1. Graphics Archive - General InterestFractals General InterestFractals. Fractals are mathematical objects that typically have the following characteristics http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Graphics Archive - General InterestFractalsClouds General InterestFractalsClouds. These pictures were created using spectral synthesis, as outlined by Dietmar Saupe and Richard Voss in The Science http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Graphics Archive - General Interest:Fractals General InterestFractals. Fractals are mathematical objects that typically havethe following characteristics. a fine structure (detail on abitrarily small http://www.geom.uiuc.edu/graphics/pix/General_Interest/Fractals/

Graphics Archive Up Comments General Interest :Fractals Fractals are mathematical objects that typically have the following characteristics a fine structure (detail on abitrarily small scales) too irregular to be described in traditional geometrical language, both locally and globally has some form of self-similarity, perhaps approximate or statistical its "fractal dimension" is greater than its topological dimension is defined in a very simple way, perhaps recursively. Fractals often are associated with natural objects, such as the branchings of a tree, or the tributaries of a stream. A great deal has been written about fractals, and there are several web sites that deal exclusively with fractals (see our list of images on the web). Subgroups: CCL - The cubic connectedness locus (CCL) is a four-dimensional analog of the familiar Mandelbrot set. Clouds - Cloud simulations using spectral synthesis. Henon - The Henon map is a 2-dimensional generalization of the logistic equation. Images: Amoeba Fractal An aperiodic tiling Antoine's Necklace Arbitrary substitution tiling Brot Cheese Fractal DodecaFoam! First Stellation

4. CrackzPlanet.com - (General Fractals) (General Fractals) CRACK CrackzPlanet.com (General Fractals) (General Fractals) CRACK KEYGEN SERIAL NOCD http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Graphics Archive - General InterestFractalsCCL General InterestFractalsCCL. These images are pictures of two dimensional slices of the cubic connectedness locus. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. General Info On Fractals General Info on Fractals. Chaos at Maryland (UMDCollege Park) Fractal Compression (UCSD Institute for Nonlinear Science) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. PV General Puerto Vallarta Welcom to visit my home PV Pictures. PV General. Storm Damage. What you left behind. Photos in and around Puerto Vallarta http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. JavaQuat 2.0 Documentation - General General Information. JavaQuat is freeware. Enjoy it. If you make enhancements or fixes I'd appreciate your sending me a copy. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. General Product Fractals HOME My_Reviews Examples My Renderosity Page What are General Use Fractals? http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Global-Online-Store (Germany) English Books - Engineering - Help English Books Engineering - General - Fractals in Engineering. From Theory to Industrial Applications 1-1 of 1 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Bibliography General Fractals Bibliography General fractals. The original BibTeX file from which this file was generated is available at http//www.dip.ee.uct.ac.za/~brendt http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. The Math Forum - Math Library - Fractals General information about Mandelbrot, fractals, and their computer generation . A general site about fractals, including image galleries, animations, http://mathforum.org/library/browse/static/topic/fractals.html

Browse and Search the Library Home Math Topics Dynamical Systems : Fractals Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category The Fractal Microscope - Education Group, National Center for Supercomputing Applications (NCSA) An interactive tool for exploring the Mandelbrot set and other fractal patterns. With the Fractal Microscope students can enjoy the art as they master the science of mathematics, and can address a variety of topics in the K-12 curriculum including scientific notation, coordinate systems and graphing, number systems, convergence, divergence, and self-similarity. The program is designed to run in conjunction with NCSA imaging tools such as DataScope and Collage. more>> Fractals - Cynthia Lanius This lesson plan for exploring fractals is designed so 4th through 8th grade students can work independently and be assessed innovatively. It conforms to the 1989 NCTM standards, and provides links to other fractal sites. Contents: Why study fractals? Making fractals: Sierpinski Triangle, Sierpinski Meets Pascal, Jurassic Park Fractal, Koch Snowflake. Fractal Properties: Self-similarity, Fractional dimension, Formation by iteration. Teacher-to-Teacher notes; Fractals on the Web. more>> Fractals (Mathematics Archives) - University of Tennessee, Knoxville (UTK)

13. The Science House - Chaos & Fractals General Fractal and Chaos Resources. Dynamical Systems and Technology Fractals Unleashed excellent descriptions and examples in the tutorial section http://www.science-house.org/student/bw/chaos/resources.html

Spring 2001 Chaos and Fractals Resources General Week 1 Week 2 Week 3 ... Programs General Fractal and Chaos Resources Dynamical Systems and Technology Project - this is where the books we use came from Center for Polymer Studies at BU - an excellent site that shows real live fractals and chaos. Good hands on activities too. Fractal Frequently Asked Questions and Answers Fractals Unleashed - excellent descriptions and examples in the tutorial section The Chaos Experience - good real world examples of chaos The Chaos Metalink - links to every conceivable chaos related site Week 1: Geometric Iteration Cynthia Lanius' Lessons: A Fractals Lesson This is Beth's new favorite fractal site! This was written for elementary/middle school students but the questions are not as trivial as they seem. Can you work them out? You must visit Sierpinski's Gasket - especially Sierpinski meets Pascal and Jurassic Park Fractal - go through all the pages it's worth it.

