 Chaos in the Classroom  Robert L. Devaney; Dept. of Mathematics, Boston University
One of the most interesting applications of technology in the mathematics classroom is the fact that it allows teachers to bring many new and exciting topics into the curriculum. In particular, technology lets teachers bring some topics of contemporary
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 The Chaos Metalink  Industrial Street Productions
A site designed as an ongoing resource for all those interested in Chaos science and things fractal. This site is sponsored by Images of Chaos, an Artwork for Television and Industrial Street Productions as a service to the Chaos community. Featured Sites;
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 Chaos Under Control  David Peak, Michael Frame; Union College, Schenectady, NY
Material designed to support the text Chaos Under Control (W. H. Freeman, 1994): Macintosh software; course syllabi; six labs exploring natural fractals, iterated function systems, dimension computations, onedimensional dynamics, fractal analysis of
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 chaotic nspace network  Jon Camp and Benjamin Martin
Fractals: an introduction, gallery of images, and evaluation of software for fractal creation, with links to download. Other mathematics resources include a brief introduction to the Fibonacci sequence.
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 Classic Iterated Function Systems  Larry Riddle
These pages investigate several of the classic iterated functions systems
and their associated fractals. Each IFS consists of affine transformations
involving rotations, scalings by a constant ratio, and translations. For
each example is given
* a
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 The Collage Theorem  Cut the Knot!, Alexander Bogomolny
To find an IFS whose attractor is "close to" or "looks like" a given set, one must endeavor to find a set of transformations  contraction mappings on a suitable set within which the given set lies  such that the union, or collage, of the images of the
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 Complexification  Jared Tarbell
View interactive, open source Java applets of fractals and other mathematically significant graphics.
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 Complexity International  An Electronic Journal of Complex Systems Research
A refereed journal for scientific papers dealing with any area of complex systems research. The theme of the journal is the field of complex systems, the generation of complex behaviour from the interaction of multiple parallel processes. Relevant topics
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 Complex Numbers (Manipula Math)  International Education Software (IES)
Java applets to investigate complex numbers, their reciprocals, powers, and other selected functions. (One function leads to a fractal.)
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 The Computational Beauty of Nature  Gary William Flake
Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation: a companion site for a book by Gary William Flake, "affectionately known as 'The Fish and Chips Book'." Contains applets and source code.
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 Computer Generated Art Gallery  Tom Ellis
Original computergenerated fractal images. Mandelbrot Sets; Mandelbrot zoom rendered onto a sphere.
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 Computing the Hausdorff Measure and Dimension of Fractals Generated by Möbius Transforms  Mark Krosky, Cornell University
An illustrated paper by a Cornell Univ. graduate student. Abstract: Möbius transforms are an important class of conformal maps. By studying fractals they generate, we can gain more information about groups of Möbius transforms. A discussion
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 Continued Fractions, Infinite Continued Fractions, and Iteration  Don Cohen, The Mathman
Ten different ways to solve a quadratic equation  an area of mathematics with applications to population increase, finding the square root of a number, chaos theory, and fractals. Sample problems from Chapter 8 (Solving Equations and Iteration) of Don
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 coolmath.com: Cool Math  Karen
A searchable "amusement park of mathematics" for exploring math: functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and problems, fun with numbers, how to succeed in math, careers in math. Also Cool Links for Math for
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 CopyCat  Jim Morey
A Java game that revolves around replicating a picture created by several patterned faces of a solid object (like a cube), challenging the mind to understand complex geometrical structures and symmetry. To do well at the game, the player must first become
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 Counting to Calculus: Mathematics  William K. Bradford Publishing Co.
Math software, printed supplements, workbooks, textbooks, posters, and teacher tools available for Elementary, Middle and Secondary math curriculum.
