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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
Computer generated artwork, with thousands of downloadable images and a new fractal every day!
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. 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.

4. 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

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.

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. Fractals Similar pages Mathematics Archives - Topics in Mathematics - fractalsKEYWORDS Monte Carlo Estimation of Pi, One-Dimensional Random Walk, Two-Dimensional Random Walk, Diffusion Limited Aggregation, Self-Avoiding Walk, Fractal
    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 M. Novak of the Faculty of CISM, Kingston University, England.

    8. 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



    9. Spanky Welcome
    The Spanky Fractal Database is a collection of programs, images, and other material all relating to the subject of fractals.
    The Elastic Fractal
    Welcome to the Spanky Fractal Database
    I also point to a great deal of material that is not at this site. Consequently I have no control of when this information or service is removed or am I notified if the URL becomes invalid. I try to check my indexes periodically to see what is still valid, but it is not an automated process. If you find URL's that I point to have become outdated and constantly fail to respond on your attempts to load them, (over several days) then please inform me of this problem and I will remove them from my lists.
    Mirrors of Spanky Fractal Database
    The main site for this fractal database
    is now completely mirrored at Many thanks to Damien M. Jones at Fractalus for hosting the mirror site and for his help in setting it up.
    New PNG image format used
    Enjoy and discover.
    A Table of Fractal Information.

    10. 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
    This site relies on advertising revenue to stay online. Please help us by clicking a sponsor's ad.
    Fractals Contents Page 01 Page 04 Page 02 Page 05 ... Conditions of Use Permission is granted for limited personal use of up to twenty (20) images from ALL collections. ALL commercial or institutional use requires licensure
    Redistribution of any image found at this web site in any format is strictly prohibited.
    Last updated:
    August 5, 2007.
    All images 1994 - 2004 Randy D. Ralph, Christopher E. Ralph, IconBAZAAR LLC. Other Resources:
    NetStrider Design

    My Realty Guide

    Web Hosting

    Web Directory
    Click the thumbnails to view the corresponding Fractals
    THUMBNAIL THUMBNAIL THUMBNAIL THUMBNAIL ... THUMBNAIL Click the thumbnails to view the corresponding Fractals
    UP BACK NEXT This site uses advertising revenues to stay online. Please click a sponsor's advertisement during your visit

    11. Fractals
    The primary focus of the Community Learning Network (CLN) is to help K12 teachers integrate Information Technology into their classrooms.
    Fractals Theme Page This "Theme Page" has links to information about Fractals. Students and teachers will find curricular resources (information, content...) to help them learn about this topic. In addition, there are also links to instructional materials (lesson plans) which will help teachers provide instruction in this theme. Please read our
    An Internet Fractal Lesson
    To study fractals using World Wide Web and generating your own f ractal. (Grades 7-12)
    Chaos Club
    Educational resources, online games and message chat areas for students and teachers exploring fractals. Be sure to check out the "tutorial" for a unit by Cynthia Lanius in which elementary and middle students utilize online resources to study properties of fractals either independently or with a teacher. Lessons can be downloaded and printed.
    The Explorer is a collection of information on educational resources (instructional software, lab activities, lesson plans, student created materials ...) that K-12 mathematics and science educators can download. Enter "Fractals" in the search engine and you'll see about a dozen resources.
    Exploring Fractals
    This site for secondary students explores several aspects of fractals. After an introduction to fractals, the author explores assigning dimensions, both non-integer and integer, and several ways of generating fractals.

    12. 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 Warping patch for Quartz Composer
    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.

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

    14. 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)

    15. 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.
    ChiaraMail(tm) Version 2.0 now available
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    Version 3.0 of WebReader(tm) includes a number of significant new features and benefits; for an overview of functional enhancements in Version 3.0, check out new features and enhancements . Beginning December 7, 1999, you can download WebReader 3.0 at no cost. Before downloading WebReader, make sure you meet the minimal system requirements
    FractalNet Commercial Links
    Linda Sy Skin Care , offering high-quality skin care products developed by a practising dermatologist. Treat yourself or your spouse to the gift of beautiful, healthy skin with our line of products previously available only from dermatologists.
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    268 Arlington Road
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    Fax: 510-528-0243

    16. 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

    17. The Geometry Junkyard: Fractals
    Apollonian Gasket, a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles. From MathWorld.

    18. Fractal World Gallery Thumbnails : Cosmic Recursive Fractal Flames Or Flame Frac
    Fractal World Gallery Home. Fractal World Gallery contains a collection of Pure flame fractals, Thanks for viewing the Fractal World Gallery.
    Fractal World Gallery contains a collection of Pure flame fractals,
    fractal flame composites, fractals, etc: established 1998
    Flame Fractals date from 1998 to the Present by Cory Enc h
    I mages from this gallery may only be used with artist 's permission
    Fractal software includes Frax Flame and Apophysis
    for cosmic recursive fractal flames.

    More art work by Cory Ench at
    images in room 6
    click on the thumbnails for full view fractal image images in room 6
    images in room 5
    images in room 4 images in room 3 images in room 2 120 images in room
    Other non fractal art by Cory Ench at home Thanks for viewing the Fractal World Gallery. Please go to next gallery room for more cosmic recursive flame fractals. Don't forget to sign our guestbook and give some feedback. Sign Guestbook

    19. 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
    var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers
    Sites for parents


    Interactive Activities
    Sites for parents
    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

    20. OnOne Software - Product Details
    Genuine fractals 5 simply produces higher quality and sharper results than traditional scaling methods in Photoshop® or in any other third party product.

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