21. Spanky Welcome Oct 15, 1999 The Spanky Fractal Database is a collection of programs, images, and other material all relating to the subject of fractals. http://spanky.triumf.ca/

THE SPANKY FRACTAL DATABASE The Elastic Fractal Welcome to the Spanky Fractal Database I also point to a great deal of material that is not at this site. Consequently I have no control of when this information or service is removed or am I notified if the URL becomes invalid. I try to check my indexes periodically to see what is still valid, but it is not an automated process. If you find URL's that I point to have become outdated and constantly fail to respond on your attempts to load them, (over several days) then please inform me of this problem and I will remove them from my lists. Mirrors of Spanky Fractal Database The main site for this fractal database spanky.triumf.ca is now completely mirrored at spanky.fractint.org Many thanks to Damien M. Jones at Fractalus for hosting the mirror site and for his help in setting it up. New PNG image format used Enjoy and discover. A Table of Fractal Information. What's New in Fractals An index of Fractal material at Spanky. Some General information about Spanky.

22. A@a__frActAl__a@a Numerous fractal images, various categories. Screensavers. http://fractales.free.fr/

23. Fractals | Define Fractals At Dictionary.com –noun Mathematics, Physics . a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale http://dictionary.reference.com/browse/fractals

24. Fractals For IPhone, IPod Touch, And IPad On The ITunes App Store Learn more, read reviews, and download fractals by Pomegranate Software on the iTunes App Store. http://itunes.apple.com/us/app/fractals/id300542371?mt=8

25. Fractals by HB IFS http://www.worldscinet.com/fractals/

Home Contact Us Join Our Mailing List New Journals ... Advanced Search Print ISSN: 0218-348X Online ISSN: 1793-6543 RSS Feed About FRACTALS Editorial Board Contact FRACTALS Sample Issue Abstracting/Indexing ... Online Gateways How To Order Order Online Price Information Request for Complimentary Print Copy Dispatch Dates For Authors Guidelines for Contributors Online Submission Call for Papers Author Rights RELATED JOURNALS International Journal of Bifurcation (IJBC) Advances in Complex Systems (ACS) RELATED BOOKS Analysis And Control Of Nonlinear Systems With Stationary Sets Handbook On Biological Networks RELATED LINKS Life Sciences Books Nonlinear Science Books Mathematics Journals HOME ... Fractals Fractals Complex Geometry, Patterns, and Scaling in Nature and Society Current Issue All Volumes (1993-2010) News The Impact Factor for FRACTALS in 2009 is Many thanks for the hard work put in by the Editorial Board and contributors of FRACTALS. An Appeal from the Honorary Editor to the Readers of Fractals Announcement: After four years of dedicated service to the Fractals journal, Dr. Janos Kertesz will retire from his role as Regional Managing Editor (Europe), but will continue to serve as a member of the Editorial Board. Dr. Kertesz will be succeeded by current editorial board member Dr. Miroslav M. Novak of the Faculty of CISM, Kingston University, England.

26. Fractals The primary focus of the Community Learning Network (CLN) is to help K12 teachers integrate Information Technology into their classrooms. This CLN menu page provides links to http://cln.org/themes/fractals.html

27. Understanding Instability: Mandelbrot, Fractals, And Financial Crises » TripleC fractals are interesting images created from complex numbers. http://triplecrisis.com/understanding-instability-mandelbrot/

Home About Blogger Bios Partners ... TripleCrisis Global Perspectives on Finance, Development, and Environment Print This Post Understanding Instability: Mandelbrot, Fractals, and Financial Crises Alejandro Nadal Lightning in the sky does not follow a straight line. The irregular patterns in a cauliflower or the capricious forms of a tree’s branch are a challenge to the clean geometric figures we learn in school. Neither the straight lines, nor the smooth curves of that geometry exist in nature. But after the wonderful work of Benoit Mandelbrot it is now possible to get closer to a theory of the manifold wrinkles and rough surfaces that are the stuff of our universe. And our economies. Ten days ago this great mathematician, the creator of fractal geometry and other wonders closely related to chaos theory, passed away. The word fractal , coined by Mandelbrot, denotes a logical semi-geometric figure that can be divided as many times as desired and every time you zoom in on these smaller fractions you end up looking at a replica of the original figure. The best example of this is the famous Koch snowflake , in which the wrinkles are intimately related to patterns of affinity between the parts and the whole. Another example is the cauliflower: no matter how many times one breaks it up, when the pieces are magnified, the same ruggedness and wrinkles of the whole reappear. The property of self-similarity emerges even in the tiniest crumbles.

