61. Citations: And Dimension - Mandelbrot, Form (ResearchIndex) BB mandelbrot. fractals Form, Chance, and Dimension. WH Freeman, San Francisco,1981. BB mandelbrot. fractals Form, Chance, and Dimension. http://citeseer.nj.nec.com/context/323811/0

11 citations found. Retrieving documents... Mandelbrot, B. Fractals-Form, Chance, and Dimension . Freeman, San Francisco, 1977. Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: On the Intrinsic Rent Parameter and Spectra-Based.. - Hagen, Kahng.. (1994) (20 citations) (Correct) ....derived the same relation from a stochastic model of a hierarchical design process. Landman and Russo [28] performed an extensive study of the relation via partitioning experiments on large real life circuits, and observed Rent parameter values p between 0.47 and 0.75. Following Mandelbrot and Keyes [21] one may view Rent s rule as a dimensionality relationship between pinout of a module and the number of gates in the module. This is in some sense a surface area to volume relationship where, for example, intrinsically 2 dimensional circuits such as memory arrays, PLAs, or meshes .... ....observations. First , the experimental results in [5] show a large difference between the predicted and actual values of r; however, r was generally found to vary up or down in accordance with the proposed model. Second, Donath s model has obvious ties to the dimensional intuition noted above

62. Benoit Mandelbrot - ResearchIndex Document Query Yazhen Wang (1997) (Correct) (2 citations) sets was introduced and popularizedby Benoit mandelbrot, fractals have now become a fascinating and www.stat http://citeseer.nj.nec.com/cs?q=Benoit Mandelbrot

63. Fractals, PHOTOVAULT Graphics: Mandelbrot And Julia Fractals PHOTOVALET (tm) Enter search term. fractals mandelbrot and JuliaSets by Wernher Krutein. Seven years ago my friend Mathemetecian http://www.photovault.com/Link/WordsGraphics/FractalsMandelbrot.html

This page contains samples from our picture files on Mandelbrot. These images are available for licensing in any media. For Pricing, General Guidelines, and Delivery information click here . You may contact us thru email or by phone for more information on the use of these pictures, and any others in our files not shown here. Page 1 of 9 Images Found for search term: "Mandelbrot" Show Images Per Page: Page 1 of 9

64. Fractal Gallery: What Is A Fractal? mandelbrot derived the term fractal from the Latin verb frangere, meaning to Thus,fractals graphically portray the notion of worlds within worlds which http://www.glyphs.com/art/fractals/what_is.html

[an error occurred while processing this directive] What Is a Fractal? And who is this guy Mandelbrot? Images and text by Alan Beck The word "fractal" was coined less than twenty years ago by one of history's most creative mathematicians, Benoit Mandelbrot, whose seminal work, The Fractal Geometry of Nature , first introduced and explained concepts underlying this new vision. Although prior mathematical thinkers like Cantor, Hausdorff, Julia, Koch, Peano, Poincare, Richardson, Sierpinski, Weierstrass and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fruitful discipline. Lamp (63 k / jpg) Mandelbrot derived the term "fractal" from the Latin verb frangere , meaning to break or fragment. 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. Traditional Euclidean patterns appear simpler as they are magnified; as you home in on one area, the shape looks more and more like a straight line. In the language of calculus such curves are differentiable. The trajectory of an artillery shell is a classic example. But fractals, like dendritic branches of lightning or bumps of broccoli, are not differentiable: the closer you come, the more detail you see. Infinity is implicit and invisible in the computations of calculus but explicit and graphically manifest in fractals.

65. DISCOVERY OF COSMIC FRACTALS of the history of the idea of selfsimilarity and of cosmological principles, fromPlato's ideal architecture of the heavens to mandelbrot's fractals in the http://www.wspc.com/books/popsci/4896.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Keyword Author Concept ISBN Series New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List DISCOVERY OF COSMIC FRACTALS by Yurij Baryshev (St Petersburg University, Russia) (University of Turku, Finland) With a foreword by Benoit Mandelbrot This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pietronero's first fractal analysis of the galaxy universe), which illustrates how new concepts and deeper observations reveal unexpected aspects of Nature. Contents: The Science of Cosmic Order: The Birth of Cosmological Principles The Gate into Cosmic Order The Paradoxal Universe of Sir Isaac The Dream of Hierarchical World: Protofractals Cosmological Physics for the Realm of Galaxies: The New World of Relativity and Quantum Forces Gravity — The Enigmatic Creator of Order The Law of Redshift in the Kingdom of Galaxies The Triumph of Uniformity in Cosmology The Elusive Simplicity of Uniform Space and Matter:

