1. Benoit Mandelbrot: Fractals And The Art Of Roughness | Video On TED.com TED Talks At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 the extreme complexity of roughness, and the way that fractal http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html

2. Mandelbrot Fractals Software - Fraqtive, M3DSaver, Fractals World ... Mandelbrot Fractals Software Listing. Fraqtive is a program for drawing Mandelbrot and Julia fractals. A Windows Screensaver featuring fractals and 3D graphics. http://www.filetransit.com/files.php?name=Mandelbrot_Fractals

3. Mandelbrot Set - Wikipedia, The Free Encyclopedia The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal. The Mandelbrot set is the set of complex values of c for which the orbit http://en.wikipedia.org/wiki/Mandelbrot_set

Mandelbrot set From Wikipedia, the free encyclopedia Jump to: navigation search Initial image of a Mandelbrot set zoom sequence with a continuously coloured environment The Mandelbrot set is a mathematical set of points in the complex plane , the boundary of which forms a fractal . The Mandelbrot set is the set of complex values of c for which the orbit of under iteration of the complex quadratic polynomial z n z n c remains bounded That is, a complex number, c , is in the Mandelbrot set if, when starting with z = and applying the iteration repeatedly, the absolute value of z n never exceeds a certain number (that number depends on c ) however large n gets. The Mandelbrot set is named after Benoît Mandelbrot , who studied and popularized it. For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c i (where i is defined as i ) gives the sequence i i i i ... i , which is bounded and so i belongs to the Mandelbrot set. When computed and graphed on the complex plane the Mandelbrot set is seen to have an elaborate boundary which, being a fractal, does not simplify at any given magnification.

4. Kozmik Shirts - Mandelbrot Fractals Shirts, posters, cards and objects with classic Mandelbrot fractal. http://www.cafepress.com/Mandel_stand

Shop CafePress tank tops baby bodysuits thongs boxers home decor aprons clocks coasters calendars ... greeting cards drinkware mugs steins posters posters framed prints buttons magnets ... mousepads topics animals careers family food ... sports gift center shop by holiday valentine's day st. patrick's day mother's day gifts ... visit gift center make your own custom t-shirts custom mugs custom stickers custom buttons ... Help Currency: AUD CAD GBP EUR USD AUD CAD GBP EUR ... Cart Kozmik Shirts - Mandelbrot fractals Categories: Shirts (short) Shirts (long) Kids Clothing Share ... Sign up for the newsletter! Shirts, posters, cards and objects with the classic Mandelbrot fractal. For more designs see our site by clicking the Kozmik Shirts logo above. Shirts (short) (back to top) Mandelbrot T-shirt Jr. Jersey T-shirt with Mandelbrot Ash grey T-shirt with Mandelbrot ... Women's T-shirt with Mandelbrot Shirts (long) (back to top) Sweatshirt with Classic Mandelbrot Long sleeve T-shirt with Mandelbrot Hooded sweatshirt with Mandelbrot Kids Clothing (back to top) toddler T-shirt with Mandelbrot (back to top) Small Poster of Mandelbrot ... Make your own t-shirts and gifts at CafePress.com International Sites: Australia Canada United Kingdom Non-US currency rates are updated daily and may fluctuate.

5. Zuk - Dynamic Fractal Viewer Dynamic, real-time Mandelbrot fractal viewer for DOS. http://wizard.ae.krakow.pl/~jb/Zuk/

screenshots version 1.08 Zuk SUSPENDED PROJECT This is dynamic, realtime Mandelbrot fractal viewer for DOS. You can smoothly zoom fractal by holding down button and moving mouse. You don't have to select view area and wait for new picture. It runs on 386+ with SVGA (640x480x8 VESA). K6 200MHz with fast video is comfortable. Download latest version: zuk108.zip Zuk is written in pure assembler. It currently runs in real mode. I'm working on 32-bit protected mode version which should eliminate overhead associated with data size changing on every 32-bit instruction. Here is experimental version at the point the project was stopped. Jan Bobrowski

