21. Bibliography General Fractals Bibliography general fractals. The original BibTeX file from whichthis file was generated is available at http//www.dip.ee.uct http://www.dip.ee.uct.ac.za/~brendt/bibliographies/html/fractals.html

22. Fractals Algorithms, Filtering and Estimation, Financial applications, fractals, Informationand For further details, please contact general Chair Associate Professor http://groups.msn.com/fractals/general.msnw?action=get_message&mview=1&ID_Messag

23. Fractals fractals, fractals@groups.msn.com, general Why are theseIFS disk tessellations important? View All Messages. http://groups.msn.com/fractals/general.msnw?action=get_message&mview=1&ID_Messag

24. Science Watch - Mathematics Links List of Great Math Programs computer algebra, geometry, fractals, AI, games an expressionevaluator, unit converter, 2D/3D graphing, general ledger, financial http://cgd.best.vwh.net/home/sci/mathl.htm

Mathematics Links Table of Contents General Indexes Organizations College and University Mathematics Departments General Resources ... TeX Information General Indexes Yahoo Mathematics links Excite's Mathematics links InfoSeek Guide: Mathematics ZIA Mathematics Resources - well done Galaxy Mathematics links WWW Virtual Library: Mathematics - Based at Florida State University Mathematics Information Servers - A large worldwide list, including university math departments, mathematical societies, research institutes, commercial pages, journals, preprint servers, and subject area pages. Based at PSU. Mathematical Resources on the Web - Extensive list, based at the University of Florida. Includes academic sites that had particularly good indexes. Math Sites on the Internet - Part of The Math Forum Useful Internet Math Resources - At Oklahoma State U, includes extensive list of links by David Wright Math-Net Links to the Mathematical World - Mostly lists of indexes and other higher-level lists University of Pennsylvania Electronic Sources for Mathematics Caltech Guide to Mathematical Resources CSC Mathematical Topics - Traditional list of links CSC TopMath - Allows anyone to add their own site. However, it is rather unusual as an index, since the interface doesn't allow direct access to the URLs.

25. The Math Forum - Math Library - Fractals World of fractals Adam Lerer A general site about fractals, including image galleries,animations, descriptions of different types of animations, explanations 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)

26. The Math Forum - Math Library - Fractals and Targeting, Dimensions, Fractal Basin Boundaries, general Chaos, Quantum Chaos,Riddled Basins, and Shadowing. more . Pascal s fractals Ivars Peterson http://mathforum.org/library/topics/fractals/?keyid=9511105&start_at=351&num_to_

27. Fractals And Chaos: General Information Math 125 fractals and Chaos. Spring 1997. general Information. InstructorAlan Durfee Office Clapp 404B; Telephone x2299 (with answering http://www.mtholyoke.edu/courses/adurfee/s97/math125/math125-gen.htm

Math 125: Fractals and Chaos Spring 1997 General Information Instructor: Alan Durfee Office: Clapp 404B Telephone x2299 (with answering machine; this is the fastest way to get in contact with me) email: adurfee Office hours: By appointment Lectures: Tuesday, Thursday 9:25-10:40 in Clapp 218 Evening help sessions: The evening help sessions will be on Sunday (Florence) and Wednesday (Burcu), starting at 7 PM and going until about 9 PM. However, if no one comes before 7:30, the TA may leave, so if you plan to arrive later, you should contact the TA beforehand and tell her you are coming. They will be in Clapp 416. They will start Feb 12. Text: "Chaos" by James Gleick (required) and "Fractals: The Patterns of Chaos" by John Briggs (recommended). Both these books are at the Odyssey, and are on reserve in the library. There will also be a xeroxing fee, about $4, which will be billed to your college account. Technology: You will need a calculator for this course, one that does logarithms. We will also be using a computer program called "Chaotic dynamical systems software". This program runs on the Mac and is available in the computer labs. Homework: Homework can be handed in during class or put in the envelope outside my office door. Graded homework can be picked up any time from the other envelope there. Homework can be redone and handed in again, if done promptly (ie, within a few days). The graders reserve the right not to accept redone homework that is too late. All homework is due at 5 PM on the date given, unless stated otherwise. Extra copies of the assignments will be available in an envelope outside my office door.

