41. General & Finite Mathematics -- Spring 2000 general Finite Mathematics Spring 2000. Finite Mathematics. Ref. No. CourseNo. 18520, MGF 1107903, TR, 0600-0715, PHY 013, S. Ratti. Chaos fractals. Ref.No. http://www.math.usf.edu/Courses/spring00/genfin.html

Finite Mathematics Ref. No. Course No. Days Time Room Instructor MGF 1106-001 MWF PHY 109 C. Dye MGF 1106-002 MWF BSN 2205 F. Burgos MGF 1106-003 MWF PHY 013 F. Burgos MGF 1106-004 MWF LIF 263 D. Benko MGF 1106-005 MWF HMS 208 R. Wooten MGF 1106-006 MWF LIF 268 A. Gauntlett MGF 1106-007 TR HMS 208 R. Wooten MGF 1106-008 TR PHY 118 R. Smith MGF 1106-009 TR LIF 261 M. Appiou MGF 1106-010 TR PHY 013 R. Smith MGF 1106-011 MWF PHY 109 CANCELLED MGF 1106-012 MWF CHE 104 I. Nikolova MGF 1106-013 TR PHY 108 R. Smith MGF 1106-014 MW CHE 204 C. Godfrey MGF 1106-016 TR LIF 260 R. Wooten MGF 1106-901 MW LIF 263 W. Albrecht MGF 1106-902 TR PHY 108 D. Kerr MGF 1106-903 (Internet Course) MW CIS 1044 I. Bello MGF 1106-904 MW PHY 108 CANCELLED Mathematics for Liberal Arts Ref. No. Course No. Days Time Room Instructor MGF 1107-001 MWF PHY 120 T. Higson MGF 1107-002 MWF LIF 266 F. Zerla MGF 1107-003 MWF LIF 263 F. Zerla MGF 1107-004 MWF LIF 266 J. Oberste-Vorth MGF 1107-005 MWF PHY 109 I. Franklin MGF 1107-006 MWF CHE 105 J. Oberste-Vorth MGF 1107-007 TR HMS 320 Sean McAveety MGF 1107-008 TR LIF 263 Sean McAveety MGF 1107-009 TR PHY 109 D. Jelsovsky

42. CHS Departments Category general Subcategory NA - Date Checked 09/03/2001 fractals in Engineeringhttp//www-rocq.inria.fr/fractales/FE97.html Rocquencourt, France. http://www.chaffey.org/departments/department_links.asp?department=Mathematics

43. Newton Fractals It is also possible to construct Newton fractals for general polynomialsof degree between three and ten by entering the coefficients. http://members.optusnet.com.au/~peterstone/nwtn.html

NEWTON FRACTALS Fractal Explorer Home Page Escape Fractals Newton Parameter Space Fractals Root-finding and the Zeta Function ... Download Fractal Explorer Fractal Explorer uses a special colouring method for fractals associated with the use of Newton's iterative formula for the calculation of complex roots of polynomials and other functions of a complex variable. The general idea is to associate a particular colour with each root chosen from the ten basic colours: red, green, blue, cyan, yellow, magenta, purple, orange, pink and lime, and then use up to 25 shades of the basic colour to indicate the number of iterations required to arrive close to the root. The icon for Fractal Explorer is based on the Newton fractal corresponding to the 4 roots of the polynomial x^4 - 1, while the following fractal is obtained by using Newton's formula to calculate the 5 roots of x^5 - 1 with different starting points. Fractal Explorer has numerous built-in fractals of the Newton type. It is also possible to construct Newton fractals for general polynomials of degree between three and ten by entering the coefficients. One can start with a built-in fractal, and then make alterations to the polynomial coefficients. Fractal Explorer calculates and displays the roots of the polynomial before starting to draw the fractal. Zoom into Newton fractal for z^10 + 0.2 i * z^5 - 1.