66. Mandelbrot Set And Fractals My Fractal Program will let you explore not only the mandelbrot Set (z z 2 ) butalso (z- z 3 ) and (z- z 4 ) as well as a number of more esoteric fractals. http://ourworld.compuserve.com/homepages/pagrosse/mandelb.htm

Index Mah Jong Mandelbrot Water Rockets SIRDS Weird ... E-Mail Fractals Fractals have always been interesting to people who like to explore but getting your hands on a program that will let you do that has always been a problem. The link at the bottom of this page allows you to download a copy of my mandelbrot program which is postcardware (you send me a post card to license it) Technical Mumbo Jumbo:- ) as well as a number of more esoteric fractals. Exploration is not limited to the x : i plane but extends to the y : z plane as well giving you Julia sets and Fatou Dusts reflecting the earlier work of the mathematicians Gaston Julia and Pierre Fatou whilst extending it into higher order mappings. Background Mumbo Jumbo:- E xisting between the -1 and +1 in four dimensions, the ginger bread man fractal figures of the Mandelbrot set (based on two of the planes, the x plane and the imaginary plane) have become familiar to us all. M andelbrot's work was a result of trying to unify the work of Gaston Julia and Pierre Fatou during the First World War. The mathematics is based upon repetitive mapping of points in the imaginary plane. T he imaginary plane was invented to explain away problems in expressing time in relativity as imaginary numbers were the only solution to the four dimensional Pythagorean solution.

67. Java Fractals This site contains some fractals I have written, implemented through Java Applets.The mandelbrot Set fractal applet is not complete, so it doesn't include http://www.daa.com.au/~james/fractals/

Home Software Talks Articles Fractals IFS fractals Mandelbrot Orbit Fractals Diary Java Fractals Update - As well as the new look, I have removed the old mandel0 applet, since it has been superceded by the Classic Mandelbrot/Julia Set applet. Also the code has been moved to the end of this contents page to make rest of the site look more user friendly. You will also notice that I have added a section on orbit fractals that contains six new applets. IFS Fractals What is an IFS fractal My Java IFS Applet Some IFS fractals Sierpinski Triangle Fern Spirals Dragon ... IFS Formula Complex Number Fractals Update - These fractals now work with Windows. Also, if they worked for you before, they will prbably run faster with more colours. (If you are interested in what changed, I have switched over to using an ImageProducer interface) If you want a better resolution, select a different pixel size from the list box (1 is best), and press the redraw button. What Does This Applet Do How the Formula is Used Different Sets: Classic Mandelbrot/Julia Set Cubic Mandelbrot/Julia Set Quartic Mandelbrot/Julia Set Phoenix Set ... Newton-Raphson type Fractal Orbit Fractals Orbit Fractals Introduction Fractal Popcorn Fractal Gingerbreadman Hopalong Orbit Fractal ... Inverse Julia Set Fractal Code Code for all my fractal applets IFS Applet Code Mandel0 Applet Code - My first attempt at a Mandelbrot Set applet.

68. Fractals And The Mandelbrot Set fractals and the mandelbrot Set. Introduction. I feel that I have achieved mygoal of providing a general overview of fractals and the mandelbrot set. 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.

69. Chaffey's Fractals - The Mandelbrot Chaffey's fractals on the WEB© Chaffey High School's fractals on the Web http//www.chaffey.org/fractals/. ChaffeyHigh School's mandelbrot Home Page Last http://www.chaffey.org/fractals/mandelbrot/

Chaffey High School's FRACTALS on the Web http://www.chaffey.org/fractals/ Chaffey High School's Mandelbrot Home Page Last Updated February 28, 2003 MANDELBROT Questions and Answers When did the mandelbrot surface? Who found the thing? How does the Mandelbrot come to form? What is ITERATION? Does the mandelbrot come from an equation? Where can I find out more about these mandelbrots? The mandelbrot was first discovered about 1980, so it is fairly new to the mathematical world. Here are some of the first sets that were seen using computer generated software. The first image is from Asking who found the Mandelbrot? Well, Mr. Mandelbrot himself (depicted to the here on the right). To be more exact, Benoit B. Mandelbrot. He is a mathematician, born in 1924 in Warsaw. He studied at the Ecole Polytechnique, Paris, and at the California Institute of Technology What is know as the mandelbrot set is.. Iteration is.. The Equation is Z=z*z+c CHS Home Fractals Home About Fractals Awards ... Theory

