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         Fractals:     more books (100)
  1. The Fractal Geometry of Nature by Benoit B. Mandelbrot, 1983
  2. Fractal Time: The Secret of 2012 and a New World Age by Gregg Braden, 2010-02-01
  3. Fractals, Googols, and Other Mathematical Tales by Theoni Pappas, 1993-02-16
  4. The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson, 2006-03-07
  5. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise by Manfred Schroeder, 2009-08-21
  6. Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer, 2003-11-14
  7. Introducing Fractals: A Graphic Guide by Nigel Lesmoir-Gordon, 2005-10-15
  8. The Science of Fractal Images
  9. Fractals: The Patterns of Chaos: Discovering a New Aesthetic of Art, Science, and Nature (A Touchstone Book) by John Briggs, 1992-11-01
  10. Chaos and Fractals: New Frontiers of Science by Heinz-Otto Peitgen, Hartmut J├╝rgens, et all 2004-02-03
  11. The Beauty of Fractals: Images of Complex Dynamical Systems by Heinz-Otto Peitgen, 1986-08
  12. Introducing Fractal Geometry by Nigel Lesmoir-Gordon, 2002-01-26
  13. Fractals Everywhere by Michael F. Barnsley, 2000-04-18
  14. Lectures on Fractal Geometry and Dynamical Systems (Student Mathematical Library) by Yakov Pesin and Vaughn Climenhaga, 2009-10-21

1. Cynthia Lanius' Lessons: A Fractals Lesson - Introduction
Mathematics lessons for elementary school, middle school fractals, fractals, fractals.
Cynthia Lanius
Pictured: A Famous Fractal - The Mandelbrot Set
A Fractals Unit for Elementary and Middle School Students
That Adults are Free to Enjoy
Table of Contents
Introduction Why study fractals?
What's so hot about

fractals, anyway?
Making fractals
Sierpinski Triangle

Using Java

Math questions

Sierpinski Meets Pascal
Using Java
Fractal Properties

Fractional dimension
Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Send mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received
What are Fractals?
They're everywhere, those bright, weird, beautiful shapes called fractals. But what are they, really? Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun! Teachers: Every lesson has a print version for classroom use.

2. Sprott's Fractal Gallery
Daily updated gallery of automatically created fractals. Fractal generating software.
Sprott's Fractal Gallery
Awards Received
MIDI Fractal background music
courtesy of Forrest Fang
Fractal of the Day
Every day at a few minutes past midnight (local Wisconsin time), a new fractal is automatically generated by a variation of the program included with the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott . The figure above is today's fractal displayed in low (320 x 200) resolution. Click on it or on any of the cases below to see them at higher (640 x 480) resolution with a code that identifies them according to a scheme described in the book. Older Fractals of the Day are saved in an archive . If your browser supports Java, you might enjoy the applet that creates a new fractal image every five seconds or so. If you would like to place the Fractal of the Day on your Web page, you may do so provided you mention that it is from Sprott's Fractal Gallery and provide a link back to this page. If you want to make your own fractals, I recommend the Chaoscope freeware.

3. Coolmath4kids - Fractals ( Geometry )
I ve really been beefing up the fractal area over on the main site, so I m just going to send you over there to check it out.
Your browser does not support the IFRAME tag. Coolmath's Fractals Your browser does not support the IFRAME tag.
What are fractals? The easiest way to explain them is that they are pictures made with math! Like this... Pretty cool, huh? They were discovered just 20 or so years ago by a man named Benoit Mandelbrot (that's French). The reason that they weren't discovered before this is that you need a computer to make them! I've really been beefing up the fractal area over on the main site, so I'm just going to send you over there to check it out. At the top of every page, you can click on the "kids" link to get back to this site. We've got a fractal gallery and generators so you can make your own fractals! Just click the link to go: Coolmath Fractals HELP SUPPORT COOLMATH
link to us
advertise with us about us safe surfing ... continuing teacher education Thanks for visiting

4. What Are Fractals?
Ahh, the beauty of noninterger self-similar dimensions. An explanation of fractals and some cool picts.

5. The Fractory: An Interactive Tool For Creating And Exploring Fractals
This page will help you learn about fractals what they are and how to design them, but it will also let you discover more on your own.
A ThinkQuest project by David Green Alex Kulesza , and Keith Bergstresser Welcome to The Fractory! This page will help you learn about fractals: what they are and how to design them, but it will also let you discover more on your own. Fractals are just now emerging as a science. They show an order in seemingly random things, and give us tools with which we can predict the weather, render natural looking objects, and help understand the order in our chaotic lives. You will also play a part in our interactive fractal creation center, designing and displaying fractals you have invented. You can even post your coolest fractals on our fractal message board.
How to Understand Fractals
Fractals can be understood on many different levels. We have separated the information on this page into the five levels listed below in increasing order of difficulty. We suggest that you start at the first one, and work your way up. You may be surprised at how far you are able to get. You are encouraged to continue as long as you are interested, but each level requires more math and more time than the previous, so you can decide what is reasonable for you.
1.The first way in which anyone can appreciate fractals is simply for their beauty. To do this, we suggest that you go to our