14. Natural Fractals Activity (part 1) fractals general fractals natural fractals activity (part 1) . generalfractals. •. fractals By Replacement. •. fractals in Crystals http://server1.fandm.edu/academics/foundations/NTW114/frac/gen/frac-gen-natfract

fractals : general fractals : natural fractals activity (part 1) Fractals Introduction General Fractals Fractals By Replacement Fractals in Crystals Natural Fractals Activity part 1 ... part 2 Bifurcations and Branching The Shortest Distance between 91 points Branching Networks Hausdorf dimension Rocks as Fractals The Dimension of Shorelines Natural Fractals Activity Materials: Background: One activity we can do with fractals is to start with the "transformations" (the rules), use these to create a fractal. This is what you did in your Fractal Activity. Another activity is to take a natural fractal (such as the Cheasapeake shore), and analyze its fractal dimension. But one of the hardest things to do with fractalsand at the same time the most usefulis to take a natural fractal and try to discover the underlying rules which generate the fractal. That is what you will attempt to do today. Fractals at the North Museum: There are a variety of fractal-like objects at the North Museum. Here is a list of some of the ones I have found:

15. Perfectly Scientific - Home the scientific algorithm company. Experts in compression, wavelets, FFT, general transforms, color graphics, Monte Carlo, fractals, convolution,signal processing, matrix algebra, genetic algorithms, number theory. http://www.perfsci.com/

PSI news bTop-1 featured George Storm discusses the bTop-1, prize-winner at ADHOC / MacHack. New hardware! New poster! New largest prime number! The prime is 2 -1, discovered in February 2005. Algorithm contracting PSI offers unique services that are hard to find elsewhere. We specialize in industrial algorithm problems. Contact us for professional help on your algorithm problems. Lab hardware PSI designs and supports laboratory peripherals for Mac OS X. More details can be found on our hardware page Free software PSI has software available for free download under this license PrimeKit GiantInt AlgorithmSampler FastAlgorithms Souvenirs PSI also provides a unique collection of scientific souvenirs and gifts. Visit our store to find posters and other scientific paraphernalia.

16. Fractals In Crystals fractals general fractals fractals in crystals .. fractals By Replacement. •. fractals in Crystals. •. Natural fractals Activity http://server1.fandm.edu/Academics/Foundations/NTW114/frac/gen/frac-gen-crystal.

fractals : general fractals : fractals in crystals Fractals Introduction General Fractals Fractals By Replacement Fractals in Crystals Natural Fractals Activity Bifurcations and Branching The Shortest Distance between 91 points Branching Networks Hausdorf dimension Rocks as Fractals The Dimension of Shorelines Fractals in Crystals Background: The first picture below is a photograph of mica which has threads of iron ore between the layers of mica: these darker lines highlight the hexagonal structure of the mica. You can click on the blotchy section toward the upper right to see a close-up version of the iron infiltration. The second picture is a photograph of a piece of bismuth. (The original is 1.6 inches long). Bismuth occurs naturally, although this piece was grown artificially in a laboratory. Notice the repeating square shapes at many scales. This is an example of a fractal formed by accretion. Bismuth forms square crystals. You can think of accretion as happening by little particles of bismuth being attracted to the existing crystal, and then becoming attached. The corners of the existing crystal have a larger region in which they can attract particles without competition from their neighbor and therefore the bismuth crystals grow more quickly at the corners than elsewhere.