28. Fractals Introduction. All of the shapes above have a common name. They are all fractals. But what really is a fractal? What words would you use to describe them? http://staff.harrisonburg.k12.va.us/~dflick/fractal/fractals.htm

F R A C T A L S Inroduction Task Process Resources Evaluation Conclusion Introduction All of the shapes above have a common name. They are all fractals. But what really is a fractal? What words would you use to describe them? Where can fractals be found in the real world? In this webquest you will find the answer to these questions and begin your understanding of the fascinating world of fractals. Task In this webquest you will learn about fractals through the internet. First, you will visit the web sites below in order to complete the the worksheet. When you are finished with the worksheet you and your partner will construct your own fractals using the internet. Process !. Get into groups of two. 2. With your partner visit the web sites listed below under resources in order to answer the questions on the worksheet. 3. Next make a Jurassic Park fractal with the 1'' by 11'' piece of paper you were given by following the directions on this web site 4. Finally create your own Sierpinski Triangle by clicking here.

29. Mathematics Archives - Topics In Mathematics - Fractals KEYWORDS Lesson Plans, SelfSimilarity and Recursion, Geometric fractals, fractals and the Chaos Game, Pascal s Triangle, Chaos, The Mandelbrot Set http://archives.math.utk.edu/topics/fractals.html

Topics in Mathematics Fractals Chaos, Fractals, and Arcadia ADD. KEYWORDS: The Chaos Game, The Sierpinski Hexagon, Iterated Function Systems Chaos in the Classroom, Boston University ADD. KEYWORDS: The Chaos Game, Self-similarity, Fractal Dimension, Iterated Function Systems Clifford A. Pickover's Homepage ADD. KEYWORDS: Cellular Automata, Carotid-Kundalini Functions, Books, Puzzles, JAVA Geometry Explorer The Dance of Chance ADD. KEYWORDS: Random Processes, Branching Structures, Patterns in Nature, Student Activities, Laboratory Experiments, Visualization, Software, Fractal Dimension, Fractal Coastlines Diffusion-limited Aggregation Exploring Fractals ADD. KEYWORDS: Lesson Plan, Tutorial, Bibliography Fantastic Fractals ADD. KEYWORDS: Tutorials, Gallery, Fractal Music, Bibliography, Software, Newsgroups Fract-ED ADD. KEYWORDS: Iteration, Attractor, Software, Tutorial, Bifurcation, Self-similarity, Strange attractor Fractal Clouds The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

30. Welcome To Mint's Fractals Several galleries of Ultra Fractal generated images. http://www.btinternet.com/~fractals/

Welcome All the fractal images on this site were created in Ultrafractal - a wonderful shareware fractal generator for Windows created by Frederick Slijkerman. ENTER Previous 15 Previous Site Next Site ... Mint

31. Fractals http//www.bugman123.com/fractals/index.html The heavens declare the glory of God; And the firmament shows His handiwork. Psalm 191. http://www.bugman123.com/Fractals/Fractals.html

This Page has Moved! You will be automatically redirected to the new address in 15 seconds. New address: http://www.bugman123.com/Fractals/index.html "The heavens declare the glory of God; And the firmament shows His handiwork." Psalm 19:1

32. Fractal: Definition From Answers.com n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. fractals are used http://www.answers.com/topic/fractal

33. 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

34. Fractals Unleashed You have found one of the most comprehensive websites about fractals on the web! fractals are very beautiful geometric figures that can be used to describe http://library.thinkquest.org/26242/full/