70. 2003_Mon_File NewYork),1982. 2. BB.mandelbrot, fractals and Scaling in Finance Discontinuity,Concentration, Risk, New York Springer, 1997. 3. BB http://www.japanprize.jp/e_2003_mon_file.htm

Dr. Benoit B. Mandelbrot Academic Degrees: Ing nieur dipl m , Ecole Polytechnique, Paris California Institute of Technology, Master of Science California Institute of Technology, Professional Engineer in Aeronautics, Facult des Sciences de Paris, Docteur d'Etat s Sciences Math matiques Professional Career: Staff member (Attach , then Charg , then Ma tre de Recherches), Centre National de la Recherche Scientifique, Paris, France Ma tre de Conf rences de Mathematiques Appliqu es, Universit , Lille, France Ma tre de Conf rences d'Analyse Math matique, Ecole Polytechnique, Paris, France Research Staff Member, IBM Thomas J. Watson Research Center, Yorktown Heights NY. IBM Fellow, IBM Thomas J. Watson Research Center Abraham Robinson Adjunct Professor of Mathematical Sciences, Yale University, New Haven, CT. 1993-present IBM Fellow Emeritus, IBM Thomas J. Watson Research Center 1999-present Sterling Professor of Mathematical Sciences, Mathematics Department: Yale University Major Books and Papers: B.B.Mandelbrot

71. Fractals, Chaos, And Cosmic Autopoiesis mandelbrot's fractals are the brainchild of mathematics and computergeneratedtechnology. They help to illustrate iterations, bifurcations http://www.bizcharts.com/stoa_del_sol/plenum/plenum_5.htm

Home The Logos Continuum The Cosmic Plenum The Imaginal Within The Cosmos ... The Cosmic Plenum : Fractals, Chaos, and Cosmic Autopoiesis In his theory of the Implicate Order, the late quantum physicist David Bohm refers to fractals in his study of the holomovement, the plenum that powers the inner universe almost in the sense of a feedback loop of unfolding-enfolding between the implicate and explicate orders of the cosmos. Fractal geometry shows that *shapes have self-similarity at descending scales.* Fractals can be generated by iteration; they are characterized by "infinite detail, infinite length, no slope or derivative, fractional dimension and self-similarity." Basically, the "system point folds and refolds in the phase space with infinite complexity." [John Briggs and F. David Peat, TURBULENT MIRROR, Harper & Row, 1989. p. 95] Benoit Mandelbrot, one of the world's mathematical giants on fractals, said that "fractal shapes of great complexity can be obtained merely by repeating a simple geometric transformation, and small changes in parameters of that transformation provokes global changes." In essencethrough a predictable, orderly process the "simple iteration appears to liberate the complexity hidden within it, thus giving access to creative potential." [Ibid, p. 104] Thus, in that misnomer called chaos theory, mathematicians and physicists have discovered an *underlying order,* a kind of memory operating in non-linear, evolving systems. Fractal geometry illustrates that shapes have self-similarity at descending scales. In other words, the form, the *information,* is enfoldedalready present in the depths of the cosmos. So this is reminiscent of the Implicate Order. Iteration liberates the complexity hidden within it. It is not dissimilar to Bohm's law of holonomy: a "movement in which new wholes are emerging." [David Bohm, WHOLENESS AND THE IMPLICATE ORDER, Ark Paperbacks, 1983, pp. 156-157.]

72. High Quality Mandelbrot Images High Quality mandelbrot Images. All images on this page have been computed by a verysimple C++ program. The emphasis lies on quality, not on computation speed. http://www.cosy.sbg.ac.at/~gwesp/fractals/

High Quality Mandelbrot Images All images on this page have been computed by a very simple C++ program. The emphasis lies on quality, not on computation speed. Therefore all internal computations, even those in color space, are done using double The YYY(TM) (Yellow Yin Yang) High quality rendering of the above image (1500x1499; 2 MB) The rotating spiral ( MPEG-1 video; 6 MB) Computation of this image took about 15 minutes on a standard PC, the animation about 20 hours. MPEG-1 encoding for the video animation was done using the Berkeley MPEG tools and took 30 minutes. The Snake, detail of the Yin Yang. High quality rendering Blue Spear High quality rendering Katja's Eye High quality rendering Three large (and an infinite number of smaller) spirals High quality rendering Homepage Hot Spots C ... Fractals last modified Wednesday, 03-Oct-2001 18:08:19 CEST by gwesp@cosy.sbg.ac.at

73. Dynamical Systems And Technology Project A project designed to help secondary school and college teachers of mathematics bring contemporary Category Science Math Chaos and fractals Chaos...... and students understand the mathematics behind such topics as iteration, fractals,iterated function systems (the chaos game), and the mandelbrot and Julia sets http://math.bu.edu/DYSYS/

