61. Digg - Flame Fractals Offer A Feast For The Eyes (52) Fantastic Fractal Flames using Apophysisa freeware Windows application with which you can design and render Fractal Flames. http://digg.com/software/Flame_Fractals_offer_a_feast_for_the_eyes

@import "/css/63/global.css"; @import "/css/63/forms.css"; @import "/css/63/permalink.css"; @import "/css/63/comments.css"; @import "/css/63/lightbox.css"; var pagetype = "permalink"; digg Join Digg About Login Username Password Remember? Search Digg... Popular Upcoming All News ... Flame Fractals offer a feast for the eyes (52) Fantastic Fractal Flames using Apophysisa freeware Windows application with which you can design and render Fractal Flames. Submitted: 38 days ago, made popular 38 days ago Submitter: Share: Share Bury It: Bury Favorite: Favorite? diggs digg it Comments ( Who Dugg or Blogged It? Blog It Email It sort by most diggs sort by date (show all) sort by date (-10 or higher) sort by date (-4 or higher) sort by date (0 or higher) sort by date (+5 or higher) sort by date (+10 or higher) Hide Profanity Expand Full Tree Global Settings +51 diggs by DeadBabySoup on All I see are hundreds of crabs trying to eat me. View replies to this comment (most popular has ... diggs) +6 diggs by on Be sure and click "Next Image" to see other pictures. You can also click any pic and see it in a larger view. View replies to this comment (most popular has ... diggs) +9 diggs by on Crab... Battle...

62. 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 CHOW: Does drinking ice water burn calories? 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 ... Self-Deception, get thee behind me! NEW What do you think?

63. Index Of Www.fractals.net/ The fractals directory ought to be self explanatory. See office for a virtual tour of our company Empire Industries. And finally, the public directory http://www.fractals.net/

Welcome to www.fractals.net! Be sure to check out the fractals. The home directory has a page I like to use as a web browser's home page as it contains many useful and cute links. The fractals directory ought to be self explanatory. See office for a virtual tour of our company Empire Industries. And finally, the public directory contains some commonly used files. It is updated frequently, but you should get current versions from the original sites when possible. This is simply a convenience intended for use by our technical support personnel. Name Last modified Size Description ... home/ 01-Apr-2006 00:00 - fractals/ 01-Apr-2006 00:00 - 01-Apr-2006 00:00 - public/ 01-Apr-2006 00:00 - pics/ 05-Jun-2006 01:11 - reunion/ 05-Jun-2006 01:11 - ware/ 05-Jun-2006 01:11 -

64. Fractal - Wikipedia, The Free Encyclopedia Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets. http://en.wikipedia.org/wiki/Fractal

Fractal From Wikipedia, the free encyclopedia Jump to: navigation search The Mandelbrot set is a famous example of a fractal A closer view of the Mandelbrot set. A fractal is generally "a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity . The term was coined by Beno®t Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A fractal often has the following features: It has a fine structure at arbitrarily small scales. It is too irregular to be easily described in traditional Euclidean geometric language. It is self-similar (at least approximately or stochastically It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve It has a simple and recursive definition Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.

65. Fractal -- From Wolfram MathWorld A fractal is an object or quantity that displays selfsimilarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same http://mathworld.wolfram.com/Fractal.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Fractal A fractal is an object or quantity that displays self-similarity , in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension . The prototypical example for a fractal is the length of a coastline measured with different length rulers . The shorter the ruler , the longer the length measured, a paradox known as the coastline paradox Illustrated above are the fractals known as the Gosper island Koch snowflake box fractal Barnsley's fern , and Mandelbrot set SEE ALSO: Attractor Backtracking Barnsley's Fern Box Fractal ... Zaslavskii Map REFERENCES: Barnsley, M. F. and Rising, H. Fractals Everywhere, 2nd ed. Boston, MA: Academic Press, 1993. Bogomolny, A. "Fractal Curves and Dimension." http://www.cut-the-knot.org/do_you_know/dimension.shtml

66. Suzanne Alejandre - Fractal Links Basic fractal information for the math teacher or interested user, with Internet resources to expand your fractal knowledge. http://mathforum.org/alejandre/workshops/fractal/fractal3.html

Suzanne's Math Lessons Fractals Suzanne Alejandre Magic Squares Multicultural Math Fair Polyhedra ... Tessellations What is a fractal? From the Fractal FAQ: "A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale." "There are many mathematical structures that are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set, and Lorenz attractor. Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes." The Fractal FAQ was created and edited by Ken Shirriff through September 26, 1994. The current editor is Ermel Stepp. Alan Beck writes: "Basically, a fractal is any pattern that reveals greater complexity as it is enlarged. Thus, fractals graphically portray the notion of 'worlds within worlds' which has obsessed Western culture from its tenth-century beginnings." Beck further explains that when we look very closely at patterns that are Euclidean, the shapes look more and more like straight lines, but that when you look at a fractal up close you see more and more details.