28. Graphics Archive - General Interest:Fractals:CCL (Science U) Graphics Archive Up Comments http://www.scienceu.com/library/graphics/pix/General_Interest/Fractals/CCL/

Browse By: Graphics Archive Up Comments General Interest ... Fractals :CCL These images are pictures of two dimensional slices of the cubic connectedness locus. The locus (CCL for short) is a four-dimensional analog of the Mandelbrot set. Just like the Mandelbrot set parametrizes the dynamics of the quadratic family z->z^2+c, the CCL describes the cubic family z->z^3+az+b, where a and b are two complex parameters. The pictures were generated by the program Brot, developed at the Geometry Center by Apprentice Linus Upson and Summer Institute participant Christine Heitsch. Brot provides a friendly user interface and computational tool to explore varying families of two dimensional slices of objects such as the CCL. It was used in the research of Apprentice David Ben-Zvi into the geometry of hyperbolic components, which generalize the discs and cardioids making up the interior of the Mandelbrot set. "Sunrise on Io" and "Black Hole" made it into the October 1993 issue of Scientific American. Like the Mandelbrot set, the CCL is connected. (The images are typically not connected, since they only represent two dimensional slices which may connect in the other dimensions.) It is NOT however locally connected, as can be seen in "Sea of Mandelbrot", "Comb of Doom" and several others. Another interesting feature is the distinction between "complex" slices, which are reminiscent of the Mandelbrot set and its variants (see for example "Electric Storm", "Frosted Pane" or "Ships on the Sea"), and "real" slices, which look more like images of cantor sets and strange attractors arising in real dynamical systems. (A typical example is "Henon Lookalike".) Most pictures combine real and complex features in often overlapping configurations. (See "Cantor Whirlpool", "Jekyll and Hyde" and "Torrential Storm".)

29. Fractals & The Fractal Dimension fractals, which are irregular geometric objects, require a third meaning scale again,we would get a similar result, a longer estimate of L. In general, as the http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

Fractals and the Fractal Dimension Mandelbrot and Nature "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."(Mandelbrot, 1983). The Concept of Dimension So far we have used "dimension" in two senses: The three dimensions of Euclidean space (D=1,2,3) The number of variables in a dynamic system Fractals, which are irregular geometric objects, require a third meaning: The Hausdorff Dimension If we take an object residing in Euclidean dimension D and reduce its linear size by 1/r in each spatial direction, its measure (length, area, or volume) would increase to N=r D times the original. This is pictured in the next figure. We consider N=r D , take the log of both sides, and get log(N) = D log(r). If we solve for D. D = log(N)/log(r) The point: examined this way, D need not be an integer, as it is in Euclidean geometry. It could be a fraction, as it is in fractal geometry. This generalized treatment of dimension is named after the German mathematician, Felix Hausdorff. It has proved useful for describing natural objects and for evaluating trajectories of dynamic systems. The length of a coastline Mandelbrot began his treatise on fractal geometry by considering the question: "How long is the coast of Britain?" The coastline is irregular, so a measure with a straight ruler, as in the next figure, provides an estimate. The estimated length, L, equals the length of the ruler, s, multiplied by the N, the number of such rulers needed to cover the measured object. In the next figure we measure a part of the coastline twice, the ruler on the

30. MathsNet Fractals What else are fractals? Addition You add these numbers just like you do in algebrain general, for example 3+2i + 45i=7-3i and 1.7-4.2i + 1.1-1.7i=2.8 - 5.9i. 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 ... Fractal Landscape generator 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

31. Fractal Art FAQ - General Information 1. FAQ general information. where the FAQ can be found will be posted periodicallyto the following newsgroups alt.binaries.pictures.fractals, alt.fractals, sci http://fractals.iut.u-bordeaux1.fr/f-art-faq/faq01.html

Table of contents Where to get the FAQ? How to contribute to the FAQ? What is the scope of the FAQ? ... Who have contributed to this FAQ? Version: Updated: Coordinator: Jean-Pierre Louvet. Maintainers: Jean-Pierre Louvet, Juan Luis Martínez, Phil Jackson (for fractal music). Another one or two volunteers are hoped. alt.binaries.pictures.fractals, alt.fractals, sci.fractals http://fractals.iut.u-bordeaux1.fr/F-art-faq/ (main site, modified address) http://www.fractalus.com/fractal-art-faq/ http://www.fractovia.org/F-art-faq/ for subscription information). But because not everybody is a member of this list, any request or suggestion formulated in any of the newsgroups listed above (in 1b) will be taken into consideration. However, in that case, send a copy of the message to the coordinator of this FAQ at: F-art.FAQ@hse.iuta.u-bordeaux.fr graphic art , but there is fractal music as well. Cynthia Church Dennis C. De Mars Dirk Meyer Frederik Slijkerman Janet Parke Preslar Jean-Pierre Louvet Juan Luis Martínez Ken Musgrave Kerry Mitchell Paul Carlson Paul Martz Phil Jackson Phil Thompson Rich Thomson (text from the previous sci.fractals-FAQ)

32. References Subject References. Q29a What are some general references on fractals,chaos, and complexity? A29a Some references are M. Barnsley http://fractals.iut.u-bordeaux1.fr/sci-faq/books.html