17. Original Fractal Art - PadleyWood Uses freeware generators, offers simple explanations and general discussion, tutorial links. http://mysite.wanadoo-members.co.uk/padleywood/fractal_art.htm

Your browser does not support script The Galleries Each image is one selected from the gallery to which it hyperlinks. Hover the cursor over the image to check the title/theme then click to visit the gallery. Previous 15 Previous Site Next Site Next 15 The image of the Mandelbrot set on the main page is one with minimal 'treatment', just colouring. To create images that constitute art requires a little more complexity. After downloading and using Sterlingware V1.7 (Iterations et Flarium24), I gradually began to understand the process. I then found that Fractal Explorer had all the Sterlingware equations built in, but I much preferred the Sterlingware interface - it's more intuitive, and all the controls are available from the menu, giving a great speed advantage to the novice. More sophisticated methods of treating the points post-iteration are employed; instead of the straight 'bail-out' method described in the introduction on the Mandelbrot set, a further 'mask' is applied, whether to examine the rate of divergence of a point or its relationship with its neighbours, or indeed more complex attributes. The result is a completely new grouping of points, hence different patterns. Given over 50 basic equations, 30 renderings, 3 Lyapunov renderings and their various further treatments, plus 26 built-in colour schemes with the ability to tweak to one's own preference, and the sheer space of possibilities begins to look as though the infinite is just over the horizon ;-)

18. Graphics Archive - General Interest:Fractals:Clouds general InterestFractalsClouds. These pictures were created using spectralsynthesis, as outlined by Dietmar Saupe and Richard Voss in The Science of http://www.geom.uiuc.edu/graphics/pix/General_Interest/Fractals/Clouds/

Graphics Archive Up Comments General Interest ... Fractals :Clouds These pictures were created using spectral synthesis, as outlined by Dietmar Saupe and Richard Voss in The Science of Fractal Images, Springer-Verlag, 1988. Comparison of this method with texture modelling and a description of the actual generation of the image can be found in the Summer Institute 1993 report, "Cloud Generation". Images: Clouds 1 Clouds 2 Clouds 3 Clouds 4 The Geometry Center Home Page Comments to: webmaster@www.geom.uiuc.edu Created: Tue Feb 11 7:10:26 CST 1997 - Last modified: Tue Feb 11 7:10:26 CST 1997 The Geometry Center For permission to use these images, please contact permission@geom.umn.edu

19. Cliff Pickover, Factals And The Pursuit Of Beauty In general, I see graphics of fractals as part of the field of scientific Pickover s love of fractals and the general field of computerized http://sprott.physics.wisc.edu/pickover/cliffpick.html

Contact News! Books Home Cliff Pickover Fractals and the pursuit of beauty Interview previously at IBM Research web site... For IBM Researcher Cliff Pickover, the passion that drives his work is the search for that delicate balance between chaos and order. At the center of his passion lie fractals, computer-generated patterns that can represent mathematical concepts. Fractals are often objects of beauty, not to mention useful tools for areas as diverse as medicine, computer science and education. When he's not busy developing code for IBM's IntelliStation (IBM's new high-end personal computer), or writing and explaining mathematical concepts to the public, Pickover is exploring ways in which fractals and computerized visualization can be stretched for aesthetic as well as practical reasons. Entering the fractal dimension "One of the most important things that fractals contribute is the concept of fractal dimension," Pickover explains. "By using a single number, scientists can characterize the behavior of systems, and the irregularity of shapes. For example, fractals can be used to characterize coastlines or the structure of blood vessels and cells. They give us insights into chaos theory, which looks at the effect of irregularity on very large systems, such as weather. Computers graphics can be used to produce visual representations with a myriad of perspectives, many of which are beautiful to the eye." The work of Pickover and his colleagues at IBM is branching into many areas to explore new ways for using computerized visualization to represent data, illuminate patterns and simulate natural forms. Pickover has worked on topics ranging from the graphical representation of genetic sequences and sounds to the simulation and rendering of huge lifelike caverns (which he calls "virtual caverns" because they can be explored using computer tools).

20. Fractal - Wikipedia, The Free Encyclopedia Quasiself-similar fractals contain small copies of the entire fractal in distortedand as well as a listing of tutorials regarding fractals in general, http://en.wikipedia.org/wiki/Fractal

Fractal From Wikipedia, the free encyclopedia. The Mandelbrot set , named after its discoverer, is a famous example of a fractal. The Mandelbrot set , named after its discoverer, is a famous example of a fractal. A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way. Some of the best examples can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and they may actually have a self-similar structure that occurs at different levels of magnification. In many cases, a fractal can be generated by a repeating pattern, in a typically recursive or iterative process. The term fractal was coined in by Beno®t Mandelbrot , from the Latin fractus or "broken". Before Mandelbrot coined his term, the common name for such structures (the Koch snowflake , for example) was monster curve Fractals of many kinds were originally studied as mathematical objects. Fractal geometry is the branch of mathematics which studies the properties and behaviour of fractals. It describes many situations which cannot be explained easily by classical geometry, and has often been applied in science technology , and computer-generated art . The conceptual roots of fractals can be traced to attempts to measure the size of objects for which traditional definitions based on Euclidean geometry or calculus fail.

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