44. Read This: Fractals, Graphics, And Mathematics Education Creating a language for the study of roughness and developing the associated computergraphics, he provided the general theory for fractals, which offer new http://www.maa.org/reviews/fractalsmathed.html

Read This! The MAA Online book review column Fractals, Graphics, and Mathematics Education by M. L. Frame and B. B. Mandelbrot Reviewed by George Ashline In the past two decades since Benoit Mandelbrot wrote Fractal Geometry of Nature (Freeman, 1982), fractals have grown in popularity and arisen in many contexts and forms in the mathematical, natural, and even social sciences. Some of the foundational ideas for this field can be traced back to the research of Pierre Fatou and Gaston Julia , who wrote important papers on the iteration theory of rational functions in the early twentieth century. Mandelbrot's pioneering work has brought fractal geometry to the fore and energized a new area of mathematics education. Creating a language for the study of "roughness" and developing the associated computer graphics, he provided the general theory for fractals, which offer new insights into understanding many aspects of Nature and the world around us. This is evidenced in such diverse examples as an island coastline or paper folding patterns or even a cauliflower head! Fractal geometry provides an accessible, interesting setting not only for mathematical research, but also for mathematics education, and there have been many curricular initiatives in this area. In addition to its impact on middle and secondary school mathematics, fractal geometry has influenced undergraduate mathematics, and has been the source for many undergraduate research efforts. For example, consider the programs for the

45. 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://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 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.. If you are interested in buying this book, please use the link on this page. Your purchase will help to support this site.

46. Cliff Pickover, Factals And The Pursuit Of Beauty Pickover's love of fractals and the general field of computerized visualizationhas made him one of the more prolific scientists at IBM. 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).

47. General Education Bibliography general Education Bibliography for Mathematics. (revised Fall, 1995) Barnsley,M. fractals Everywhere, Academic Press, San Diego, 1988. http://www.math.nmsu.edu/morandi/math210gf97/210gbibliography.html

General Education Bibliography for Mathematics (revised Fall, 1995) These books are available at the NMSU library Abbott, E. Flatland Dover, New York, 1952 Ackoff, R. L. The Art of Problem Solving: Accompanied by Ackoff's Fables Wiley, New York, 1987 Adler, H. Introduction to Probability and Statistics, 3rd. Ed. W. H. Freeman, San Francisco, 1964 Ascher, Marcia Ethnomathematics Chattman and Hall, 1990 Asimov, Isaac The Foundation Trilogy Doubleday, New York, 1982 Barnett, Lincoln The Universe and Dr. Einstein William Sloane Associates, New York, 1957 Barnsley, M. Fractals Everywhere Academic Press, San Diego, 1988 Baumgart, J. Historical Topics for the Mathematics Classroom National Council of Teachers, Reston, VA, 1989 Becker, K. Dynamical Systems and Fractals Cambridge Press University, Cambridge, UK, 1989 Beckmann, P. A. A History of Pi St. Martin's, New York, 1971 Bell, E. T. The Men of Mathematics Touchstone, New York, 1986 Biggs, N. Graph Theory Clarendon Press, Oxford, 1936 Bonola, R. Non-Euclidean Geometry Dover Publications, New York, 1955 Box, G.

48. Fractals For fractals we have in general. where is the fractal dimension of theobject. From B.1 we obtain the definition of the fractal dimension http://www.fys.uio.no/~eaker/thesis/node67.html

Next: Scaling behavior and Power Up: No Title Previous: The Conjugate Gradient Method Fractals Figure B.1: Three generations of the Cantor set. The generations are denoted by n . The Cantor set is constructed by taking a straight line of unit length (0th generation). Remove from its middle a section of length . In the figure . What remains are two pieces each of length (1th generation) to which the same procedure is repeated by removing a relative section of length . The process is to be continued indefinitely. In this thesis we have frequently used the concept of fractals when the structures between the invading and the defending fluids have been analyzed. To clarify, I will give a comprehensive introduction to some aspects in fractal geometry used in this thesis. Excellent books such as Fractal written by Feder (1988) [ ] and Fractal Concepts in Surface Growth ] give a complete introduction to these topics and should be read for further details. A fractal is called self-similar if the structure is invariant under isotropic scale transformation which means that the structure is enlarged uniformly in every spatial direction. This is a special case of the more general self-affine fractal which is invariant under anisotropic transformation. That is, when the structure is rescaled with different scaling factors in different spatial directions. One of the simplest self-similar objects is the Cantor set shown in figure B.1

49. Linux Online - Category: Graphics / Fractals Linux Server Hacks. fractals. GLfract uses the file format conventions of Eyefractto view fractal sets in 3D space, Licence GNU general Public License (GPL), http://www.linux.org/apps/all/Graphics/Fractals.html

