Editor's Pick 5 Star Download). Doug's fractal art has been featured at M.O.C.A.(Museum of Computer Art) and has won several other site awards. Art Matrix Fractals A company producing fractal posters, postcards, slides, videos, etc. Don Archer's Fractal Art and Music An impressive site with many pages of interesting fractal images. Earl's Computer Art Gallery Fascinating images created by Earl Hinrichs using his own software. Fractal eXtreme Useful pages giving an introduction to fractal theory, and a gallery of images produced by the software. Fractal Gallery by Ken Keller Many stunning images, categorized as: Lucid Forms (fractals that are recognizable as everyday objects), Traditional Forms (fractals that do not greatly deviate from Magnification 1, or contain commonly found features within typical fractal formulas), Abstract Forms (fractals that seek to convey atmospheres, emotions and ideas). All images displayed may be purchased as prints. Fractalism The images in these galleries are snapshots from one artist's vision of a place he calls Fractal Land.

39. Cool Math - Fractals - Fractal Art, Lessons And Generators To view the fractal in all its glory, just click on it! To learn about what a fractal is, check out my lesson The Math of fractals http://www.coolmath.com/fractals/gallery.htm

Your browser does not support the IFRAME tag. Your browser does not support the IFRAME tag. Coolmath's Fractal Gallery Very cool fractals made from math! Check out the new stuff at the bottom of the page! Sorry, your browser doesn't support Java. To view the fractal in all its glory, just click on it! Please do not link to any individual image - the URLs will change. To save an image, right click on the image - PC's only... Mac's, you're on your own! Students are the only ones who can use these images and it must be for a school project, but not if it's a website. fractals 1 fractals 2 fractals 3 fractals 4 fractals 5 fractals 6 fractals 7 fractals 8 fractals 9 fractals 10 fractals 11 fractals 12 fractals 13 fractals 14 fractals 15 fractals 16 fractals 17 fractals 18 fractals 19 fractals 20 fractals 21 fractals 22 fractals 23 fractals 24 fractals 25 fractals 26 fractals 27 fractals 28 fractals 29 fractals 30 To learn about what a fractal is, check out my lesson: The Math of Fractals Create your own fractals: Coolmath's Fractal Generators: Fractal Generator 1 Fractal Generator 2 Fractal Generator 3 Fractal Generator 4 ... Fractal Generator 5 Your browser does not support the IFRAME tag.

40. Fractal Gallery The Beauty of fractals. Gallery of Fractal Images generated by FractInt. http://fractals.hauner.cz/

Adam Hauner Adam Hauner

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