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35. Fractals Unleashed You have found one of the most comprehensive websites about fractals on the web! fractals are very beautiful geometric figures that can be used to describe nature. http://library.thinkquest.org/26242/full/index.html

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36. Fractalus (Fractals/Fractal Art, Contests, And Info) fractalus.com is a site dedicated to fractal art, information, and software. Artwork by Damien M. Jones, Sharon Webb, Alice Kelley, Linda Allison, http://www.fractalus.com/

Galleries Damien M. Jones Sharon Webb Alice Kelley Linda Allison ... Dan Kuzmenka Contests Information Resources Infinite Fractal Loop Fractal Information Fractal-Art FAQ File Libraries ... Other Fractal Sites fractalus.com About Us Send Feedback Site Map Search: Advanced Search June 25, 2008 Ultra Fractal 5 has been released. This major upgrade adds layer grouping, image importing, thumbnail browsing, and a brand-new object-oriented formula compiler.

37. Fractal Images By Jon Stoppard Galleries of traditional fractals and quaternions. http://www.omriva.com/fractal/

Fractal Images Click here to escape from frames Fractal and quaternion images by Jon Stoppard Fractal images gallery 1 Fractal images gallery 2 Fractal images gallery 3 Fractal images gallery 4 Fractal images gallery 5 Fractal images gallery 6 Fractal gallery 1 Fractal gallery 2 Fractal gallery 3 Fractal gallery 4 ... Fractal gallery 6 Most of the fractal images on this site were originally rendered at a resolution of 360 or 720dpi. Quality prints are available by private arrangement. Website design by Jon Stoppard. Chesterfield, Derbyshire , UK.

38. Fractals fractals. Nature is full of shapes that are alike to themselves on different scales. A boulder looks like the mountain to which it was once attached. http://www.emayzine.com/infoage/math/math4.htm

Fractals Nature is full of shapes that are alike to themselves on different scales. A boulder looks like the mountain to which it was once attached. The structure of a twig is a lot like that of the tree from which it has fallen. A coastline has the same irregular shape when viewed from various altitudes. The surfaces of certain cheeses and the random distribution of the stars in the sky display the property known as statistical self-similarity. These phenomena and many others, such as the scattering of nuclear particles, are examples of fractals that happen in nature. Many of nature's irregular and fragmented patterns exhibit a much greater level of complexity than can easily be explained with standard Euclidean geometry. Such features have escaped the application of classical mathematics for a long time. But now, due primarily to the work of Benoit Mandelbrot, this is quickly changing Mandelbrot is an IBM Fellow at the Thomas J. Watson Research Center. His essay The Fractal Geometry of Nature is commonly received as the definitive work on the subject of fractals.

39. Fractal Links - Amazing Seattle Fractals! Fractal art tutorials and free fractal software. http://fractalarts.com/ASF/Fractal_Links.html

Amazing Seattle Fractals! Home Fractal Art Galleries Fractal Tutorials Fractal Of The Week ... About Fractal Links I've included many resources on this page if you are looking for more information on fractals, including other fractal artists, tutorials or more information about fractals in general. If you are looking for fractal software programs check out my software page. Enjoy! Seattle Fractals Digital Art If you are interested in any prints of my art, or downloading any of my screensavers for a free evaluation, you can find them here. High resolution art prints, fractal art galleries, fractal screensavers and more! Fractal Tutorials and Related Links Fractal Geometry A thorough examination into fractals from Yale University by authors including Michael Frame, Benoit Mandelbrot, and Nial Neger. UF Spiral Tutorial Dr. Joseph Trotsky's excellent tutorial on creating the classic fractal spiral form as well as other helpful UF info. He has also written helpful info on the program Fractal Explorer. Janet Parke Preslar's excellent tutorials on using the Ultra Fractal Program. Prof. John Matthew's

40. Fractals I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images http://local.wasp.uwa.edu.au/~pbourke/fractals/

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