Fractals Click Here to go back to the index Sort by: [Name] [Last updated] [Author] GLfract Version: More.. GLfract uses the file format conventions of Eyefract to view fractal sets in 3D space Licence: GNU General Public License (GPL) Click Here to go back to the index Maintained by: Webmaster, Linux Online Inc Linux Online Inc Linux Online, Inc Canada Hotels ... Cheap Hotels

50. 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)

51. JosseyBass :: Fractals, Random Shapes And Point Fields: Methods Of Geometrical S JosseyBass Mathematics Statistics Probability Mathematical Statistics general Probability Mathematical Statistics fractals, Random Shapes and http://www.josseybass.com/cda/product/0,,0471937576|desc|2737,00.html

By Keyword By Title By Author By ISBN By ISSN Shopping Cart My Account Help Contact Us ... JosseyBass Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics Related Subjects Bayesian Analysis Multivariate Analysis Related Titles By These Authors Comparison Methods for Stochastic Models and Risks (Hardcover) Stochastic Geometry and Its Applications, 2nd Edition (Hardcover) Aspects of Statistical Inference (Hardcover) A. H. Welsh Design and Inference in Finite Population Sampling (Hardcover) A. S. Hedayat, Bikas K. Sinha Modern Mathematical Statistics (Hardcover) Edward J. Dudewicz, Satya N. Mishra Modern Probability Theory and Its Applications (Paperback) Emanuel Parzen Limit Theorems in Change-Point Analysis (Hardcover) Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics Dietrich Stoyan, Helga Stoyan ISBN: 0-471-93757-6 Hardcover 406 Pages September 1994 US $160.00

52. Fractals And The Mandelbrot Set I feel that I have achieved my goal of providing a general overviewof fractals and the Mandelbrot set. When researching the topic http://www.david-lindsay.co.uk/fyessay.html

Fractals and the Mandelbrot Set Introduction The breathtaking beauty and intrigue that surrounds the subject of fractals has captivated both layman and professional alike. We seem to have an inbuilt fascination with these fractal images, as they exhibit an eerie 'familiarity' with the natural world around us. I chose this assignment to further my existing knowledge of fractals. Earlier this year I worked on a project about recursive graphics for my computer science half of my degree. This investigation sparked my interest into the subject of fractals. In this assignment I hope to provide the following: A simple overview of fractals A brief background of Benoit Mandelbrot and his work An explanation of the mathematics that is used to create the Mandelbrot set Discussions on the applications of fractals ... Bibliography of my sources of information A simple overview on fractals Such striking fractal images can be created by the use of very simple mathematics, however the definition of fractals is far from being trivial. One key feature that lies behind all fractals is the concepts of recursion, which produces the appearance of self similarity in these images. This is best illustrated by an early type of fractal published in 1904 called Koch's curve. The pictures above are generated by applying a simple algorithm through increasing levels of iterations. The 'curve' starts off as an equilateral triangle and then is created by applying the geometric transformation of replacing a ? of the central part of each side of a triangle, with a further 2 segments having the same length as the part being taken away. After the first iteration the image obtained resembles 'David's star'. After successive iterations the result becomes more complex and looking like a snowflake. In summary the image is created by breaking up the overall image, and then breaking these subsequent parts down into smaller versions of the bigger image. This breaking into self similar parts demonstrates the recursive nature of fractals.

53. General Chatter & Frac Posting Couple of new fractals, 7, 10/22/02 90558 pm by PeapodGurrl, Mark. Printingyour images. http://pub82.ezboard.com/fthefractalartistsringfrm4

Wanna show off your newest frac? When you're full of Ring news, and you're all fractal'd out, how about just good conversation and gorgeous fractal images? The Fractal Artists' Ring Invite Friends! Login Register Your Free Account (Required) Search Help ... Need help logging in? Please be respectful of each other. Make fractals, not war. :) Page Topic Replies Last Comment Started By Printing your images. 3/22/03 4:46:52 pm by: Expository one PeapodGurrl showing off ;) 2/3/03 9:21:40 am by: Fractal Grrl ladykeyla Intelligence 1/3/03 6:52:13 am by: PeapodGurrl Caesare Help! I need links! 1/2/03 3:44:36 am del (NT) 12/21/02 10:55:02 am Caesar Contest rules/info right here. 12/3/02 8:19:58 pm PeapodGurrl new fractal 12/2/02 2:09:22 pm by: PeapodGurrl Mark Couple of new ones 12/2/02 2:08:48 pm by: PeapodGurrl Mark New UF utility for importing images 11/3/02 11:02:30 pm by: Fractal Grrl Mark Couple of new fractals 10/22/02 9:05:58 pm by: PeapodGurrl Mark So...how did you guys like the screensaver? 9/27/02 12:30:53 pm by: HiddenDimension PeapodGurrl I need some nicely composed screenshots. 9/21/02 9:14:56 am PeapodGurrl New Gallery and Images...

