61. Les St Clair's Fractal Panorama - Fractal Home Page Les St Clair s fractal images, Paint Shop Pro tubes and fractal Java applets. http://www.les-stclair.co.uk/fractals/fracindex.htm

Fractint Galleries Ultra Fractal Galleries Tiera-Zon True-Color Fractal Gallery Flarium 24 True-Color Fractal Gallery Fractal eXtreme Zoom Movies Chebyshev Formulas for Fractint Fractal Picture Tubes for Paint Shop Pro If you have a Java friendly browser try - Fractal Java Applets Fractint Mail List - Parameter Files May.03.2003. Fractint Pars Galore! (inc. Jim Muth's FOTD) Jul.13.2006. Thank you to the 9000+ visitors who stopped by my CompuServe Site (1998-2000) This page last updated on: Jul.13.2006 You can contact me at: les.stclair[no-spam]btinternet.com ...Just replace the square brackets with @ Return to Les St Clair's WWW Home Page Free counter

62. 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 -

63. Blatte's Fractals Welcome to Blatte s fractals. I generally work in three different programs; KPT Fraxplorer, Ultra Fractal and Apophysis, and I previously did some work in http://exoteric.roach.org/frax/index.html

Welcome to Blatte's Fractals. I generally work in three different programs; KPT Fraxplorer, Ultra Fractal and Apophysis, and I previously did some work in KPT Fraxflame. All images are high-quality jpgs at approximately 640x480 pixels. If the background of this webpage appears black to you, you are likely seeing these images darker than I intend. If you would like to use these images on your personal webpage, you must read my Nightingale The Number of the Hours Legacy Valiant Apophysis Gallery 24 August 24, 2007 16 Images Ultra Fractal Gallery 15 July 15, 2007 16 Images Apophysis Gallery 23 July 2, 2007 16 Images Apophysis Gallery 22 June 11, 2007 16 Images Apophysis Gallery 21 May 21, 2007 16 Images Apophysis Gallery 20 January 27, 2007 16 Images Apophysis Gallery 19 January 8, 2007 16 Images Ultra Fractal Gallery 14 December 12, 2006 16 Images Fraxplorer Gallery 14 October 29, 2006 16 Images Fraxplorer Gallery 13 October 20, 2006 16 Images Ultra Fractal Gallery 13 August 18, 2006 16 Images Ultra Fractal Gallery 12 June 5, 2006 16 Images Apophysis Gallery 18 April 28, 2006

64. TED | Talks | Ron Eglash: African Fractals, In Buildings And Braids (video) TED Talks I am a mathematician, and I would like to stand on your roof. This is how Ron Eglash greeted many African families while researching the http://www.ted.com/index.php/talks/view/id/198

Themes Talks Speakers Joining TED ... TED Prize dojo.require("form.widget.InputClear"); Talks Ron Eglash: African fractals, in buildings and braids Filmed Jun 2007; Posted Nov 2007 close video You either have JavaScript turned off or an old version of Macromedia's Flash Player. Get the latest Flash player Ratings Rate this talk View all ratings ( Rate this talk with 3 clicks. You can choose 3 words, or vote for the same word 3 times. Rate Once Rate Twice Rate Three Times Jaw-dropping Rate Once Rate Twice Rate Three Times Persuasive Rate Once Rate Twice Rate Three Times Courageous Rate Once Rate Twice Rate Three Times Ingenious Rate Once Rate Twice Rate Three Times Fascinating Rate Once Rate Twice Rate Three Times Inspiring Rate Once Rate Twice Rate Three Times Beautiful Rate Once Rate Twice Rate Three Times Funny Rate Once Rate Twice Rate Three Times Informative Rate Once Rate Twice Rate Three Times OK Rate Once Rate Twice Rate Three Times Unconvincing Rate Once Rate Twice Rate Three Times Confusing Rate Once Rate Twice Rate Three Times Longwinded Rate Once Rate Twice Rate Three Times Obnoxious Rate This Talk About this Talk "I am a mathematician, and I would like to stand on your roof." This is how

65. Java Fractal Generator And Introduction To Fractal Mathematics Java Fractal Generator and Introduction to Fractal Mathematics. http://www.utopiansky.com/labratory/fractals/

Please support this site by getting t-shirts and gifts at MagentaStudios.com JavaMan Mandelbrot Fractal Generator Java Applet by Nick Lilavois What is this thing? This is a Fractal generator written in the Java programming language How to use the Applet You can zoom into the fractal image by either clicking on it or drawing a square around an area. The best places to zoom in are right on the edge of the black shape, near the colored bands. You can also set the fractal's parameters in each of the selectors and fields to the left of the fractal image. The first selector is the formula selector. With this box you can choose which fractal formula will be rendered. The first option on the list is the Mandelbrot set. This applet has a highly optimized Mandelbrot equation, and that formula will render much faster than any of the other formulas. The second selector is the plane selector- what the plane options are is explained below in the Introduction to Fractal Mathematics section.