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 Culturally Situated Design Tools: Teaching Math through Culture  Ron Eglash
Java for creating your own Mangbetu design, cornrow curves, graffiti, bead looms, SimShoBan, Yupik star navigator, Yupik parka patterns, PreColumbian pyramids, and rhythm wheels  and learning the mathematics behind them. Organized into African, African
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 The Dance of Chance Science Museum Exhibit  Center for Polymer Studies, Boston University
An online version of an exhibit focused on the emergence of patterns in Nature from physical and biological processes that appear to be chaotic. Exhibit kiosks, many of which are fractals, include Music of the Heart, Frozen Lightning, Erosion, Viscous
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 Dave's Geometric Pix Gallery  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mandelbrot and Julia sets, with a generation form and an Explorer on which you can point and click to get more refined images;
Newton Basins and a form to generate them; a page describing tiling the hyperbolic plane; some wallpaper groups; a gallery
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 David Goodman's Math Links  David Goodman, editor
Link listings for a variety of topics, organized by those topics.
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 Description of the Julia sets of the Cauliflower fractal  Frans Faase
Investigation of the Julia sets of the Cauliflower fractal, which is a fractal generated by two linear translations with three parameters. The generated fractal can either be solid, connected, or disconnected. The author shows that two Julia sets consisting
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 Diario Fractal  Today´s Fractal  Juan Pablo Braña
A site from Buenos Aires, in English and Spanish, with a different fractal art image every day and archived galleries of past images.
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 Divisor Plot  Jeffrey Ventrella
"We hear of primes described as the 'building blocks' of all numbers. Let's turn that concept on [its] head. Instead, let's think of primes as the negative spaces behind complex objects. Imagine a series of picket fences stacked in front of each other.
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 Doodal  Neil Thapen
Draw fractals freehand using a computer mouse: select a "brush size" to specify width in pixels, then click and drag in the large orange frame, the contents of which get copied in however many blue frames you specify. To rotate a blue box, click it while
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 Dot Patterns and Sierpinski Gasket  Cut the Knot!, Alexander Bogomolny
How many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? The author has counted a respectable 9 but would be happy to learn of more. An applet with rows of digits or circles with colors corresponding to the digits shows
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 Doug's Home Page  Douglas J. Ingalls
Includes mathematical interests such as images of fractal applications of Newton's Method and Gibb's Phenomena, with related programs in FORTRAN and BASIC, a discussion of the apparent depth problem in optics, and how multiple decisions can be reduced
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 The Dynamical Systems and Technology Project at Boston University  Robert L. Devaney; Dept. of Mathematics
An NSFsponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process.
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 Dynamic Mathematics Visualization for Young Learners
Sketchpad in Grades 38  a working conference, held at the University of Illinois at Chicago in February, 2003. Researchers, curriculum developers, and educators began developing a curriculum and software structure around The Geometer's Sketchpad technology
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 Educational Interests  Keith Lynn
See, in particular, Lynn's Math Modeling Project, which features Java applets to produce quadratic and sine examples; and Dynamics Project, on the Julia and Mandelbrot sets.
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 efg's Computer Lab: Fractals & Chaos Page  Earl F. Glynn II
Links to programs for creating fractal images and examples of chaos, and to the Glynn Function Study Center Gallery, with various views of the Julia set, z > z^1.50.2, where z is a complex number.
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 The Element: Science and Math  Deja.com
Searchable archives of math and science newsgroup postings. This community aims to share resources and give people an easy way to ask questions within relevant newsgroups, providing broad discussions of mathematical concepts from beginning to advanced
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 Elements Of Design  Colleen Deery
Explore galleries of fractal art by artist Colleen Deery.
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 Environmental Sciences Division (ESD)  Oak Ridge National Laboratory (ORNL)
A multidisciplinary research and development organization whose mission is to understand and evaluate how the development and use of energy affect the environment. The division conducts basic and applied research, assesses environmental impacts of projects
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 e to the i pi  Kevin Bertman
Investigations for teachers to use in mathematics classes. Posts include Phantom Traffic Jams (velocities); Hypotrochoids (Spirographs); Cartograms; Rogue Waves; Fractal Trees; Stereoscopic Images; Six Degrees of Separation; Shoelaces (applying the Pythagorean
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 Everywhere, Butterflies
A gallery of fractal pictures created using Sterling, a shareware program by Stephen Ferguson.
