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. Cynthia Lanius' Fractals Unit: The Sierpinski Triangle You may obtain a print version of this page. lanius@math.rice.edu. Copyright 19962004 Cynthia 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.

3. Mathematics Archives - Topics In Mathematics - Fractals 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. Software, Bibliography, Music Example. fractals A fractals Lesson for Elementary and Middle 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

4. 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

5. Fractals fractals is an interdisciplinary journal devoted exclusively to phenomena involving complex geometry, patterns, geometrical and/or temporal scaling. http://www.worldscinet.com/fractals/fractals.shtml

6. Fractals The primary focus of the Community Learning Network (CLN) is to help K12 teachers integrate Information Technology into their classrooms. This CLN menu page provides links to mathematics fractals Theme Page. This "Theme Page" has links to information about fractals. Students and teachers will find curricular http://www.cln.org/themes/fractals.html

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. Explorer 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.

7. Fractalus Entrance (Fractal Art, Info, And Contests) Along with some more traditional fractal images, Sharon uses fractals as components and textures in other compositions. Cheshire http://www.fractalus.com/

Main: Galleries: Contests: Other: fractalus home fractalus galleries Images by Sharon Webb Cheshire Cat Fractals ... SteveC's Home Welcome! If you're looking for the Fractal-Art 2000 Contest , it's on its own site this year, so head on over to www.contest2k.com and take a look. Same people, same contest, just a new site! (Don't forget to come back here when you're done.) fractalus home This is the main area of the site. In addition to hundreds of images created by Damien M. Jones, you can also find detailed information on fractal techniques, fractal generating software and screen savers, Windows themes, and more. Images by Sharon Webb This site has won numerous awards. Along with some more traditional fractal images, Sharon uses fractals as components and textures in other compositions. Cheshire Cat Fractals By "rogue fractal artist" Alice Kelley, these galleries contain over one hundred and fifty fine images. She claims to be a "chimp at the keyboard"; don't you believe it. Gumbycat's Cyberhome This is the hub for the fractal galleries of Linda Allison. Most of her artwork is available on this site, and she has some FractInt tutorials as well.

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. 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

10. Fractals fractals , Chaos. Index. fractals and Computer Graphics Interface Magazine Article Colouring Attractors. http://astronomy.swin.edu.au/~pbourke/fractals/

F r a c t a l s , C h a o s Index Geometry Formats Curves Surfaces Polyhedra Fractals, Chaos Projection Stereographics Rendering Radiance PovRay OpenGL Modelling Terrain Colour Textures Other Data Formats Analysis Fun Puzzles Old Stuff Papers POVRay Fractal Raytracing Contest Fractal Dimension Calculator - FDC Box counting software for the Macintosh and Linux. Ruler or Compass Dimension Multifractal spectrum Lacunarity Recurrence plots ... 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. Self similarity Examples of self similarity in fractals with examples from mathematics and photos of the physical world. I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, that it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel? P. W. Atkins

11. A Fractals Unit For Elementary And Middle School Students A fractals unit for elementary and middle school students This web site, for students and teachers in grades 4 to 8, provides a unit on fractals. The unit is designed to introduce students to http://rdre1.inktomi.com/click?u=http://math.rice.edu/~lanius/frac/&y=020A62

12. Efg's Fractals And Chaos Page Several Fractal and Chaos projects, including Evolution of Mandelbrot Set, Fractal Discovery Lab, IFS images, Lorenz and other Strange Attractors. http://www.efg2.com/Lab/FractalsAndChaos

