 Shodor Education Foundation, Inc.
A nonprofit research and education organization dedicated to the advancement of science and math education, specifically through the use of modeling and simulation technologies. Interactive middle school lessons aligned with curricula are available through
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 The Sierpinski Carpet Project, 20002001  Tom Canright
Instructions and pictures of The Sierpinski Carpet Project, from Tom Canright and Linda Gazzola's sixth grade mathematics classes at the Latin School of Chicago. All of the carpets are a type of fractal, meaning that the basic patterns are reiterated
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 Sierpinski Shapes  Rick and Donna Joi
An interactive Java applet that allows you to create hundreds of fractal shapes using a variation of the Sierpinski triangle algorithm. Includes a page that provides a nontechnical explanation (with pictures) of the fractal math.
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 Sierpinski Tetrahedron: A Metal Sculpture  Stan Goldade
Pictures and background information on the sculpture, with some Sierpinski facts.
Breckenridge Senior High School students welded 4,096 equilateral metal triangles together to form 1,024 tetrahedra to form a stage5 Sierpinski Tetrahedron. It is located
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 The Sierpinski Triangle  Robert L. Devaney; Dept. of Mathematics, Boston University
Section from the paper "Chaos in the Classroom," describing the deterministic (rather than random) construction of the Sierpinski triangle.
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 A Site For Cyber Eyes  BZLeonard
Fractals, graphics, photos and altered photos, 3D graphics, links, Sherman's Humor Column, and Ginger's Diary (A teenager describes being bombed by the Japanese on December 7, 1941).
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 Sketchpad Activity Center  Bill Finzer, Key Curriculum Press
Interactive lessons for use with an early version of the Geometer's Sketchpad. Construct a fractal tree using a recursive script; use the Point on Object command to study random phenomena. These lessons have been used in Key Curriculum Press's summer
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 The Snowflake Curve, Perimeter and Area  Don Cohen (The Mathman)
Young children start with an equilateral triangle, then go 1/3 of the way along each side, then add a smaller equilateral triangle, protruding out from every side to get the next figure. A sample problem with answers from Chapter 4 of Don Cohen's worksheet
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 Soler's Fractal Site
Fractal galleries of images made using Tierazon and other programs, links, downloads of fractalgenerating programs, and articles on fractals.
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 Star Fractal  Pierre Dufilie IV
A Java Applet displaying the Mandelbrot fractal set using exponential color smoothing. The program allows the user to zoom in and out of the fractal in the complex plane.
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 Stephen P. Booth
A researcher working in physics and parallel computing. Articles and source  code for random number generation (parallel generation and a generic Fortran90 interface), and the xmountains program, which uses fractals to generate computer images of landscape.
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 Stone's Free Mac Programs  Ishihama Yoshiaki
Free Mac software and images illustrating dynamical systems: applets (see the 4D Rubiks Cube), fractal generators, etc. Topics include artificial life, AfterDark modules, cellular automata, chaos, fractals, graphics, hyperdimension, genetic programming,
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 studio:ludens  Wouter Walmink and Alexander Rulkens
Free online tools that "let you play with your own creativity," designed by two Dutch industrial and interaction designers in Eindhoven. Create your own patterns with Repper; your own tessellating coasters with Epa:kato; your own fractals and other complex
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 Studying Dimensionality through a StairStep Fractal  Burrill, Frost, Anderson, Burkett, Gribble, Ryerson, & Williams
A background paper and a related classroom activity about a lesson studyproduced activity on using a stairstep fractal to study other dimensions.
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 Superliminal  Daniel Green
Use the Tyler applet to create polygons of various sizes and attach them to edges of other polygons. Read about deltahedra, flexible polyhedra, and infinite polyhedra  figures made of an infinite number of polygons which would then fill all of space
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 Think Maths  Matt Parker
This group of mathematics speakers visits schools to perform maths talks and workshops in the UK. Sessions present math in ways that "grab the attention of students and remind them that maths is something to be enjoyed." Free downloads include domino
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 Third Apex to Fractovia  Juan Luis Martínez
Several galleries, each with up to 18 fractal images, and discussions on fractals as art. Also an uptodate list of freeware fractal generators, screen savers, and fractal music software, with links and reviews.
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 Thom's Fractals
A collection of fractal creations: images and wallpaper tiles, and links.
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 A Tour of Fractions  Math Forum
The Web often seems more like a maze than an organized set of resources. To help you find what you need, the Math Forum presents a 'tour' of fractions, offering links to lessons, activities, and materials, questions and answers from Ask Dr. Math, and
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 Ultra Fractal  Frederik Slijkerman
A Windows shareware program that creates images of fractals, allowing you to write your own fractal formulas, coloring algorithms, and geometric transformations in a simple formula language. A layering feature lets you combine different fractals and coloring
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 Ultra Fractal Gallery  Frederik Slijkerman
A gallery of fractal images created using Ultra Fractal, a Windows shareware program.