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 Experimentàlis Hunlap (hun meg nem) a Titkos Tudományokról  Ferenc Molnár
New geometric discovery (site is in Hungarian).
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 Explore Patterns in Pascal's Triangle  Jeremy Baer
In 1653, a French mathematician named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose n objects from a group of m indistinguishable objects. It
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 Exploring Chaos and Fractals  RMIT Publishing
An electronic textbook on CDROM which covers the subject of chaos theory and fractal geometry and includes text, worksheets, sound, video, and animation. Course material is presented with multiple entry points and themes, and can be used within a single
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 Exploring Fractals  Mary Ann Connors, Dept. of Mathematics & Statistics, Univ. of Massachusetts at Amherst
Exploring Fractal Dimensions of Strictly SelfSimilar Fractals: Cantor Dust to the Fractal Skewed Web: what are fractals? selfsimilar shapes; what is dimension; a mathematical interpretation; noninteger and integer fractal dimensions; generating fractals;
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 FAME (Fractal Art Museum Enterprise)  Joseph Trotsky, Director
A display of fractals by hundreds of artists. The site hosts permanent expositions, along with thematic and periodic exhibitions, annual contests, papers on fractal theory, software and tutorials for making fractals, and more.
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 Famous Equations and Inequalities  Peter Alfeld, University of Utah
An idiosyncratic and personal selection of particularly important or particularly intriguing mathematical equations, not all of them complicated. Mathematical Constants; The definition of Pi; The definition of e; A differential equation; The Pythagorean
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 Fantastic Fractals  Sheu, Turvey
A comprehensive fractals site with tutorials for all ages, fractalgenerated music, and realistic landscapes. Download Fantastic Fractals 98 software; interact with others through the fractal workshop message boards, and discussion forum.
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 Fantastic Fractals  ThinkQuest 1997
All about fractals: including: fully interactive fractal tutorials, a gallery, landscapes, music, a reference desk and types of fractals, downloads, a fractal workshop (build your own fractals), a fractal challenge (test yourself  how much have you learned
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 A farewell to chaos: Mandelbrot's fractal dimensions...  Christian Ricordeau
Where is the order of deterministic chaos hiding? About decimal numbers and the 4th dimension  a conception of decimal numbers that shows the birth of a new dimension in a natural phenomenon, and the inevitable and simultaneous surge of chaos. Here Mandelbrot
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 Fast Marching Methods and Level Set Methods  J. A. Sethian, University of CaliforniaBerkeley
Fast Marching Methods and Level Set Methods are numerical techniques that can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The techniques have a wide range of applications, including
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 The Feigenbaum Fractal  Havard Berland
A natural (but unfinished) starting point for anyone wanting to know more about the Feigenbaum fractal, both beginners and experienced mathematicians. With explanations of iterations in general, information about the fractal, and some general information
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 The Fibonacci Numbers  David Schweizer; Math Department, College of the Holy Cross
A directory of material related to the Fibonacci numbers. Math material  the Fibonacci numbers' appearance in the Mandelbrot set; the first 500 Fibonacci numbers in blocks of 100; factorizations; Web resources.
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 Fibonacci Rabbit Sequence  Ron Knott
One way to look at Fibonacci's Rabbits problem gives an infinitely long sequence of 1s and 0s, the Fibonacci Rabbit sequence: 1 0 1 1 0 1 0 1 1 0 1 1 0 ..., also called the Golden string or Golden sequence since it is a close relative of the number Phi,
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 Filmer V2.0  A program for creating fractal animation  Julian Haight
Filmer is a frontend program for Fractint (for DOS/Windows) that generates fractal animations. Fractint is a program for calculating still fractal images (you need Fractint installed to use Filmer). Filmer uses Fractint parameter (.par) files to specify
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 Fractal Alhambra  Philip Northover
Galleries of fractal art, in an array of sizes and colors. Fractal prints for sale, and MP3s of fractal music.
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