Contents Fractals Chaos Glynn Function Gallery Also see the Fractals and Chaos Section of the Math Reference Library in look for Mathematics Fractals / Chaos Note: If you have a fast machine (233 MHz Pentium II or faster), you'll likely need a patch to run TP 7 programs on this page. See this fix for "Runtime Error 200." Fractals Program Description Files Keywords Tutorial about Mandelbrot and Julia sets. Mandelbrot Set, Julia Set Evolution of the MandelbrotSet Mandelbrot Set Fractal Discovery Lab Art Gallery, Microscope, Movies, Tools, Library Fractals Show 2 Fractals, Chaos, Mandelbrot Set, Julia Set, Biomorph, Rainbow, WavelengthToRGB, pf32bit, Delphi Sierpinski Triangle Gasket Sierpinski triangle, Sierpinski gasket, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion von Koch Snowflake von Koch curve, von Koch snowflake, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion Chaos Program Description Files Keywords Iterated Function System to create four ferns (Also see, Mathematical Recreations

13. Fractals fractals fractals is an interdisciplinary journal on the complex geometry of nature. This quarterly international journal, launched in March 1993, publishes peerreviewed papers including full- http://rdre1.inktomi.com/click?u=http://www.wspc.com/journals/fractals/fractals.

14. Spanky Welcome The Spanky Fractal Database is a collection of programs, images, and other material all 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.

15. Fractint Homepage Fractint now has a listserver set up for general questions and discussion about the 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.

16. Desktop Wallpaper, Computer Screensavers, And Free Ecards 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/

The Mind's Eyes Computer Wallpaper - Desktop Screensavers - Free Ecards - Digital Photography HOME Contact Me Guestbook ScreenSavers ... LOGIN Wallpaper What's New FREE Section The Top 10 3D Creations ... Hot Cars Information Privacy About Quotations Webmasters There are 325 desktop images currently available! New Wallpaper Free Wallpaper Top 10 Wallpaper Wallpaper Photography Wallpaper Fractal Wallpaper Military Wallpaper NASA Wallpaper Animal Wallpaper Car Wallpaper What other visitors have to say about The Mind's Eyes: "I check out a lot of 3D image sites 'cause I love to see other people's art, and I really have to say that this is definitely one of the best sites I've visited - I'm really impressed! I like the quotes also!" "It was a pleasure perusing your site. Very nice images. High quality. Impressive. Thank you." "Thank you for your sight. It makes it easier for me to look at my computer all day long!" var sc_project=250735; "The most rewarding things you do in life are often the ones that look like they cannot be done." Arnold Palmer Sites of Interest Add Your Site!

17. The Spanky Fractal Database The Spanky fractal database This Internet site is a collection of fractals and fractal related materials for free distribution on the Internet. Most of the software is gathered from various ftp ( http://rdre1.inktomi.com/click?u=http://spanky.triumf.ca/&y=02178F70CAAFF928

18. Sprott's Fractal Gallery Older fractals of the Day are saved in an archive, which you can access. VCLUTQ (121,428 bytes); WLJFQE (85,678 bytes). Natural fractals. Broccoli. 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

19. 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 Click the thumbnails to view the corresponding fractals. THUMBNAIL. THUMBNAIL. THUMBNAIL 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 - 2004 Randy D. Ralph, Christopher E. Ralph, IconBAZAAR LLC. Sponsored Links: Web Directory Connect now to find a world of information. 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

20. Directory Of /fractals/collect/ Directory of /fractals/collect/. Switch to plain format. The images in this directory were 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 16:08 12-Mar-2004 13:22 Folder (sub-directory) 03-Feb-2004 16:42 Folder (sub-directory) 13-Apr-2004 15:28 Folder (sub-directory) 13-Apr-2004 15:18 Folder (sub-directory) 09-Apr-2004 11:29 Folder (sub-directory) 07-Apr-2004 10:05 Folder (sub-directory) 16-Mar-2004 12:46 Folder (sub-directory) 12-Mar-2004 13:20 Folder (sub-directory) 12-Mar-2004 13:16 Folder (sub-directory) 12-Mar-2004 13:03 Folder (sub-directory) 12-Mar-2004 12:37 Folder (sub-directory) Back to Sprott's Fractal Gallery

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