6. Math Forum: Suzanne Alejandre - MandelBrot Activity Studying Mandelbrot Fractals Fractals. NOTE Use of Internet Explorer 5.0 is recommended. What is a fractal? Alan Beck in What Is a Fractal? And who is this guy Mandelbrot? writes http://mathforum.org/alejandre/applet.mandlebrot.html

Studying Mandelbrot Fractals Fractals NOTE: Use of Internet Explorer 5.0 is recommended. What is a fractal? Alan Beck in What Is a Fractal? And who is this guy Mandelbrot? 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." 1. Click on the button Col+ or Col- to change the colors of the fractal image. 2. Now that you have the colors set to your liking, it is time to investigate the fractal itself! 3. Using the mouse, draw a small rectangle on the fractal image. Click on Go and watch as the smaller section of the image is redrawn to fill the fractal screen. 4. What do you notice? How do the images compare? Click on the Out button to revisit the first image and the In button to return to the enlarged image. 5. Continue going into the fractal image. What do you observe? 6. It has been stated that fractals have finite areas but infinite perimeters . Do you agree? Why?/Why not?

7. Animating Mandelbrot Fractals With Silverlight 3 WriteableBitmap: DigWin Use the new WriteableBitmap class in Silverlight 3 Beta to render an animated zooming Mandelbrot Set fractal image. I've been a student of fractal geometry for many years. is http://www.digwin.com/animating-mandelbrot-fractals-with-silverlight-3-writeable

8. MASS DEFACED?! Een simpele uiteenzetting van de Mandelbrot Fractal. http://www.stuif.com/fractals/

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9. Fractal Science Kit - Mandelbrot Fractal Overview Discussion of Mandelbrot fractals, Julia fractals, Convergent fractals, Newton fractals, Orbit Traps, Apollonian Gasket, Circle Inversion, Schottky Group, and Kleinian Group. http://www.fractalsciencekit.com/types/classic.htm

Mandelbrot Fractals Home Gallery Tutorials Download ... Site Map Mandelbrot Fractal Overview The Fractal Science Kit fractal generator Mandelbrot fractals encompass several related fractal types including Mandelbrot fractals, Julia fractals, Convergent fractals, Newton fractals, and Orbit Traps Mandelbrot Fractals Mandelbrot fractals are the result of iterating a fractal formula. A fractal formula is a statement like: z = z^2 + c This statement takes 2 complex values found in the variables z and c , and combines them based on the expression to the right of the equal sign; in this case, by squaring z and adding c to the result. The resulting complex value is assigned to the variable z , replacing the previous value of z . This completes the 1 st iteration of the formula. A 2 nd iteration would evaluate the expression again, this time starting with the new value of z computed in the 1 st iteration. This process continues with each step producing a new value for z . The process terminates when the magnitude of z exceeds some threshold value or the specified maximum number of iterations is reached. The magnitude of z is the distance of the point z from the origin of the complex plane ( ). The set of all the

10. Benoit Mandelbrot: Fractals And The Art Of Roughness - Benoit Mandelbrot (2010) David Byrne sings (Nothing But) Flowers Thomas Dolby / Ethel / David Byrne (2010) TecNoesis 84 mins ago http://vodpod.com/watch/3972014-benoit-mandelbrot-fractals-and-the-art-of-roughn

11. ColorAura Networks -- Applets A growing collection of small applets with source code. Mandelbrot fractals, Conways Game of Life, and spinning stars are just some of the applets appearing here. http://turquoise.coloraura.com/artwork/

Art Applets Name Summary Fractal Tree V1.2 This is the second version of the Colorful Fractal Tree Fractal Tree V1.0 The original Fractal Tree Spinning Stars Stars spinning around in 3D Moving Circle Fractal Recursivly drawn circles, with a varying angle. Blazing Fire A pretty fire simulator Moving Plasma A dynamic display of plasma. Wavy Pattern A pattern that waves around. Fractal Boxes A moving spiraling box fractal. Sierpinski's Valentine A Valentine's day Sierpinkski's gasket. Another Fire A different implementation of the Fire effect Blaze A different fire effect. Note: Some applets require a newer version of the java plug in. You can download and install the Java runtime environment if any applet doesn't work. Main page This page has been viewed 21147 times.

