1. Cynthia Lanius' Lessons: A Fractals Lesson - Introduction Mathematics lessons for elementary school, middle school fractals,fractals, fractals. Cynthia Lanius. fractals. Pictured A http://math.rice.edu/~lanius/frac/

Cynthia Lanius Fractals 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 Self-similarity Fractional dimension Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals 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. Spanky Welcome Large categorized index.Category Science Math Chaos and fractals......The Spanky Fractal Database is a collection of programs, images, and other materialall relating to the subject of fractals. THE SPANKY FRACTAL DATABASE. http://spanky.triumf.ca/

THE SPANKY FRACTAL DATABASE 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 If you find URL's that I point to have become outdated and constantly fail to respond on your attempts to load them, (over several days) then please inform me of this problem and I will remove them from my lists.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 spanky.triumf.ca is now completely mirrored at spanky.fractint.org 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. What's New in Fractals An index of Fractal material at Spanky. Some General information about Spanky.

3. This Site Has Been Moved - Ce Site A Changé D'adresse Ce site a changé d'adresse This site has been moved Veuillez svp mettre à jour votre signet et noter la nouvelle adresse Please update your bookmark and note the new URL as http://www.cnam.fr/fractals.html

This site has been moved Please update your bookmark and note the new URL as : http://graffiti.u-bordeaux.fr/MAPBX/roussel/

4. Fractint Homepage Fractint now has a listserver set up for general questions and discussion aboutthe Fractint program and technical questions about fractals in general. http://spanky.triumf.ca/www/fractint/fractint.html

WELCOME to the Fractint WWW pages What is Fractint and what's it all about? Fractint is a freeware fractal generator created for IBMPC's and compatible computers. It is the most versatile and extensive fractal program available for any price. The authors (of which I am not one), work very hard to keep it that way. It has many great features and it is constantly being upgraded and improved by the Stone Soup team. Keep this link as a reference to stay up-to-date with the latest developments. Check out in the latest release. Check out in web resources. Check out on these pages. Getting Fractint Version 20.0 of Fractint Now available. New Image format on these Pages I've started the long process of replacing all the GIF images stored and displayed on these pages over to the PNG image type. If your web browser is having problems displaying them, it may mean you have to update/upgrade your browser. I apologise for any inconvenience, but the issue is being forced by the stance that Unisys has chosen in regard to LZW patent issues and the use of GIF images on Web servers. For more info on this topic see the Burn All Gifs site.

5. Fractals And Scale may be copied and used provided that this notice and the authorship details remain attached. fractals AND SCALE http://life.csu.edu.au/complex/tutorials/tutorial3.html

Revised 1995. This preprint may be copied and used provided that this notice and the authorship details remain attached. FRACTALS AND SCALE David G. Green Environmental and Information Sciences Charles Sturt University Introduction How long is the coast-line of Great Britain? At first sight this question may seem trivial. Given a map one can sit down with a ruler and soon come up with a value for the length. The problem is that repeating the operation with a larger scale map yields a greater estimate of the length (Fig. 1). If we actually went to the coast and measured them directly, then still greater estimates would result. It turns out that as the scale of measurement decreases the estimated length increases without limit. Thus, if the scale of the (hypothetical) measurements were to be infinitely small, then the estimated length would become infinitely large! Lewis Fry Richardson (quoted in Mandelbrot, 1983) noted this dependence of measured length to the measuring scale used. In discussing measurement, scale can be characterized in terms of a measuring stick of a particular length: the finer the scale, the shorter the stick. Thus at any particular scale, we can think of a curve as being represented by a sequence of sticks (Fig. 1), all of the appropriate length, joined end-to-end. Clearly, any feature shorter than the stick will vanish from a map constructed in this way. Of course, no one actually makes maps by laying sticks on the ground, but the stick analogy reflects the sorts of distortions that are inevitably produced by the limited resolution of aerial photographs, by the length of survey transects, or by the thickness of the pens used in drafting. There is an analogy here, too, with the accuracy or frequency with which any sort of biological measurements are made.

