21. 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.

22. 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.

23. 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.

24. Fractals Easier A fractal is a shape, often drawn by a computer, that repeats itself in a pattern. The design shapes usually reoccur http://42explore.com/fractal.htm

The Topic: Fractals Easier - A fractal is a shape, often drawn by a computer, that repeats itself in a pattern. The design shapes usually reoccur in different sizes. Harder - Fractals are endlessly repeating patterns that vary according to a set formula, a mixture of art and geometry. Fractals are any pattern that reveals greater complexity as it is enlarged A real-life example of fractals is ice crystals freezing on a glass window. You can see countless variations of the same pattern emerge in the crystals over time. Exploring Fractals (Grades 9-12) by M.A. Connors http://www.math.umass.edu/~mconnors/fractal/fractal.html This website explores fractal dimensions of strictly self-similar fractals, from Cantor Dust to the Fractal Skewed Web. Includes a teacher information section. Related Websites: 2) Fract-ED (Grades 8 and Above) http://www.ealnet.com/ealsoft/fracted.htm

25. 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

26. 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

27. 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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28. Math.com Wonders Of Math Build your own fractals and learn about the math behind the images. Mandelbrot and Julia Set Explorer Zoom into fractals. Fractal Galleries http://www.math.com/students/wonders/fractals.html

29. 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.

30. 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.

31. 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

32. Fractals fractals. by Dale Winter. In several of the lessons we have described objects as fractals, for example, the Julia set known as the ‘Rabbit.’ The important property that we http://www.math.lsa.umich.edu/mmss/coursesONLINE/chaos/chaos7/index.html

Fractals by Dale Winter In several of the lessons we have described objects as fractals, for example, the Julia set known as the �Rabbit.� The important property that we were trying to capture by the label �fractal� was the property of self-similarity . When you zoom in on a part of the Julia set, you may notice a strong resemblance between the part of the Julia set that you have zoomed in on, and the original view of the Julia set before zooming. For example, if you look at the colored picture of The Rabbit , there is a large, black region in the center of the picture that you might think of as the body of the rabbit. Attached to the body of the rabbit are some small black areas about half-way along each side of the body, some larger areas that you might think of as the legs and the ears , and some larger areas that you could think of as the head and the tail of the rabbit. If you look carefully at the head of the rabbit, there are two small lobes about halfway along its length, just like the body of the rabbit. If you pretend that the head of the rabbit is going to be the body of a smaller rabbit, then there are lobes that could be the head and tail of the smaller rabbit. Although these sets are clearly very intricate, complicated and detailed, they also have

33. ALicia's FractaLs Collection of images generated in Tiera-Zon, and related links. http://www.alicia-logic.com/fractals/

Click here to minimize or maximize the link bar. Your display preference will be remembered if your browser accepts cookies. Share Page 1 Page 2 Page 1 Page 2 Page 3 Page 4 Page 5 Page 1 Page 2 Page 3 Coming soon! Tiera-Zon bitmaps and source files Intro and Informational sites Image galleries Software sources

34. Fractals fractals is an interdisciplinary journal devoted exclusively to phenomena involving complex geometry, patterns, geometrical and/or temporal scaling. Through the application of http://www.worldscinet.com/fractals/fractals.shtml

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.

35. BBC News - How Mandelbrot's Fractals Changed The World Chaos, fractals, and Arcadia ADD. KEYWORDS The Chaos Game, The Sierpinski Hexagon, Iterated Function Systems Chaos in the Classroom, Boston University http://www.bbc.co.uk/news/magazine-11564766

blq.setEnvironment('live'); $loadView("0.0",["bbc.fmtj.view"]); $render("livestats-heatmap"); $loadView("0.0",["bbc.fmtj.view.news.story"]); British Broadcasting Corporation Home Accessibility links Skip to content Skip to local navigation Skip to bbc.co.uk navigation Skip to bbc.co.uk search ... Accessibility Help Magazine $render("advert","advert-sponsor-section"); $render("advert-post-script-load"); Home Latin America UK Africa ... Magazine $render("advert","advert-leaderboard"); $render("advert-post-script-load"); 18 October 2010 Last updated at 09:15 ET Share this page Delicious Digg Facebook reddit ... Print By Jack Challoner Science writer Fractals have become a common sight, thanks to computer imagery In 1975, a new word came into use, when a maverick mathematician made an important discovery. So what are fractals? And why are they important? During the 1980s, people became familiar with fractals through those weird, colourful patterns made by computers. But few realise how the idea of fractals has revolutionised our understanding of the world, and how many fractal-based systems we depend upon. Continue reading the main story Start Quote End Quote Benoit Mandelbrot Maths visionary Mandelbrot dies On 14 October 2010, the genius who coined the word - Polish-born mathematician Benoit Mandelbrot - died, aged 85, from cancer.

36. Flying Frog Fractals Gallery of fractal images created using Fractint and Winfract. http://members.tripod.com/afractal/

Build your own FREE website at Tripod.com Share: Facebook Twitter Digg reddit document.write(lycos_ad['leaderboard']); document.write(lycos_ad['leaderboard2']); Original album: Flying Frog Fractals This album has post processing. New albums at Smugmug These albums have fractint original fractals with no post processing. I still use Fractint. I don't think it can ever be exhausted.

37. NOVA | Hunting The Hidden Dimension Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature. http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html

38. Andrew Que's Fractals Created using original software. Contains image galleries, zoom animations, and program downloads. http://drque.net/Fractals/

Andrew Que's Fractals Fractal art, links and software Home Images Video Software/ ... (DrQue.Net) Welcome to Andrew Que's site on Fractals This site is dedicated to one of the most beautiful mathematical art forms that exists Fractals . Primarly on this site are images create by Andrew Que using the Mandalbort fractal set. The images on these pages were created using my own fractal generating software. Also found here is software, source code and links relating to fractals. I do hope you enjoy! Proceed to the fractal art galleries Home Images Video ... Contact Designed and maintained by Andrew Que (C)

39. Fractals - UEN Themepark is the place to find Internet resources organized around broadbased themes. http://www.uen.org/themepark/patterns/fractal.shtml

40. Fractals - Answers In Genesis Did you know that amazing, beautiful shapes have been built into numbers? Believe it or not, numbers like 1, 2, 3, etc., contain a “secret code”—a hidden beauty embedded http://www.answersingenesis.org/articles/am/v2/n1/fractals

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