Subject: References : What are some general references on fractals, chaos, and complexity? : Some references are: M. Barnsley, Fractals Everywhere , Academic Press Inc., 1988, 1993. ISBN 0-12-079062-9. This is an excellent text book on fractals. This is probably the best book for learning about the math underpinning fractals. It is also a good source for new fractal types. M. Barnsley, The Desktop Fractal Design System Versions 1 and 2. 1992, 1988. Academic Press. Available from Iterated Systems. M. Barnsley and P H Lyman, Fractal Image Compression . 1993. AK Peters Limited. Available from Iterated Systems. M. Barnsley and L. Anson, The Fractal Transform , Jones and Bartlett, April, 1993. ISBN 0-86720-218-1. This book is a sequel to Fractals Everywhere . Without assuming a great deal of technical knowledge, the authors explain the workings of the Fractal Transform (tm) . The Fractal Transform is the compression tool for storing high-quality images in a minimal amount of space on a computer. Barnsley uses examples and algorithms to explain how to transform a stored pixel image into its fractal representation. R. Devaney and L. Keen, eds.

33. Fractal Links - Amazing Seattle Fractals! on this page if you are looking for more information on fractals, including otherfractal artists, tutorials or more information about fractals in general. http://www.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 of my art prints or downloading any of my screensavers for a free evaluation, you can find them here. High resolution art prints, fractal art galleries, fractal screensavers, custom made to order screensavers and more! Link Spectrum Fractal Tutorials and Related Links Fractal Types Explantions and illustrations of various types of fractals. 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

34. Amazing Seattle Fractals 2000 - Download Shareware Software From Our General Cat Windows Themes general Amazing Seattle fractals 2000. Newslettersignup Amazing Seattle fractals 2000, Theme Type Screen Saver. http://freethemes.forthnet.gr/preview/144154.html

Search our site: This Site Domains Windows Macintosh Linux Epoc Newton Palm OS Pocket PC RIM Series 3 Siena Windows CE Advanced options Windows Macintosh Linux ... General Newsletter sign-up: Amazing Seattle Fractals 2000 Theme Type: Screen Saver License: Shareware Information: Changing fractal artwork images are displayed. Download Win 95 Win 98 Win NT Win 2k ... Win XP File details Date: Oct 25, 2000 Size: Estimated download time: ISDN DSL Cable Developer Fractalarts/Doug Harrington View a screen shot E-mail a friend Advertisement Choose new mirror Newsletters Privacy statement Site map ... Terms and conditions

35. The Science House - Chaos & Fractals general Fractal and Chaos Resources. Center for Polymer Studies at BU an excellentsite that shows real live fractals and chaos. Good hands on activities too. 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 Fantastic Fractals The Chaos Metalink - links to every conceivable chaos related site The Fractal World of Astrology - why not?

36. Fractal Curves And Dimension are known as the selfsimilar fractals and, because of that ease, the propertyof self-similarity is often considered to be germane to fractals in general. http://www.cut-the-knot.org/do_you_know/dimension.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Fractal Curves and Dimension Fractals burst into the open in early 1970s. Their breathtaking beauty captivated many a layman and a professional alike. Striking fractal images can often be obtained with very elementary means. However, the definition of fractals is far from being trivial and depends on a formal definition of dimension. It takes a few chapters of an Advanced Analysis book to rigorously define a notion of dimension. The important thing is that the notion is not unique and even more importantly, for a given set, various definitions may lead to different numerical results. When the results differ the set is called fractal. Or in the words of Benoit Mandelbrot [Ref 2], the father of fractals: A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension. The topological dimension of a smooth curve is, as one would expect, one and that of a sphere is two which may seem very intuitive. However, the formal definition was only given in 1913 by the Dutch mathematician L. Brouwer (1881-1966). A (solid) cube has the topological dimension of three because in any decomposition of the cube into smaller bricks there always are points that belong to at least four (3+1) bricks.

37. DataCompression.info - Fractals This FAQ is not intended as a general introduction to fractals, or a set of rigorousdefinitions, but rather a useful summary of ideas, sources, and references http://www.datacompression.info/Fractal.shtml

Fractals Fractal image compression is a lossy compression technique. Compression is performed by locating self-similar sections of an image, then using a fractal algorithm to generate the sections. Fractals are a very interesting field of study, but this page won't attempt to cover everything there is to know about fractals. For the most part, we will only look at fractals as they relate to compression. To learn more about this fascinating subject, try looking into some of the resources pointed to by the Fractal FAQ Search compression newsgroups for references to this topic Please be sure to visit Friends of DataCompression.info! Badtz Maru will be your guide. Books Fractals Everywhere Rate by Michael F. Barnsley. A revised and updated textbook focusing on how fractal geometry can be used to model real objects in the physical world. DCL reader TJ says This is, in my experience, the best mathematics book I have ever seen If you are interested in buying this book, please use the link on this page. Your purchase will help to support this site. Fractal Image Compression : Theory and Application Rate by Yuval Fisher (Editor). Featuring a collection of articles by twelve experts in the field of fractal image compression, this book contains the complete details of how to encode and decode images, offering working codes that are usable in applications. Includes some of the latest results in this field..