6. Sprott's Fractal Gallery Artist presents a library of images, including a Fractal of the Day. Browse chaos demonstrations and strange attractors. them according to a scheme described in the book. Older fractals of the Day are saved in an archive, which you can http://sprott.physics.wisc.edu/fractals.htm

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 , which you can access. 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 you provide a link back to this page. fracday0.gif Today's fractal of the day fracday1.gif

7. Mathematics Archives - Topics In Mathematics - Fractals Topics in Mathematics. fractals. Chaos, fractals, and Arcadia. ADD. KEYWORDS The Chaos Game, The Sierpinski Hexagon, http://archives.math.utk.edu/topics/fractals.html

Topics in Mathematics Fractals Chaos, Fractals, and Arcadia ADD. KEYWORDS: The Chaos Game, The Sierpinski Hexagon, Iterated Function Systems Chaos in the Classroom, Boston University ADD. KEYWORDS: The Chaos Game, Self-similarity, Fractal Dimension, Iterated Function Systems Clifford A. Pickover's Homepage ADD. KEYWORDS: Cellular Automata, Carotid-Kundalini Functions, Books, Puzzles, JAVA Geometry Explorer The Dance of Chance ADD. KEYWORDS: Random Processes, Branching Structures, Patterns in Nature, Student Activities, Laboratory Experiments, Visualization, Software, Fractal Dimension, Fractal Coastlines Diffusion-limited Aggregation Exploring Fractals ADD. KEYWORDS: Lesson Plan, Tutorial, Bibliography Fantastic Fractals ADD. KEYWORDS: Tutorials, Gallery, Fractal Music, Bibliography, Software, Newsgroups Fract-ED ADD. KEYWORDS: Iteration, Attractor, Software, Tutorial, Bifurcation, Self-similarity, Strange attractor Fractal Clouds The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

8. Aros Fractals A hires, true-color fractal generation program for Macintosh and Windows 95/98/ME/2000/NT. http://www.arosmagic.com/Fractals/default.htm

F i lle Download more cool software! Aros Magic Viewer Aros Magic Checkers Aros Magic Reversi Aros Fractals W elcome to the world of Fractals! With Aros Fractals you can explore some classical fractal images at extremely high resolutions (physical size and color depths). For the current version of Aros Fractals and other information, you've reached the correct destination. We are constantly updating information here, so visit often and let us know if there is additional material you would like to see here. System Requirements Minimum All Platforms: Floating Point Unit (FPU). 8-bit video card (256 colors). Sufficient hard disk space to store large images. 486DX/25. 8M RAM. Windows NT: 486DX/25. 16M RAM. Macintosh: 68020. System 7.0. Thread Manager. 8M RAM. (Aros Fractals will let you know if it is missing any additional required components at startup time). Recommended All Platforms: 32-bit video card (True Color) Pentium. 24M RAM.

9. IconBAZAAR - Fractals - Page 01 A gallery of free clipart, graphics, images, webdings and webart for use in HTML development. fractals. Contents. Page 01. Page 04 http://www.iconbazaar.com/fractals

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. In place: July 2, 1995. Last updated: February 28, 2002. All images 1994 - 2003 Randy D. Ralph, Christopher E .Ralph. Visit our online store for great gift ideas! WARNINGS UP BACK NEXT Click the thumbnails to view the corresponding Fractals THUMBNAIL THUMBNAIL THUMBNAIL THUMBNAIL ... THUMBNAIL Click the thumbnails to view the corresponding Fractals UP BACK NEXT

10. Chaos Theory And Fractals History of chaos as well as extensive information on Chaos Theory and fractals. Contains several pictures of fractals and links to other Chaos Theory and fractals pages. http://www.mathjmendl.org/chaos/

Chaos Theory and Fractals By Jonathan Mendelson and Elana Blumenthal Outline Introduction to Chaos Determinism Early Chaos Edward Lorenz ... Works Cited Introduction to Chaos The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. A chaotic system can actually develop in a way that appears very smooth and ordered. Determinism Sir Isaac Newton Determinism is the belief that every action is the result of preceding actions. It began as a philosophical belief in Ancient Greece thousands of years ago and was introduced into science around 1500 A.D. with the idea that cause and effect rules govern science. Sir Isaac Newton was closely associated with the establishment of determinism in modern science. His laws were able to predict systems very accurately. They were deterministic at their core because they implied that everything that would occur would be based entirely on what happened right before. The Newtonian model of the universe is often depicted as a billiard game in which the outcome unfolds mathematically from the initial conditions in a pre-determined fashion, like a movie that can be run forwards or backwards in time. Determinism remains as one of the more important concepts of physical science today. Early Chaos