67. Infinite Fractal Loop Many sites, graphical and text listings, statistics, news. http://www.fractalus.com/ifl/

This is the new home page of the Infinite Fractal Loop, a web ring dedicated to fractal art . To begin browsing fractal galleries in the Loop, click either of the large arrow buttons at the bottom of the page. Graphical list of all sites in the Loop Text-only list of all sites in the Loop Frequently Asked Questions (FAQ) Join the Loop ... About the Infinite Fractal Loop Web site hosted by fractalus.com

68. Ultra Fractal: Advanced Fractal Animation Software Ultra Fractal is the best tool for creating fractal art. It creates smooth, truecolor fractal images with a wealth of fractal formulas and coloring http://www.ultrafractal.com/

Buy Now Upgrade Free Trial Ultra Fractal is the best tool to create fractal art. It is very easy to use and yet more powerful than any other program. Download the free trial and learn how to create fractals with the great built-in tutorials Buy Ultra Fractal now and start creating fractals today! Visit the Showcase galleries to see more fractals created with Ultra Fractal View more screen shots Join the Ultra Fractal mailing list to share your fractals and ask questions Ken Childress Showcase Galleries Ultra Fractal features Layering, animations, render to disk, write formulas, direct coloring algorithms... View online manual Download PDF manual Ultra Fractal 4.04 released April 12, 2007 - This free update adds Windows Vista compatibility and fixes various other issues Ultra Fractal courses Take an online course at the Visual Arts Academy: Working with Ultra Fractal or Ultra Fractal Formulas Spanish German help files and PDF manuals Frederik Slijkerman

69. A Fractal Art Gallery By Ken Keller Exploring the bounderies between Creation and Discovery. A growing gallery of original fractal images. Come explore the infinite Fractal Universe. http://home.inreach.com/mapper/

A Fractal Art Gallery by Ken Keller Shore Along the Void -UPDATED- Gallery 80 High Resolution Wallpaper Win a Free Fractal Print! ENTER DRAWING HERE BUY ART Free fractal Screen Savers Most Popular Fractals ... Join the Gallery secure double opt-in Send a Fractal greeting card Landscapes Fractal Faces Early Earth II Mardi Gras Mask For More Information on Fractals Click Here Fractals for Beginners - Fractal Software Fractal Science - Fractal Links Fractal Verse Short Poems inspired by the Fractal image Trance Dance and Fractal Art "Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently." Benoit Mandelbrot Search the Fractal Gallery What is Fractal Art? Fractals Published Fractal Art Essays Viewer's Comments ... The Spheres of Consciousness Wonder comes from the awareness of ignorance. Awe comes from the loss of scale.

70. Fractalarts.com - Fractal Art Prints, Screensavers, Software & Tutorials Original fractal art, free trial fractal screensavers, fractal tutorials, fractal software. http://www.fractalarts.com/

FractalArts.com E-Mail: Seattle Fractals Digital Art: Fractal Art Prints Fractal Screensavers Purchase Screensavers ... Fractalarts Link Spectrum - Internet Resources Directory

71. Fractal Software Programs & Links On Paul N. Lee's Website Fractal related software and program application links on Paul N. Lee s website. http://home.att.net/~Paul.N.Lee/Fractal_Software.html

Fractal Links If you can't find what you are looking for in the below table of software programs, applications, tutorials and more, then additional fractal related information may be found in this 1,300+ line text file . Also, further information may also be found within the world renowned Fractal Census , where over 4,200 individuals are listed (plus statistics on software use and number of users per country). Even the first portion of the table below (which previously was in alphabetical order) is now listed in the order by programs having been acquired, tried, and/or used the most, so as to match the statistics from the Fractal Census list of applications. Software and Various Items Product / Type OS Description FractInt 20.0.00 (official release) FractInt 20.4.04 (developer's version) FractInt 21.0.05 (Beta for Windows) DOS, Win9x/ME/NT/2K/XP The best known FREEWARE fractal generator created for IBM PC's and compatible computers. It is the most versatile and extensive fractal program available for any price. This is the fractal program most used by schools, colleges, and universities. Also, other ports of the program may be found for MAC, UNIX/Linux Windows , etc. It is one of the oldest free software programs still being maintained (according to many sources, such as

72. Sekino’s Fractal Gallery Art from math professor Junpei Sekino, blended with discussion of formula types and colouring methods. http://www.willamette.edu/~sekino/fractal/

