 Exploring the Space of Cellular Automata  Langton, Hayden, Gutowitz, Carr, Fraser
Cellular automata (CA) are discrete space/time logical universes, obeying their own local physics according to given rules. Space in CA is partitioned into discrete volume elements called "cells" and time progresses in discrete steps. Each cell of space
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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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 Feigenbaum's Constant  Anders Skovsted Buch
A picture showing a fraction of the Feigenbaum tree.
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 Fluid Mechanics, Chaos and Mixing  Julio M. Ottino, Chemical Engineering Dept., Northwestern University
Research Interests of the Chaos and Mixing Group include: Granular Flows and SolidSolid Mixing; Competition Between Chaos and Order; LiquidLiquid Mixing; Mixing in 3D Flows; Mixing in Cell Culture Systems; SolidLiquid Mixing; and Geometric Aspects
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 Fractal Dimension  Robert L. Devaney; Dept. of Mathematics, Boston University
A section from the paper "Chaos in the Classroom," describing the concept of fractal dimension, using the Sierpinski triangle as an example.
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 Fractal Expressionism  Richard Taylor, Adam P. Micolich and David Jonas
Can science further our understanding of art? An article discussing the connection between fractals and Jackson Pollock's paintings.
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 Fractal FAQ  Shirriff, Stepp
Basic frequently asked questions, suggestions for fractal resources and sites, software, archives, tutorials, from the newsgroups sci.fractals, sci.answers, news.answers. Sample questions: What is a fractal? What are some examples of fractals? What is
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 Fractal Metaphysics Home Page  Christopher Sunami
A clearinghouse of (serious) materials on the web focused on the relationship between fractal geometry, chaos theory, and metaphysics. Essays, related sites, galleries, and recommended reading.
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 Fractals, Art, Pattern, Symmetry...  Clifford A. Pickover
Melding art, science, mathematics and other seemingly disparate areas of human endeavor. Links to detailed information on Pickover's books (of particular math interest are: Chaos and Fractals: A Computer Graphical Journey; The Loom of God; Fractal Horizons
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 Fractals (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive list of links to sites with information about fractals, classified by level and type of resource.
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 FractEd: The FractEd Information Pages  Douglas Martin; EALSoft
FractED is an introductory fractal tutorial for high school and college students that discusses elements of fractal geometry and chaos theory. It includes interactive programs which demonstrate the techniques of fractal generation and provides links
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 The Fractory: An Interactive Tool for Creating and Exploring Fractals  Green, Kulesza, Bergstresser; ThinkQuest 1996
Learn about fractals  what they are and how to design them  and discover more on your own. Fractals show an order in seemingly random things, and give us tools with which we can predict the weather, render natural looking objects, and help understand
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 FroZenLight  Zoltan Palmer
Interrelating line arts, mathematics, and cryptography, this free Java application simulates experiments in classic optics. Use FroZenLight to see how beaming a light ray onto circular mirrors would produce reflection patterns ranging from the symmetric
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 Gallery of Mathematical Images  Dept. of Mathematical Sciences, Loughborough University, UK
The Mandelbrot Set (frames from an animation); Quaternionic Fractals (an extension of the complex numbers  Mandelbrot and Julia sets); Hyperspace (4dimensional structures projected into 3dimensional space); Molecular Dynamics (images from simulations,
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 The Game of Chaos  Juergen Giesen
This applet performs the following game at varying speeds: Choose a random starting point (o) within the triangle ABC. Roll a die. Connect the point with point A, when you roll 1 or 2; with point B, when you roll 3 or 4; with point C, when you roll 5
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 Generalized Logistic Equation  Douglas J. Ingalls
A logistics equation is one of the simpler chaos equations. This site explores the property of the general equation with respect to immigration/emigration of the world's population. Includes graphs and a QBASIC program for generating logistic graphs.
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 Geometry  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
More than 95 games or puzzles having to do with geometry, chaos, fractals, and topology with extensive discussions and solutions. Most require a browser capable of displaying JavaScript or Java.