6. Exploring Fractals
It is is based on a curriculum, entitled Exploring Fractal Dimension, developed by Mary Ann Connors and Anna Rose Haralampus at an NSF funded Institute
Exploring Fractals
Mary Ann Connors
publications and photos
Department of Mathematics and Statistics
University of Massachusetts Amherst
This World Wide Web project commenced in July 1994. It is is based on a curriculum, entitled "Exploring Fractal Dimension," developed by Mary Ann Connors and Anna Rose Haralampus at an NSF funded Institute for High School Mathematics Teachers at Georgetown University July - August, 1991. Its revision entitled "Exploring Fractals: From Cantor Dust to The Fractal Skewed Web" has been edited by Mary Ann Connors 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, and 2004.
Exploring Fractal Dimensions of Strictly Self-Similar Fractals:
Cantor Dust to the Fractal Skewed Web
What is a fractal? A fractal is a geometric shape which
  • is self-similar and has fractional (fractal) dimension.
  • An introduction
    So, what are fractals?
    What does it mean for a shape to be self-similar
    Strictly Self-similar shapes
    What is dimension?
    How do we assign dimension to an object intuitively?
    What is the dimension of a geometric object?
    Mathematical Interpretation
    Dimension of a Fractal
    Non-integer and integer dimensions
    Questions and Answers
    Generating Fractals
    Strictly Self-similar Fractals
    Teacher Information
    Sources Sources for Exploring Fractals Some Interesting Links for Further Exploration If you wish to use any of the text or images in Exploring Fractals please contact its author Mary Ann Connors at the following address.

    7. Mathematics Archives - Topics In Mathematics - Fractals
    KEYWORDS Monte Carlo Estimation of Pi, OneDimensional Random Walk, Two-Dimensional Random Walk, Diffusion Limited Aggregation, Self-Avoiding Walk, Fractal
    Topics in Mathematics Fractals

    8. Fractals Similar pages The Spanky Fractal DatabaseThe Spanky Fractal Database is a collection of programs, images, and other material all relating to the subject of fractals.
    News New Journals Browse Journals Search ... Fractals

    Complex Geometry, Patterns, and Scaling in Nature and Society The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, technology and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. More News
    An Appeal from the Honorary Editor to the Readers of Fractals Announcement:
    After four years of dedicated service to the Fractals journal, Dr. Janos Kertesz will retire from his role as Regional Managing Editor (Europe), but will continue to serve as a member of the Editorial Board. Dr. Kertesz will be succeeded by current editorial board member Dr. Miroslav Novak of the Faculty of CISM, Kingston University, England.

    9. Fractals - Fractal Recursions
    Jock Cooper s gallery of still images and animations.
    News! Order the new The Fractal Recursions DVD through Amazon or Createspace Welcome to the ever-evolving exhibition of Jock Cooper's Fractal Art. A noteworthy recent addition to the site is the Zoomable Fractal Gallery; an interactive playground that allows one to zoom through six levels in each quadrant of a given fractal image. As always, the newer images are in the highest gallery numbers, and new images are added several times a week.
    Traditional Gallery
    788 images
    Mechanical Gallery
    274 images
    Miscellaneous Gallery
    233 images
    Limited Palette Gallery
    161 images
    Fractal Animations Gallery
    29 animations
    Zoomables Gallery
    6 Zoomable Fractal images
    Some (mostly older) images are available as high quality prints on photo paper or posters . If you are interested in an image not available let me know, I can generally add it within a day or two.
    Please send comments to me at Jock.Cooper At Gmail Dot Com
    For commercial use please contact Bruststrokes At Comcast Dot Net
    You can now view gallery images on your Hires or Lores mobile device. Most recent images are shown first.

    10. Fractals: An Introductory Lesson
    The purpose of this site is to present material to learn very simple methods to construct fractals, to do and practice some math, to appreciate the beauty
    Fractals: An Introductory Lesson
    Last Updated: Friday, 11-Aug-2000 22:59:35 GMT

    Java Home



    11. Fractals
    Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse
    Fractals, Chaos
    New FAQ: Spherical mirror projection for hemispherical domes
    Representing and modelling geometry in SecondLife

    Announcements 2008 Australasian Planetarium Society Conference
    Index Papers, Articles, Seminars Exhibitions Projection Data Formats Fractals, Chaos Surfaces, Curves Modelling, Rendering Texture, Colour Geometry Fun, puzzles Other Old stuff
    Representing geometry in SecondLife

    Some comments on the suitability of SecondLife as a way of presenting fractal geometry POVRay Fractal Raytracing Contest Rendering Wada-type basins of attraction
    Here's a party trick for over Christmas. Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season. Fractal Dimension Calculator - FDC
    Box counting software for the Macintosh and Linux. Ruler or Compass Dimension Time exists so that not everything happens at once. Multifractal spectrum Lacunarity Recurrence plots By Gayla Chandler
    Natural Fractals in Grand Canyon National Park

    Fractals: A Symmetry Approach

    Gasket Photography
    Self similarity Examples of self similarity in fractals with examples from mathematics and photos of the physical world.