1997-2008 Junpei Sekino Stories about Fractal Plotting and Fractal Art The Divergence Scheme The Convergence Scheme Fatou Patterns Julia Patterns ... Experiments in Three-Dimensional Plotting Speaking loosely without technical terms such as the Hausdorff-Besicovitch dimension and topological dimension of a set of points, a fractal , which was coined by Benoit Mandelbrot in 1975, is a geometric shape that is self-similar , i.e., a large part of it contains a great many smaller parts that resemble the large part in some way see Figure 1 below. Nature is filled with fractals as seen in such objects as mountains, shorelines, trees (branches, barks and roots), ferns, fluid flow patterns, cloud formations (with or without lightning), blood vessels and mycelium strands. Mathematicians conceived the notion of fractal more than a hundred years ago and have since developed deep and extensive theories to formulate a field now referred to as fractal geometry . A novel and intriguing computer-generated fractal image plotted by Mandelbrot in 1979 and later called the Mandelbrot set stimulated and accelerated the development. It is now known that fractal geometry not only provides mathematical insights into natural objects and phenomena that are beyond the reach of Euclidean geometry, but also has numerous applications in and significant influence over surprisingly many areas in sciences, mathematics and art.

73. Illuminations Fractal Tool You can make changes to these shapes to create your own fractal. After you have made changes, use the Forward, Back, and Play buttons to watch the http://illuminations.nctm.org/ActivityDetail.aspx?ID=17

74. Welcome To The Fractal Foundation The Fractal Foundation is a nonprofit organization whose mission is to educate and inspire people about the joy of math, art, science and technology. http://www.fractalfoundation.org/

Home Fractals in Schools Public Speaking Chaos Theory? ... Join Mailing List Albuquerque Fractal Challenge Winners Announced! Eight winners and eight finalists have been chosen from the entries to the Albuquerque Fractal Challenge. See the winning artworks , and what we plan to do with them... FIRST FRIDAY FRACTALS Next Shows: April 4'th 6:00, 7:00 and 8:00 PM in the Natural History Museum Planetarium. ***Buy Tickets Now!*** Zoom deep into fractals in this educational and extremely entertaining immersive presentation, suitable for all ages. Learn More... Over 7000 people have now seen this show, which was awarded "Best Event Unique to our City" in the Alibi's 2007 Best of Burque. Albuquerque Community Foundation has awarded a grant to the Fractal Foundation to bring fulldome fractal shows into schools in Albuquerque using a portable, inflatable planetarium. Please Contact Us if you're interested in bringing a presentation to your school in Albuquerque. Invite the Fractal Foundation to bring a fractal presentation to your school. More info...

75. "of A Fractal Nature" Photography By Gayla Chandler Shown here, the stage4 Sierpinski tetrahedron provides a powerful visual introduction to fractal geometry and the concept of self-similarity , http://www.public.asu.edu/~starlite/

of a Fractal Nature photographic Math-Art essays highlighting mathematics in the natural world (geometric fractals mimic magnification dilitational symmetry in Nature) inspired by the teachings and scientific investigations of Heinz-Otto Peitgen and Richard F. Voss Shown here, the stage-4 Sierpinski tetrahedron provides a powerful visual introduction to fractal geometry and the concept of "self-similarity", in which a shape can be broken into smaller copies of the whole. Each new stage is composed of 4 smaller copies of the previous stage. As the number of stages increases, the Sierpinski tetrahedron approaches "exact self-similarity". Such geometric fractals provide an important scientific model for characterizing many of the complex processes and shapes found in the natural world, that are echoed in the settings of the tetrahedra. Trees, land formations, clouds, and their images exhibit "statistical self-similarity" in which a small part "looks like", but not "exactly like" the whole. Just as a part of the Sierpinski tetrahedron reminds one of the whole, a small branch of a tree reminds one of the entire tree. The mathematics of fractal geometry and the science of chaos are now bridging the gaps between math, science, art, and culture. They treat the messiness of the everyday world. They are based on natural self-similarity and observations of complicated behavior from simple equations. They provide a new mathematical language for capturing, manipulating, and simulating nature.

76. More Fractal Pictures More Fractal Pictures THIS SIT E IS NO LONGER AVAILABLE. ALL IMAGES FROM THIS SITE CAN BE FOUND AT THE FOLLOWING WEB SITES! http://www.lerc.nasa.gov/Other_Groups/K-12/fracpage.html

More Fractal Pictures THIS SIT E IS NO LONGER AVAILABLE. ALL IMAGES FROM THIS SITE CAN BE FOUND AT THE FOLLOWING WEB SITES!!!! ftp://ftp.csus.edu/pub/alt.fractals.pictures/ Spanky Fractal Page Please send any comments to: Web Related: David.Mazza@grc.nasa.gov Technology Related: Thomas.J.Benson@grc.nasa.gov

77. ICM 2006 Benoit Mandelbrot Fractal Art Contest The Benoit B. Mandelbrot Fractal Art Contest is being held to select artwork for ICM 2006 (International Congress of Mathematicians), Sponsored by FECYT http://www.fractalartcontests.com/2006/

@import "/2006/common/icm2006.css"; About Sponsors Winners Entries ... Hosted by fractalus network.

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