54. University Of Wyoming General Bulletin: A&S Special Courses 6). Courses of broad general appeal and an interdepartmental flavor will be offeredfrom time to time under this title. 4280. Chaos, fractals and Complexity. http://siswww.uwyo.edu/reg/bulletin/ans_.html

Main Page Front Section University Calendar College/Division Programs ... 4000 Level 1100. Academic and Career Orientation. 1. Provides students with opportunity to explore areas of study available within the colleges of the university and to evaluate their own abilities, interests, and skills relative to career choice. Emphasis is placed upon study skills, self-awareness, exploration of the work world and preparation for entry into a given career. Offered for S/U only. (Normally offered both semesters) 2000. Study Abroad. 1-18 (Max. 18). Students may register through the University of Wyoming for up to two semesters of academic work abroad with the approval of the academic adviser, head of the major department and coordinator of the Study Abroad Program. 2200. British Life and Culture 3. A study of contemporary British institutions and significant aspects of the culture, with a focus on London. Offered as S/U only. Prerequisite: participation in London semester. 2490. Special Topics in. 1-3 (Max. 6). Courses of broad general appeal and an interdepartmental flavor will be offered from time to time under this title. Permits utilization of unusual faculty expertise and provides highly-specialized and particularly pertinent, timely subject matter. See current class schedule for topics. Prerequisite: sophomore standing.

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

Chaos and Fractals in Financial Markets Part 7 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

56. Reference: Fractals It's a general book about fractals, but concentrating a lot on how fractalsoccur everywhere you look, and the different applications of fractals. http://www.cs.stir.ac.uk/~scu/Reference/fractals/

Sharon Curtis Reference Other reference pages: Research/Project Work Java HCI Web Authoring ... Anamorphic Images Fractals Web pages sci.fractals FAQ ThinkQuest's Fantastic Fractals pages, including fractal landscapes, fractal music, galleries, workshops and more Sprott's Fractal Gallery is pretty extensive covering many different types of fractal. There is also a "fractal of the day" feature. Paul Bourke's fantastic graphics pages include a good section on Fractals and Chaos . Lots of articles on various fractal topics, and there are galleries too, including a 3D one you can take a virtual tour of! Wizzle's Mathemagic Images , a gallery with lots of beautiful fractals Jeff Field's Fractal Gallery Fractal Landscapes (a project by Bill Nell at Cornell University) Yuval Fisher's highly informative pages about Fractal Image Compression Fractint is a freeware DOS fractal generator. There is also a Fractint Screen Saver available. Linda has some Fractint lessons , useful for finding your way about the program. Filmer , by Julian Haight, is an animation program that uses Fractint to create fractal movies. Fractal Dimension in Nature (includes clouds project) Cynthia Lanus' Fractal Pages includes information about fractal dimensions A tutorial on Fractal Dimension Books I own copies of some of these books, which I have indicated. If you can't get these through your local bookshop

57. Fractals Some of these are fractals that describe general randomness, while others are fractalsthat can describe chaotic, or nonlinear, systems (where the factors http://www.fortunecity.com/emachines/e11/86/mandel.html

web hosting domain names email addresses related sites Fractals-a geometry of nature Fractal geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies Benoit Mandelbrot Science and geometry have always progressed hand in hand. In the 17th century, Johannes Kepler found that he could represent the orbits of the planets around the Sun by ellipses. This stimulated Isaac Newton to explain these elliptical orbits as following from the law of gravity. Similarly, the back-and-forth motion of a perfect pendulum is represented by a sine wave. Simple dynamics used to be associated with simple geometrical shapes. This kind of mathematical picture implies a smooth relationship between an object's form and the forces acting on it. In the examples of the planets and the pendulum, it also implies that the physics is deterministic, meaning that you can predict the future of these systems from their past. Two recent developments have deeply affected the relationship between geometry and physics, however. The first comes from the recognition that nature is full of something called deterministic chaos. There are many apparently simple physical systems in the Universe that obey deterministic laws but nevertheless behave unpredictably . A pendulum acting under two forces, for example.