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 Graphical Iteration  Mark Scheuern
This applet demonstrates graphical iteration, using the quadratic iterator xn+1 = fa(xn) , fa(x) = ax(1x), 0<=a<=4 and iterating for twenty steps. Try different values of x0 and a. Note that some values will produce a stable state and others result
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 Groupe Fractales (INRIA)  Benoît Leblanc and Frédéric Raynal
A group of researchers studying the application of fractal techniques to complex systems, especially signal processing. Introduction to the theoretical aspects of fractal analysis; genetic algorithms; introduction to timescale analysis, in French; applications,
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 Home Pages for Developing Courses  Mathematics Throughout the Curriculum, Indiana University
Interdisciplinary courses under development and close to finished: Life Sciences (BioMath Problems, Mathematical Foundation for Speech and Hearing Sciences), Business and Economics (Games and Decision Making, Games for Business and Economics, Mathematics
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 How Does Biology affect Mathematics?  Louis J. Gross, University of Tennessee
Four examples of fields of mathematics that have been developed in part due to the biological underpinnings: Chaos Theory; Reaction diffusion equations; Genetic algorithms; and Neural Nets. A 1999 Math Awareness Month theme essay, with links to sites
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 Images and Mathematics (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
A large collection of images based on or related to mathematical principles, many purely mathematical abstractions, such as fractals; others of natural objects whose shape is explained by equations and mathematical models (for example, a drum vibrating).
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 Innovation in Education  M. Casco Associates
Educational software and free online courses in classical mechanics and chaos theory, free (demo version) downloads of mathematical modeling laboratories, and tutoring by email in physics and math. Math modeling programs include classical mechanics and
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 Interactive Mathematics Online  ThinkQuest 1996
Algebra (Postulates  Things you can do with equations and inequalities, Function Basics and Simple Graphing, Kinds of functions (periodic, odd, even, etc.), Function Squashing); Geometry (an introduction, applications, glossary, sample problems); Trigonometry,
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 The InterFACE: Internet Fractal and Chaos Education  ThinkQuest 1997
Lessons, games, activities, demonstrations, and software, to inform users of the science and mathematics behind fractal images and chaos theory. The lessons, identified by subject and level of difficulty and including quizzes, are designed to promote
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 Introduction to Chaos Theory  Andrew Ho
Designed for those with little background in mathematics. Topics covered include bifurcation diagrams; the Lorenz, Rossler, and Henon strange attractors; KolmogorovArnoldMoser orbits; and fractal geometry, including the Sierpinski Triangle, Von Koch
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 Iterated Function Systems  David Arnold; Mathematics Dept., College of the Redwoods, CA
What will the final image look like after you have plotted the infinite collection of points X1, X2, X3, ... generated by the chaos game? What if you plotted the infinite set of points generated by Barnsley's rules? This page provides a program that you
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 JAVA Gallery of Interactive OnLine Geometry  The Geometry Center
Applets illustrating geometry concepts. WebEQ, Hyperbolic Triangles, Lorenz Simulation, OneDimensional Iteration, Tetris, Leap Fractal, Fractals from Iterated Function Systems, Kali: Wallpaper Patterns. Created by The Geometry Center.
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 John Allen Paulos
John Allen Paulos is a mathematician and author of the books Mathematics and Humor, I Think, Therefore I Laugh, Innumeracy  Mathematical Illiteracy and Its
Consequences, Beyond Numeracy  Ruminations of a Numbers Man, A Mathematician Reads the Newspaper,and
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 Journal of Difference Equations and Applications
This journal presents papers on difference equations and the academic, analytical and engineering problems in which they arise. The journal is composed of original research, expository and review articles, as well as papers that present new concepts in
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 Ken Monks's Software  Ken Monks; University of Scranton
Links to some programs written by the author, as well as by others, that have been useful in his mathematics courses. Ken Monks's software includes Lurch, a word processor that can check your mathematical reasoning; RevSolid, a Maple program for making
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 Lavarand  LavaLite
Lavarand is a system by which a pseudorandom number generator is seeded by the digital output of a photograph of six Lava LiteŽ lamps.
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 Living Graphs  Living Graphs Inc.