Dancing Triangles The Dynamical Systems and Technology Project at Boston University Zooming Sierpinski This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iteration, fractals, iterated function systems (the chaos game), and the Mandelbrot and Julia sets. Available at this site: JAVA Applets for chaos and fractals Play the chaos game; explore iterated function systems; and make fractal movies, like the Dancing Triangles and Zooming Sierpinski above, all at your own computer. These applets are now up and running! The Mandelbrot Set Explorer This is an interactive site designed to teach the mathematics behind the Mandelbrot and Julia sets. It consists of a series of tours in which you will discover some of the incredibly interesting and beautiful mathematics behind these images. The site is designed to be used by readers of

74. Devaney Books Topics include iteration, chaos, fractals, the mandelbrot and Julia sets.CHAOS AND fractals THE MATHEMATICS BEHIND THE COMPUTER GRAPHICS. http://math.bu.edu/people/bob/books.html

Books by Robert L. Devaney A TOOLKIT OF DYNAMICS ACTIVITIES This is a series of four paperback books on dynamical systems for high school students and their teachers. The books progress in level from grades 7-9 (Iteration and Fractals), grades 10-11 (Chaos), and grade 12 (The Mandelbrot and Julia Sets). Iteration: A Toolkit of Dynamics Activites. Key Curriculum Press, 1998. With J. Choate and A. Foster. Fractals: A Toolkit of Dynamics Activities. Key Curriculum Press, 1998. With J. Choate and A. Foster. Chaos: A Toolkit of Dynamics Activities. Key Curriculum Press, 1999. With J. Choate. The Mandelbrot and Julia sets: A Toolkit of Dynamics Activities. Key Curriculum Press, 1999. AN INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS. Second Edition. Now published by Perseus Publishing Co. , a division of Harper/Collins, 1989. ISBN 0-201-13046-7. Telephone: 800-386-5656. This book is intended for graduate students in mathematics and researchers in other fields who wish to understand more about dynamical systems theory. Half the book is devoted to one-dimensional dynamics, the remainder equally split between higher dimensional dynamics and complex dynamics. The book has been used in undergraduate courses with success. However, it is advisable to cover only the material on one-dimensional dynamics in such a course. Want to see some happy readers of the first edition? Click

75. Math.com Wonders Of Math The word FRACTAL was invented by Benoit mandelbrot. fractals are interesting becauseas you zoom in closer, the pattern is just as beautiful and complex as http://www.math.com/students/wonders/fractals.html

Home Teacher Parents Glossary ... Email this page to a friend More Wonders Fractals Spirograph Conway's Game of Life Roman Numeral Calculator ... Lissajous Lab Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search Fall Into Fractals The word FRACTAL was invented by Benoit Mandelbrot Fractals are interesting because as you zoom in closer, the pattern is just as beautiful and complex as when you start. Learn about fractals and create your own beautiful fractal images by following the links below. Interactive Fractal Sites Mandelbrot Set Zoom into a fractal in your browser window. Mandelbrot Explorer Make and post your own images. The Fractory A site built by students for the Thinkquest contest. Build your own fractals and learn about the math behind the images. Mandelbrot and Julia Set Explorer Zoom into fractals. Fractal Galleries Fractalus The fractal from an artist's point of view. Sprott's Fractal Gallery You won't believe the fractal art, animations, and even music! Be sure to visit

76. VMI Fractals Scholz, Christopher H. and Benoit B. mandelbrot. fractals and Geophysics. Basel ;Boston Birkhauser Verlag, 1989. UCB Earth Sci QC801 .G37 v.13112; Schroeder http://www.visual-chaos.org/fractals/books.html

Fractal Geometry Books Bassingthwaighte, James B., Larry S. Liebovitch, and Bruce J. West. Fractal Physiology. New York : Oxford University Press, 1994. Notes: Part III, Physiological applications of fractal geometry: ion channels, heart muscle, neurons, vascular flows, growth. Crilly, A. J., R. A. Earnshaw, and H. Jones, eds. Fractals and Chaos. New York: Springer-Verlag, 1991. Notes: Part 1: 7 chapters on fractal geometry including applications to growth, image synthesis, and neural nets. Part 2: 6 chapters on chaos theory, including applications to physical systems. Dubrulle, B., F. Graner, and D. Sornette. Scale Invariance and Beyond. New York: Springer-Verlag, 1997. Notes: Applications of fractals and wavelets to: condensed matter, cosmology, earthquakes, biology, finance, turbulence, DNA sequences, gravity, metallurgy. Devaney, Robert L., and Linda Keen, eds. Chaos and Fractals: The Mathematics Behind the Computer Graphics. Providence, RI: Amer. Math. Soc, 1989. Notes: Lecture notes from an AMS short course from 1988, by Devaney, Holmes, Alligood and Yorke, Keen, Branner, Harrison, and Barnsley.