12. Realtime Mandelbrot Fractal Generation CGI This site is a program that allows everyone to explore the fashinating word of Fractals. Fractal is a term coined by Benoit Mandelbrot to refer to a structure bearing http://mandelbrot.collettivamente.com/

Mandelbrot Fractals Generator This site is a program that allows everyone to explore the fashinating word of Fractals. Fractal is a term coined by Benoit Mandelbrot to refer to a structure bearing statistically similar details over a wide range of scales. Click on the image to zoom, on borders to pan Restart Image size: infx: -2 supx: 1 infy: -1.5 supy: 1.5 colormap: volcano.map Sponsored Links: Cucina Alimentazione Newsgroups italiani Archivio Discussioni ... Discussioni Scientifiche

13. Areas Of Mandelbrot Fractals - By Don Cross, February 2005 back to Cosine Kitty's math page Areas of Mandelbrot fractals by Don Cross, February 2005 I am currently investigating the areas of the Mandelbrot fractals formed by iterating the http://cosinekitty.com/mandel_area.html

[back to Cosine Kitty's math page] Areas of Mandelbrot fractals - by Don Cross, February 2005 I am currently investigating the areas of the Mandelbrot fractals formed by iterating the formula z' = z n + c Below is a table of areas of these fractals as a function of n , as determined by C++ software I wrote. Because I am using a fairly low-resolution pixel-counting algorithm, I am listing the areas to only 4 places after the decimal. By comparing the value of A(2) with other people's empirical results, chances are the values here are only correct to 3 places after the decimal. Area of Mandelbrot fractal n A( n n References A Statistical Investigation of the Area of the Mandelbrot Set by Kerry Mitchell MathWorld's entry for the Mandelbrot Set contains the quote: " The area of the set is known to lie between 1.5031 and 1.5702; it is estimated as 1.50659...." Robert P. Munafo's Pixel Counting page

14. Introduction To The Mandelbrot Set A simple explanation of how the Mandelbrot set fractal is calculated and graphed. Includes a progression of images to demonstrate zooming. http://www.ddewey.net/mandelbrot/

Site Sponsor... Introduction to the Mandelbrot Set A guide for people with little math experience. By David Dewey According to Web-Counter you are visitor number since November 02, 1996. The Mandelbrot set, named after Benoit Mandelbrot, is a fractal . Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers. Understanding complex numbers The Mandelbrot set is a mathematical set, a collection of numbers. These numbers are different than the real numbers that you use in everyday life. They are complex numbers . A complex number consists of a real number plus an imaginary number . The real number is an ordinary number, for example, -2. The imaginary number is a real number times a special number called i , for example, 3 i . An example of a complex number would be -2 + 3 i The number i was invented because no real number can be squared (multiplied by itself) and result in a negative number. This means that you can not take the

15. Oxymoronical » Mandelbrot Fractals These fractals are generated using the classic Mandelbrot fractal formula as well as a few slight variants of it. http://www.oxymoronical.com/web/fractals/mandelbrot?g2_page=6

16. Understanding Instability: Mandelbrot, Fractals, And Financial Crises » TripleCr Mandelbrot's page at Yale; Ted talk Benoit Mandelbrot Fractals and the art of roughness 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.