Makers of ChaosLab, an interactive math package for visualizing and understanding fractal geometry and chaos theory. This PC software title covers bifurcation diagrams, the chaos game, coin tosses, diffusion limited aggregation, Levy flight, Pascal's
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 Liz's Research Interests  Liz Bradley, Department of Computer Science, University of Colorado
Artificial intelligence projects include Chaography, a pair of tools that use mathematics to generate choreographic variations: Chaographer, which uses a chaotic mapping to generate variations on a musical piece; and MotionMind, which uses machine learning
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 Lorenz Attractor: Simulation/Plotter  John Brecht
This program is a threedimensional plotting package and a numerical integrator. As an example, it is set to integrate the Lorenz Attractor problem. The applet features userdefined rotations of the coordinate system, depthbased shading of the colors,
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 The Magic Sierpinski Triangle: (Serendip: Complex Systems)  Bryn Mawr College
Order dependent on randomness: the Chaos Game. Construct Sierpinski's Triangle using Java interactively on the Web and focusing on one particularly interesting question: what is the right way of choosing the vertices? In the construction, the elegant
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 Making Order Out of Chaos  Andrew Davenport, Shane Kraynak, and Brian Timko  ThinkQuest 97
An introduction to chaos and fractals: history, theory, and a gallery of fractal images. Includes a review of complex numbers and a Java applet to investigate sensitive dependence on initial conditions.
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 Math Alive  Ingrid Daubechies, Princeton University
Materials from a course designed for those who have not had college mathematics but would like to understand some of the mathematical concepts behind important modern applications. Interactive "virtual labs" address cryptography; error correction and
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 Mathematical and Computational Sciences  National Institute of Standards and Technology (NIST)
Part of the Information Technology Laboratory of the National Institute of Standards and Technology (NIST) (an agency of the Department of Commerce, U.S. Government), this was formerly CAML. Mathematicians of the Applied and Computational Mathematics
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 Mathematical Biology Pages  Brandeis University
In contemporary biology there are many areas which depend heavily on rather advanced mathematics. This site demonstrates a few of these through Shockwave, Java, and JavaScript explorations. Dixon's Population Pages (exponential growth, nonlinear terms
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 Mathematical Connections  Whittle, Luoma; Dept. of Learning Support, Augusta State University
"Exploring the Interplay Between Mathematics and the Humanities." A forum for exploring the interplay between mathematics and the humanities, including, but not limited to, the relationship between mathematics and the arts, anthropology, history, literature,
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 The Mathematical Explorer  Stan Wagon and Wolfram Research, Inc.
Based on Mathematica technology, The Mathematical Explorer mixes text, graphics, and formulas in an easytouse notebook interface, offering a set of explorations for investigating some of the most fascinating topics in mathematics, from Escher patterns
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 Mathematics Across the Curriculum (MATC)  Dartmouth College
An NSFfunded project which strives to integrate the study of mathematics into the whole curriculum. MATC Courses: Mathematics and the Humanities (Pattern, Chaos, Late Renaissance Thought and the New Universe, Math and Science Fiction, Geometry in Art
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 Mathematics Archives  University of Tennessee, Knoxville (UTK)
A comprehensive site for finding mathematics on the Internet; particularly strong in its collection of educational software and links to other sites of interest to mathematicians that provide access to electronic journals, preprint services, grant information,
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 Mathematics Illuminated  Annenberg Media
A video course for adult learners, high school and college teachers; 13 halfhour video programs, online text, course guide, and Web site; graduate credit available. "Rather than a series of problems to be solved, mathematics is presented as play we engage
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 Mathematics Journals: Electronic and Printed  Mathematics Dept., Penn State University
Links to dozens of journals, from the Academic press electronic journal library to the Ulam Quarterly, and spanning printed journals from Abstract and Applied Analysis to the Zentralblatt für Mathematik. See also Penn State's page of preprints.
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 Mathematics Teacher: Geometry Bibliography  Hubert Ludwig
Hubert Ludwig, a math professor at Ball State University, has compiled an index of all the geometryrelated articles that appeared in the Mathematics Teacher through 1996. This page provides the index of the archive, with links to the documents in the
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 Math Exploration Quilt  Rik Littlefield; Hanford School
[Note: this is a historical archive of a site last modified in January 1997.] A computerized environment that can be applied to everyday life, for learning advanced mathematics and modern software: at the middle school level the concept of exponential
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 MathGifs
"Illuminating mathematics through animations." This blog, which dates back to September, 2013, has included illustrated posts such as "Reflective Property of the Ellipse," "Rotations Through Translations," "Fourier Pumpkins," "Sonic Booms," and "The Mandelbrot
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 Math in Arcadia  Ivars Peterson (MathLand)
It's unusual to find mathematics in a play, and at a sophisticated level in a witty, fastpaced, popular romp... there was little time to savor the nuances of the mathematics and to ponder the deep questions about the nature of scientific discovery that
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