38. BookLists: General Topology - NoiseFactory Science Archives (http://noisefactory Paperback (June 1999) Amazon (USA) $24.95 24 hours fractals NonIntegral 1996)Amazon (USA) $64.95 24 hours Fundamentals of general Topology Problems http://noisefactory.co.uk/reading/gentop2.html

This site makes extensive use of JavaScript. Please make sure JavaScript is re-enabled, and then reload the page. Sorry for the inconvenience. Click topic headings for more detailed lists, including basic reviews. Click author names for lists of their relevant books available online. Click book titles for further details, reviews, and offers specific to that book. Security You should only supply credit card details over secure server connections (Amazon use a secure server). Never send credit card details over standard email. Notes for UK Visitors Even though NoiseFactory is based in the UK, most prices here are quoted in US dollars - the slightly longer shipping time is usually more than made up for by considerably lower prices in America. Buying goods online is just as easy in dollars as Sterling, because credit card transactions are automatically converted to local currency at the prevailing exchange rate. In fact, online dollar purchases are cheaper even than getting your bank to generate a money order, because banks typically charge extortionate conversion fees, whereas credit cards usually charge none at all. To buy a book or CD in dollars, just fill out the online forms provided - the rest happens automatically. Further Reading General Topology > (page 2 of 6) Page 1 Page 3 Page 4 Page 5 ... Page 6 Visit our Sponsors General Topology (Page 2) Differential Equations : Geometric Theory by Solomon Lefschetz. Paperback (June 1977)

39. Chaos And Fractals In Financial Markets, Part 7, By J. Orlin Grabbe Chaos and fractals in Financial Markets. Let me give a specific example ofHurst exponent calculation which will illustrate the general rule. http://www.aci.net/kalliste/chaos7.htm

Chaos and Fractals in Financial Markets Part 7: Grow Brain and the Flooding of the Nile by J. Orlin Grabbe Grow Brain Many dynamical systems create solution paths, or trajectories, that look strange and complex. These solution plots are called "strange attractors". Some strange attractors have a fractal structure. For example, we saw in Part 3 that it was easy to create a fractal called a Sierpinski Carpet by using a stochastic dynamical system (one in which the outcome at each step is partially determined by a random component that either selects among equations or forms part of at least one of the equations, or both). Here is a dynamical system that I ran across while doing computer art. I labeled it "Grow Brain" because of its structure. To see Grow Brain in action, make sure Java is enabled on your browser (you can turn it off afterward) and click here . (The truly paranoid can, of course, compile their own applet, since I provide the source code, as usual.) The trajectory of Grow Brain is amazingly complex. But is it a fractal? That is, at some larger or smaller scale, will similar structures repeat themselves? Unlike the case of the Sierpinski Carpet, the answer to this question is not obvious for Grow Brain. Some dynamical systems create fractal structures in time (as Brownian motion does, in

40. Chaos And Fractals In Financial Markets, Part 1, By J. Orlin Grabbe I had read a number of books on general systems theory by Ervin Laszlo and Fractalsled me back into chaos, because maps (graphics) of chaos equations create http://www.aci.net/kalliste/chaos1.htm

Chaos and Fractals in Financial Markets Part 1 by J. Orlin Grabbe Prologue: The Rolling of the Golden Apple In 1776, a year in which political rebels in Philadelphia were proclaiming their independence and freedom, a physicist in Europe was proclaiming total dependence and determinism. According to Pierre-Simon Laplace , if you knew the initial conditions of any situation, you could determine the future far in advance: "The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence which at a given instant comprehends all the relations of the entities of this universe, it could state the respective positions, motions, and general effects of all these entities at any time in the past or future." The Laplacian universe is just a giant pool table. If you know where the balls were, and you hit and bank them correctly, the right ball will always go into the intended pocket. Laplace's hubris in his ability (or that of his "intelligence") to forecast the future was completely consistent with the equations and point of view of classical mechanics. Laplace had not encountered nonequilibrium thermodynamics, quantum physics, or chaos. Today some people are frightened by the very notion of chaos. (I have explored this at length in an essay devoted to chaos from a philosophical perspective . But the same is also true with respect to the somewhat related mathematical notion of chaos.) Today there is no justification for a Laplacian point of view.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 2     21-40 of 100    Back | 1  | 2  | 3  | 4  | 5  | Next 20