77. The Wu! © Fractals: The Mandelbrot Set fractals The mandelbrot Set http://www.ocf.berkeley.edu/~wwu/fractals/mandelbrot.html

Fractals: The Mandelbrot Set Home Introduction to Fractals Mandelbrot Sierpinski ... Gallery Construction: The Mandelbrot set is the set of all complex numbers c such that iterating z <= z^2 + c does not ascend to infinity, starting with z=0. The terms z and c are complex numbers (see Note 1 for an overview of complex numbers, if necessary). "Ascend to infinity" means that z will continue to grow with each iteration; in calculus terms, it means that z diverges; more on this, as well as the initial condition z=0 , later. I will proceed with explaining simply how to graph the set, and place explanations for the mathematical intricacies in footnotes for those curious. We could probably find a few elements in the Mandelbrot set by pencil and paper, but in order to crank out enough iterations to produce even a semi-decent graph before dying of either old age or a mental segmentation fault, we will want to determine the elements of the Mandelbrot set using a simple computer program. I will use Java-like pseudocode. Let us first declare a complex number class complexNumber // A class for complex numbers.

78. History Of Mandelbrot And Julia Fractals history of the mandelbrot and julia fractals. Fractal is a term coined by Benoitmandelbrot (1924) to describe an object which has partial dimension. http://www.icd.com/tsd/fractals/beginner1.htm

history of the mandelbrot and julia fractals "Fractal" is a term coined by Benoit Mandelbrot (1924-) to describe an object which has partial dimension. For example, a point is a zero-dimensional object, a line is a one-dimensional object, and a plane is a two-dimensional object. But what about a line with a kink in it? Or a line that has an infinite number of kinks in it? These are mathematical constructs which don't fit into normal (Euclidean) geometry very well, and for a long time mathematicians considered things like these as "monsters" to be avoided - lines of thought that defied rational explanation in known terms. Within the past few decades, "fractal math" has exploded, and now there are "known terms" for describing objects which heretofore were indescribable or inexplicable. There are an infinite variety of fractals and types; those that I focus on in my gallery are Mandelbrot and Julia fractals. Gaston Julia (1893-1978) was a French mathematician whose work (published in 1918) inspired Mandelbrot in 1977 (the second time Mandelbrot looked at Julia's work). Mandelbrot used computers to explore Julia's work, and discovered (quite by accident) the most famous fractal of all, which now bears his name: the Mandelbrot set. Menu Next Topic

79. Fractals -- An Introduction It is also important to note that several images, now considered fractals predatethe work of mandelbrot. Last Updated Friday, 02Feb-2001 051705 GMT http://ejad.best.vwh.net/java/fractals/intro.shtml

Fractals An Introduction The purpose of this lesson is to learn very simple methods to construct fractals, to do and practice some math, to appreciate the beauty of fractals, and finally to have fun with math. The lesson includes several Java applets for hands-on construction and interaction with simple fractals. Lets start with definitions. In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules. In many cases, the rules to make the figure grow from one stage to the next involve taking the original figure and modifying it or adding to it. This process can be repeated recursively (the same way over and over again) an infinite number of times. The fractals' growth mechanism can be visualized very easily with a simple example. Start with a + sign and grow it by adding a half size + in each of the four line ends. Repeat the exact same process recursively as many times as desired. We'll call this the Plusses fractal: Notice how the + sign grows into a rhombus (popularly known as diamond) in very few simple steps. Further in the lesson we'll count the number of +'s in each of the stages to see how quickly its complexity grows.

80. Aburns Orbits, mandelbrot Set and Julia Sets; Persian Recursion; Real and ImaginaryInflorescences; Other Applets. Gallery of MathScapes; fractals; Download Vnature http://phoenix.liunet.edu/~aburns/webpage/aburns.htm

Department of Mathematics Long Island University C.W. Post Campus Brookville, NY 11548 aburns@liu.edu Mathematics and Art Applets Plants using String Rewriting Imaginary Gardens M-furcations, M = 2,3,4,... or Around the boundary of M0 Orbits, Mandelbrot Set and Julia Sets ... Links to interesting math-related web sites

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