17. Mandelbrot Fractals Any iterated function can be used to build a Mandelbrot set. The original Mandelbrot set uses iterated squaring. Mandelbrot sets with iterated cubing, third power, fourth power http://orion.math.iastate.edu/danwell/Fexplain/Mandel2.html

Mandelbrot fractals Squared, cubed, fourth, and fifth power Mandelbrot sets. Any iterated function can be used to build a Mandelbrot set. The original Mandelbrot set uses iterated squaring. Mandelbrot sets with iterated cubing, third power, fourth power, and fifth power are shown above. The sets exhibit an n -fold rotational symmetry where n is one smaller than the iterated power used to generate the set. Click on one of these images to enlarge the image. The Mandelbrot set below is derived from the complex sine function. The exscape conditions for this function are different. A point escapes if its complex part grows to more then 2xPI. Complex sine Mandelbrot.

18. Mandelbrot Fractals The Mandelbrot set is a set of points that fail to escape under an iterated point process. Readers may want to review the complex arithmetic rules in the articles on Newton's method http://orion.math.iastate.edu/danwell/Fexplain/Mandel1.html

Mandelbrot fractals A loud coloring of points outside the Mandelbrot set. The Mandelbrot set is a set of points that fail to escape under an iterated point process. Readers may want to review the complex arithmetic rules in the articles on Newton's method fractal. To decide if a complex point z=x+yi is in the Mandelbrot set, generate the following sequence of complex points. The first is z itself. The next point is the square of the current point plus z . The first part of this sequence is thus: The Mandelbrot sequence for a point z If a point, under the operation of this iterated squaring, gets more than a distance of 2 from 0+0 i then it is not in the Mandelbrot set. Click on the example above and you will see that this set of non-escaping points has a very complex shape. Later we will show that there is added complexity visible as we zoom in at each level of the set. New features appear forever. The set above is colored using a rainbow palette and choosing the color by the number of iterations required for the moving point to escape. This is a fairly standard algorithm for coloring the points not in the Mandelbrot set. The flat, cosine, and clarity methods from the Newton's method article can also be used.

19. TGD Diary: How To Define 3-D Analogs Of Mandelbrot Fractals? TGD diary Daily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background. http://matpitka.blogspot.com/2009/11/how-to-define-3-d-mandelbrot-sets.html

TGD diary Daily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background. Thursday, November 19, 2009 How to define 3-D analogs of Mandelbrot fractals? In New Scientists there was an article about 3-D counterparts of Mandelbrot fractals +c with a more general map (see this ). c must be restricted to a 3-D hyperplane to obtain 3-D Mandelbrot set. It occurred to me that there exists an amazingly simple manner to generate analogs of the Mandelbrot sets in 3 dimensions. One still considers maps of the complex plane to itself but assumes that the analytic function depends on one complex parameter c and one real parameter b so that the parameter space spanned by pairs (c,b) is 3-dimensional. Consider two examples: + z + c, b real, + c + bz +bc Both options might produce something interesting. One could also construct dynamical 3-D Mandelbrots by allowing b to be complex and interpreting real or imaginary part of b of the modulus of b as time coordinate. One can deduce some general features of these fractals.

20. Astropixie: Mandelbrot Fractals beno t mandelbrot died on october 14th, 2010 at the age of 85. he was the mathematician who invented fractals rough (not smooth) geometric shapes that have the cool http://amandabauer.blogspot.com/2010/10/mandelbrot-fractals.html

skip to main skip to sidebar astropixie things and stuff astronomy and life Thursday, October 21, 2010 mandelbrot fractals benoît mandelbrot died on october 14th, 2010 at the age of 85. he was the mathematician who invented fractals : rough (not smooth) geometric shapes that have the cool property that if you look at small parts of the whole, they look (almost) exactly like the whole, only smaller. here is the famous mandelbrot set fractals occur all over in nature including clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and even our blood vessels. in july of this year, mandelbrot gave an interesting TED talk called Fractals and the art of roughness describing how he came about the idea of fractals, and how they are used in a wide variety of ways today: ps. someone sent me this fractal which could sort of maybe loosely qualify as dirty space news content: dirty space news science video reactions: Post a Comment Newer Post Older Post Home Subscribe to: Post Comments (Atom) AMANDA bauer nottingham, robin's hood, United Kingdom

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