11. Dynamical Systems And Fractals Lecture Notes Lecture Notes by David J. Wright in HTML. http://www.math.okstate.edu/mathdept/dynamics/lecnotes/lecnotes.html

Next: Contents Up: Dynamical Systems and Fractals Dynamical Systems and Fractals Lecture Notes David J. Wright Contents Introduction to Dynamical Systems Symbolic dynamical systems Discrete-time systems ... About this document ... David J. Wright Mon Aug 19 17:21:15 CDT 1996

12. Fantastic Fractals Tutorials for all ages, fractalgenerated music and realistic landscapes. The Fantastic fractals 98 software is available for download. Workshop, message boards, and discussion forum. http://tqd.advanced.org/12740/index.html

13. Cynthia Lanius' Fractals Unit: The Sierpinski Triangle Center for Excellence and Equity in Education (CEEE). Copyright 19962002Cynthia Lanius. URL http//math.rice.edu/~lanius/fractals/. http://math.rice.edu/~lanius/fractals/

Cynthia Lanius Making a Fractal: The Sierpinski Triangle 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 Jurassic Park Fractal ... Using Java Fractal Properties Self-similarity Fractional dimension Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received Let's make a famous fractal called the Sierpinski Triangle. *You may print and use this triangular gridpaper. Step One Draw an equilateral triangle with sides of 2 triangle lengths each. Connect the midpoints of each side. How many equilateral triangles do you now have? Shade out the triangle in the center. Think of this as cutting a hole in the triangle. Step Two Draw another equilateral triangle with sides of 4 triangle lengths each. Connect the midpoints of the sides and shade the triangle in the center as before. Notice the three small triangles that also need to be shaded out in each of the three triangles on each corner - three more holes.

14. Free Wallpaper From The Mind's Eyes Computer generated 3d art for use as desktop wallpaper, sizes include 800 x 600 and 1024 x 768. Images include digital scenery, and fractals. http://www.themindseyes.com/

Free Wallaper and 3D Images Saturday March 22nd, 2003 7:15PM PST HOME - Wallpaper - What's New Fractals Scenery Objects ... Military - Information - Privacy About FAQ - Help - More - Send Email Contact Me Guestbook Welcome to The Mind's Eyes Featuring 122 images spanning 6 different categories. Free wallpaper comes in many shapes and sizes on the internet. The Mind's Eyes hopes to provide you with quality as well as unique wallpaper options. There are currently six categories of free wallpaper to choose from. I hope you find the images attractive enough to use for your desktop wallpaper. Please come back in the future for new images and features. Use the links to the left to browse the free wallpaper categories. You can also use the what's new link to check out my newest additions. Feel free to drop me a line via email anytime. You can also sign the guestbook and let me know how I'm doing. I always enjoy hearing from my visitors. New images are typically added a couple times per month. Thanks for visiting. Your interest is appreciated.

15. The Chaos Hypertextbook The theory behind the sumptuous images and technical jargon of chaos, fractals, and nonlinear dynamics. Simple experiments for programmable calculators, instructions for drawing fractal images, and the meanings of dimension. http://hypertextbook.com/chaos/

The Mathematics in the Age of the Computer Prefaces What's New About This Book (abstracts) Links to This Site 1 Mathematical Experiments Iteration Bifurcation Universality Strange Attractors ... Mandelbrot Sets 3 About Dimension Euclidean Dimension Topological Dimension Fractal Dimension 4 Measuring Chaos Harmonic Oscillator Logistic Equation Lyapunov Exponent Lyapunov Space A Appendices A.1 Print Resources A.2 Software Resources A.3 Internet Resources A.4 Eye Candy bent chaos eworld ... physics Another quality web page by Glenn Elert email elert@hypertextbook.com www hypertextbook.com

16. AbstraXness-Digital Art Karin Kuhlmann shows facets of digital arts in 3Dimages, photo-paintings, fractals, abstract paintings, and flower pictures. In English and German. http://www.karinkuhlmann.de/