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 Understanding Mathematics: A study guide  Peter Alfeld, University of Utah
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that
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 Using the Fibonacci numbers to represent integers  Ron Knott
We use base 10 for written numbers, and computers use base 2, but what about using the Fibonacci numbers as the column headers? or base Phi (1.618034...) instead of base 10? There are some interesting infinite series that relate to these  each with a
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 Using the Internet: Mathematics  Douglas Butler; Pearson Publishing (U.K.)
A 55page looseleaf book compiled to save teachers time finding excellent resources on the WWW and to provide a curriculumbased bank of ideas. Support activities do not demand that students have free access to the Web. The pack is divided into ten main
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 Video Lectures in Mathematics  Jerry Farlow
An online pinboard gathering thousands of visual links to a broad range of math videos. Categories include applications of math; famous mathematicians; math education; math humor; math on TV, movies; STEM math initiatives; and "instructional: K12." Farlow
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 The Virtual Mathematics Center  Martindale's Graduate & Undergraduate Center
Preprints and online journals from a wide variety of math and science organizations; Online math dictionaries and encylopedias; mathematics courses, tutorials and databases; courses by subject; related mathematics information and databases.
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 A Virtual SpaceTime Travel Machine  JeanFrançois Colonna, École Polytechnique
Still Pictures and MPEG Animations (Images Fixes et Animations MPEG): Art and Science, Artistic Creation, Astrophysics, Celestial Mechanics, Deterministic Chaos, Deterministic Fractal Geometry, Fluid Mechanics, From the Infinitely Small to the Infinitely
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 Visions Of Chaos  Jason
A Windows application that generates fractals, cellular automata, attractors and other chaos simulations. Supports 2D images, 3D images and AVI movie creation. With galleries of fractals and Mandelbulbs; cellular automata and Lsystems music; and chaos
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 Visualization Laboratory of Geometric Objects  Mathematics Dept., Universidad Autónoma de México
An electronic journal and works from professors, researchers and students from the Mathematics department of the School of Science of the Universidad Autonoma de Mexico, with a gallery of geometric objects (fractals), and links to other Web pages. Versions
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 Walking Randomly  Michael Croucher
Croucher's blog, which dates back to August of 2007, has included posts such as "Logo Programming on the pocket PC," "Christmas gifts for math geeks (like me!)," "Martial Mathematics," "R Compared to MATLAB (or 'learning a thing or two from your students'),"
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 Waterloo Fractal Compression Project  Edward R. Vrscay
A research project dedicated to the study of fractal analysis and Iterated
Function Systems/Fractal Transforms from theoretical and practical perspectives, focussing on image and signal compression. Both mathematical and nonmathematical introductions
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 weed's fractal gallery
A small gallery of fractal images and a few fractal links.
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 What are Fractals?
A short description of fractals, with illustrations.
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 What is a Fractal?  Sarah Seastone, Math Forum
A short description (with illustrations of the Mandelbrot Set) of fractals, paraphrased from Chapter 1, "A Mathematical and Historical Tour," of Robert Devaney's book, A First Course in Chaotic Dynamic Systems.
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 The Why Files  University of Wisconsin
An electronic exploration of the issues of science, math, and technology that lurk behind the headlines of the day, presenting those topics in a clear, entertaining and accessible manner. Provides a bimonthly feature on the science of everyday life, archived
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 A World of Color  Graphx Edge
Royaltyfree color fractal images and fractal collections available on CDROM. Also clip art, fonts, textures, and a Fractal Showcase.
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 World of Words, Numbers, and Notes  Mike Keith
Mostly original diversions in the areas of mathematics, word play, and music, including a Cadaeic Cadenza, a long pi mnemonic. Also, Ailihphilia (literature and word play) and Scitamatics (mathematical diversions): the recreational study of words, numbers
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 Writings for a General Audience  Marcus Jaiclin
PDF articles on popular and recreational mathematics by Jaiclin, an Assistant Professor at Westfield State University: Notes on Mathematics of Voting Methods; Fractals, Pascal's Triangle, and the padic Numbers; Airplane Passenger Seating Problem; No
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 Yahoo! Science: Mathematics  Yahoo! Inc.
All the best on the Web in math including Indices, alphabetically listed by category: Academic Papers; Algebra; Applied Mathematics; Books; Calculus; Chaos; Combinatorics; Complex Systems; Conferences; Education; Employment; Entropy; Equations; Ethnomathematics;
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 Zuk  Jan Bobrowski
Download an experimental version of a dynamic Mandelbrot/Julia fractal viewer for DOS.
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