58. Fractal Web Sites Excellent source of information on fractal art and fractals in general. If you area neophyte in fractal matters, this would be a good place to start learning. http://www.fractaldomains.com/html/sites.html

Fractal Web Sites Home News Download Register ... Fractal Domains Gallery The fractal sites listed on this page will lead you to dazzling images and mind boggling information about chaos and fractals. Even if you didn't find my site too entertaining, do yourself a favor and check out some of the sites listed below! Galleries Fractal Information Other Sites Of Interest Galleries Infinite Fractal Loop Index I already have a link to the Infinite Fractal Loop on my gallery page, but I want to put an extra plug in for the graphical index that was recently added for the Infinite Fractal Loop. The fractal gallery sites that are members of the loop are all of high quality, and this page has a representative thumbnail for practically every site in the loop. Takes a while for this page to load, but it's worth it! This is the single best starting point I know of for exploring fractal galleries on the Web an unparalleled portal to the world of fractal images. Gumbycat's Cyberhome Gumbycat is the nom de plume of Linda Allison. Her talent continues to grow and amaze. The Gumbycat gallery is now a collection of galleries spread around the net. This link will take you to the starting point. You'll find striking fractal images plus helpful tips on choosing color maps for fractals in Fractint. A unique site in offering how-to tips for fractal fans. A really excellent resource for Fractint users, but anyone who is interested in fractal coloring techniques can learn something. Updated frequently.

59. Mathematics - Lesson Plans Webquests Mathematics general (445) (+93 WebQuests!) Arts (1199) (+42 WebQuests!) Computers(70 School Student Cynthia Lanius' Lessons A fractals Lesson Recognitions http://www.edhelper.com/cat197.htm

Mathematics - Addition - Algebra - Applied Math - Arithmetic - Calculator - Calculators - Calculus - Discrete Math - Division - Fractions - Functions - Games - Geometry - Graphing - Measurement - Money - Numbers - Operations - Pre-calculus - Probability - Statistics - Stories - Trigonometry - Worksheets Return to edHelper.com Lesson Plans, Webquests, and Worksheets. Search: Categories Mathematics WebQuests! Mathematics General (+93 WebQuests!) Arts (+42 WebQuests!) Computers Dance Drama Economics (+23 WebQuests!) Environment Geography Health (+27 WebQuests!) History Holidays Journalism Language (+173 WebQuests!) Languages Literature Mathematics (+93 WebQuests!) Music Physed Reading Science (+375 WebQuests!) Social Studies (+399 WebQuests!) Thematic Webquests (+146 WebQuests!) Math Worksheets ClassBuilder Gradebook Grading can now be more convenient with ClassBuilder! Maintain a gradebook, build exams, create lessons, and more. Version 2.0 now includes Palm Support!

60. Diffusion In Fractal Media There has been a move to discuss general classes of fractals and the behaviour ofdiffusion in the class of deterministic finitely ramified fractals is quite http://www.maths.ox.ac.uk/~hambly/frac.htm

Diffusion in Fractal Media Background Fractals are sets with some form of self-similarity and are often regarded as good models for natural structures. A simple example is provided by certain soils which can show features over a range of length scales. However being able to calculate the dimension of a soil aggregate is purely a recognition of the fact that the soil is highly irregular and does not provide information about how the fractal nature of soil affects the processes that occur within it. In order to make good use of fractal models we need to develop the mathematics to describe the behaviour of partial differential equations, such as the heat and wave equation, in fractal media. Over the past 10 years there has been developing mathematical interest in these questions, with an important approach being to construct stochastic processes on fractals. The connection between Brownian motion and heat flow allows us to give a probabilistic description of the solution to the heat equation. Early work in this area has concentrated on fractals which have exact self-similarity and showed that there is rather different behaviour of the diffusion than that observed in Euclidean space or on manifolds. Some of the phenomena observed are that the transition density of the diffusion is not Gaussian, that there can exist localised eigenfunctions of the Laplacian on a fractal, and that fractals can support stochastic processes which do not have equivalents in Euclidean space. Recent Work

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