Deutsche Seite 3D-Bilder 3D-Illustrationen ... Artlinks Digitale Kunst, Computerkunst Online-Galerie der Grafikerin und Fotografin Karin Kuhlmann. Ausgewaehlte digitale Arbeiten, die seit 1996 am Computer entstanden sind: 3D-Bilder, Foto Paintings, Blumenbilder, Rosenbilder, Fraktale und abstrakte Arbeiten. Digital Art, Computer Art Personal exhibition of the photographer and graphic designer Karin Kuhlmann, showcasing 3D-images, photo paintings, pictures of flowers and roses, fractals and abstract mathematical works. e-mail: digitalworlds@karinkuhlmann.de Artworks, Digital Art, Digitale Kunst, Computer Art, Computer Kunst, Computer Graphics, Computer Generated Graphics, Computer generierte Kunst. Last update: March 22nd, 200 Top 100 Art Sites by: ArtPromote.com Winner of the IDAA 2003. Laurence Gartel Award For Excellence. MOCA Digital Art Contest 2003: First Price in Fractal and Mathematical Art BTDesign Awards: Master of 2002 - Digital Arts var site="sm3Floribundi"

17. Faqsys - Your New Lifestyle - Introduction A wealth of programming links, including 3D/2D math, fractals, optimization, compression, video cards, graphics file formats. http://thorkildsen.no/faqsys

Introduction Faqsys search Faqsys news Faqsys links ... Gems 1-5 ..........:::::::::::;;;;;;;;[ do you wanna do a successful thing in your life? :: join the Faqsys Club today! ];;;;;;;;;;:::::::::::.......... Faqsys - your new lifestyle. Yes, finally I've updated and redesigned Faqsys. Everything is now automatic, so more updates will come! Hope you find Faqsys useful, and by the way, you are visitor Steffen Visit the ultimate scene-party in Norway, Bush Party 6.0 in late June. Last updated 26th of May 1999 old + new = total

18. Directory Of /fractals/collect/ Directory of /fractals/collect/. Switch to plain format, The images in this directorywere mostly obtained from the alt.binaries.pictures.fractals newsgroup. http://sprott.physics.wisc.edu/fractals/collect/

Directory of /fractals/collect/ Switch to plain format Name Last Modified Size Description Parent Directory 11-May-2002 15:08 11-May-2002 14:29 Folder (sub-directory) 11-May-2002 14:37 Folder (sub-directory) 11-May-2002 14:38 Folder (sub-directory) 11-May-2002 14:40 Folder (sub-directory) 11-May-2002 14:42 Folder (sub-directory) 11-May-2002 14:45 Folder (sub-directory) 11-May-2002 14:48 Folder (sub-directory) 11-May-2002 14:48 Folder (sub-directory) 13-Dec-2002 11:25 Folder (sub-directory) 17-Mar-2003 12:06 Folder (sub-directory) Back to Sprott's Fractal Gallery

19. Coolmath.com - An Amusement Park Of Mathematics... And More! An amusement park of mathematics. Puzzles and number problems, fractals, geometry, calculus, algebra, online games, online calculators, and links. http://www.coolmath.com/

an amusement park of math ... and more for back to school fun! about us awards media kit press kit ... safe surfing Coolmath.com, Inc.

20. The Fractal Microscope Provides an interactive tool that helps kids explore the Mandlebrot Set and other fractal patterns. Includes a gallery of images. immediately drawn to the bizarrely beautiful images known as fractals. Extending beyond the typical perception of http://www.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html

The Fractal Microscope A Distributed Computing Approach to Mathematics in Education The Fractal Microscope is an interactive tool designed by the Education Group at the National Center for Supercomputing Applications (NCSA) for exploring the Mandelbrot set and other fractal patterns. By combining supercomputing and networks with the simple interface of a Macintosh or X-Windows workstation, students and teachers from all grade levels can engage in discovery-based exploration. The program is designed to run in conjunction with NCSA imaging tools such as DataScope and Collage. With this program students can enjoy the art of mathematics as they master the science of mathematics . This focus can help one address a wide variety of topics in the K-12 curriculum including scientific notation, coordinate systems and graphing, number systems, convergence, divergence, and self-similarity. Why Fractals? Many people are immediately drawn to the bizarrely beautiful images known as fractals . Extending beyond the typical perception of mathematics as a body of sterile formulas, fractal geometry mixes art with mathematics to demonstrate that equations are more than just a collection of numbers. With fractal geometry we can visually model much of what we witness in nature, the most recognized being coastlines and mountains. Fractals are used to model soil erosion and to analyze seismic patterns as well. But beyond potential applications for describing complex natural patterns, with their visual beauty fractals can help alter students' beliefs that mathematics is dry and inaccessible and may help to motivate mathematical discovery in the classroom.

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