    12. Fractal Geometry
    An educational resource on the mathematical framework and formalism from the Yale University, covering the concept of self similarity.

    13. IconBAZAAR - Fractals - Page 01
    Click the thumbnails to view the corresponding fractals. arach.gif THUMBNAIL bay.gif Click the thumbnails to view the corresponding fractals

    14. The Fractal Microscope Similar pages fractalsThe primary focus of the Community Learning Network (CLN) is to help K-12 teachers integrate Information Technology into their classrooms.

    15. Fractals
    Easier A fractal is a shape, often drawn by a computer, that repeats itself in a pattern. The design shapes usually reoccur in different sizes.
    The Topic:
    Fractals Easier - A fractal is a shape, often drawn by a computer, that repeats itself in a pattern. The design shapes usually reoccur in different sizes. Harder - Fractals are endlessly repeating patterns that vary according to a set formula, a mixture of art and geometry. Fractals are any pattern that reveals greater complexity as it is enlarged A real-life example of fractals is ice crystals freezing on a glass window. You can see countless variations of the same pattern emerge in the crystals over time.
    Exploring Fractals (Grades 9-12) by M.A. Connors This website explores fractal dimensions of strictly self-similar fractals, from Cantor Dust to the Fractal Skewed Web. Includes a teacher information section. Related Websites: 2) Fract-ED (Grades 8 and Above)

    16. What Are Fractals?
    A definition of fractals as a unique digital art form and in the broader sense of fractal geometry.
    Seattle Fractals Digital Art
    Experience the "Art Of Infinity"
    Site Menu

    Home What Are Fractals? Screensavers Art Prints Purchase Screensavers Special Offers Support Testimonials Artist Bio Contact Links What are fractals?
    Fractals : A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature. Iteration : The process of repeating a set of instructions a specified number of times or until a specific result is achieved. Click for larger image Relative to this art form, fractals are a unique art form using mathematical formulas to create art with an infinite diversity of form, detail, color and light. In simple terms, a fractal is a graphical image that represents the behavior of a mathematical equation. The formula used determines how each pixel in an image is formed and colored. (Pixels are the smallest display elements that make up the images you see on a computer monitor or television.) A typical fractal image contains millions of these pixels. These complex images of extraordinary beauty can arise out of fairly simple mathematical functions and then by selectively modifying these formulas, changing coloring algorithms etc. one can create unique compositions previously unseen to the human eye. In the broader scientific sense, they are essentially geometric shapes or forms that are represented in natural objects, from a fern leaf or tree, to a spider web or snowflake, to larger phenomena such as clouds or even galaxies in space.

    17. Fractal Explorer: Mandelbrot And Julia Sets (by Fabio Cesari)
    Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms,
    var track_id=9988; var sc_project=1438278; var sc_invisible=1; var sc_partition=13; var sc_security="919ae89d"; Keywords: fractals, mandelbrot set, fractal, julia sets, quaternion, quaternion julia sets, Mandelbrot, Julia Your browser doesn't support frames. This site is best viewed with , or an equivalent browser that supports JavaScript and frames
    You can always access this no-frames version of this site. If you have troubles accessing it, please let me know Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms, how the Mandelbrot set and Julia sets are generated. This document provides an informal introduction to these subjects, and is only intended to be a starting point to learn more about fractals and fractal geometry.
    You can contribute to the future development of this site by filling out the feedback form
    Comments and suggestions are very appreciated.
    Have fun! About complex numbers
    Mandelbrot set

    Julia sets

    Images gallery
    Quaternion Julia sets images gallery"

    Other pages: About the author

    Feedback form
    Sign my guestbook ... View my guestbook This page hosted by Get your own Free Home Page

    18. Untitled
    Genuine fractals 5 simply produces higher quality and sharper results than traditional scaling methods in Photoshop® or in any other third party product.

    19. FractalNet Home Page
    The Fractal Images Company 268 Arlington Road Kensington, CA 94707. Voice 510528-0258 Fax 510-528-0243 e-mail
    Best experienced with
    Click here to start.
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    FractalNet Commercial Links
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    20. Graphics Archive - General Interest:Fractals
    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
    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.
  • Amoeba Fractal
  • An aperiodic tiling
  • Antoine's Necklace
  • Arbitrary substitution tiling
  • Brot Cheese Fractal
  • DodecaFoam! First Stellation
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