66. [ Wu :: Fractals ] an introduction to fractals. topics discussed include fractals in nature and industry, and the basic mathematics behind generating several classic http://www.ocf.berkeley.edu/~wwu/fractals/fractals.html

FRACTALS an introduction to fractals. topics discussed include fractals in nature and industry, and the basic mathematics behind generating several classic structures, including the mandelbrot set and sierpinski triangle. also included is a gallery of choice fractal art, including a few pieces made by myself. Fractal Intro Mandelbrot Sierpinski Gallery ... Return to Homepage A Short And Entertaining Introduction to Fractals a fractal is a geometric shape that can subdivided into parts, each of which is a reduced-size copy of the whole. the term was coined in the 1960s by benoit mandelbrot, a mathematician at IBM who adapted it from the latin adjective fractus , meaning "fragmented." to get a feel for what a fractal is, imagine inspecting a long, craggly, leafless tree branch on a frosty winter day. as your eyes scan the branch from its base to its tips, you notice that many sub-branches are generated along the way, and each sub-branch has a structure symmetric to the original, but smaller in scale. these sub-branches in turn fork off self-symmetric branches of their own. in the purest sense of a fractal, we imagine this branching process as never ending. you could compare it to the effect produced when two mirrors are faced toward each other, producing a claustrophobic, tunnel-like view of infinite imitation at smaller and smaller scales. a nice example of this is seen in the mandelbrot fractal at left, designed by Paul deCelle. usually one's first response to fractals is simply this: they are beautiful! indeed, they are visually arresting, and there are many reasons why. perhaps one reason is that they exhibit extreme levels of

67. Kepler's Fractals Kepler s solids can be fractalized in the same manner the Star of David is made into a Koch Snowflake. http://www.tabletoptelephone.com/~hopspage/Kplrfrct.html

This page has moved to http://clowder.net/hop/kepler/Keplrfrct/Keplrfrct.html

68. Kevin Gross Home Page Kevingross.Net is a fractal artwork exhibit and sales website. Contemplating Chaos 2008 Fractal Calendars Now Available! http://www.goshen.edu/~kevin/fractals.html

69. 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 boundary of the Mandelbrot set is a famous example of a fractal Another 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.

70. 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

Search Site Algebra Applied Mathematics Calculus and Analysis ... Fractals 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 Sierpinski sieve ... Barnsley's fern , and Mandelbrot set SEE ALSO: Attractor Backtracking Barnsley's Fern Box Fractal ... [Pages Linking Here] 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

71. 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.

72. 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

73. 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

74. 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.

75. 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

76. 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

77. Fractal Art By Vicky - Fractal Wallpaper For Desktop Fractal art free desktop fractal art wallpaper from images by Vicky Brago-Mitchell. http://www.abm-enterprises.net/wallpaper.html

Art Fractal Classical Music FRACTAL ART BY VICKY Welcome to my gallery! These images are based on a kind of math called fractal geometry, and are created by repeating simple patterns billions and trillions of times. Until today's fast computers became widely available, only mathematicians had seen fractals; now everyone can enjoy their intricacy and beauty. (For more explanation read Fractal Geometry Except for a few of the first pictures that have only one layer, everything here was made with Ultra Fractal software on a PC. I usually start with five or six layers and end up with three or fourUltra Fractal's layering is a lot like Photoshop's. My pictures were shown at the Biennale Internazionale dell'Arte Contemporanea Film: biennale-firenze.mp4, 327 MB which opened on Saturday, December 3, 2005 at the Fortezza da Basso in Florence, Italy. ( Cascade is at about 18:18 of the film.) Also at the Agora Gallery in NYC December 15, 2005 - January 10, 2006. I did the cover art for the December 2005 issue of Latin Finance pdf ) magazine. They wanted bluebrown with the colors in Glitter. I tried!

78. 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/

1997-2007 Junpei Sekino Stories about Fractal Plotting 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.

79. A Fractal Christmas - Inside Science News Service Short Article from Inside Science News Service describing the basics. Includes illustrations and links. http://www.aip.org/isns/reports/2003/086.html

SEARCH AIP More information: Boston University James Riordon American Institute of Physics A fractal Christmas In the case of the fir tree standing in a Christmas tree lot, each branch has structure that, when studied up close, resembles a whole tree, and on each branch there are a smaller, tree-like branches. Even the needles on the tiniest branch are arranged in patterns reminiscent of the structure of the entire fir tree. The tree's structure can be described by a mathematical equation. The equation and the tree are fractals, patterns that repeat at various scales. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines. Fractals will look the same regardless of the scale shown. For instance, an ice crystal viewed at full size and a detail of one small branch of the ice crystal have a similar structure it's often difficult to tell which is the magnified image.

80. "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.

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