 Michelitsch Fractals  Michael Michelitsch
A gallery of "Burning Ship" and other fractal images generated by Albert Mürle's TurboBasic and TurboPascal programs iterating nonlinear feedback equations.
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 Millefiori!  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Fractal patterns produced by an algorithm with changeable parameters.
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 Miscellaneous: projection, modelling, rendering  Paul Bourke
Projection and displays, data visualization, photography and image manipulation, signal processing, and more.
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 Miscellaneous Sketches: Linear Sketch, MidRhombus...  Key Curriculum Press
Sketches: a dynamic display of the equation of a line as you move it around; an illustration of the midpoint figure of a quadrilateral; a tessellation made in the pattern of a Navajo rug; a sketch that draws the regular polygon with given internal angle;
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 MOTIVATE  Univ. of Cambridge, UK
MOTIVATE is a project incorporating a series of videoconferences, run by the Millennium Mathematics Project at Cambridge. The objectives of MOTIVATE are: to enrich the mathematical experience of school students, to broaden their mathematical horizons,
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 Mozart's Musikalisches Würfelspiel: A Musical Dice Game for Composing a Minuet  John Chuang
During his life, Mozart wrote the measures and instructions for a musical
composition dice game that cuts and pastes prewritten measures of music together to create a minuet. Compose a minuet online in one of three ways: CGI generates all random numbers,
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 Multithreaded Fractal Generator  Martin Hilpert
A fractal generator that is platform independent (running on any Java Virtual Machine) and uses many threads to calculate fractals for improved speed on multiprocessor/multicore computers.
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 Music and Virtual Flowers  Robert Walker
Fractal music, fractally based flowers, and geometrical models.
Programs are available for download. Make four and higherdimensional cubes and simplexes, then rotate them into the higher dimensions (so that the three dimensional projections change
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 The Music of José Oscar Marques
Listen to fractal music compositions in General MIDI file format, designed to show that recursive algorithms can be employed to create music of the same strange beauty as the richly decorated fractal picture on the site.
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 National Curve Bank  Gray, Venit; California State University, Los Angeles
Animation and interaction, and geometric, algebraic, and historical aspects of curves. Topics include Calculus, PreCalculus, History of Math, Limits, and Fractals. Submissions are encouraged.
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 The Nature of Physical Science  Richard Brill
A Honolulu Community College course, based around the Web and a series of television programs, that focuses on the history of science and its effects on our culture. Study guides are detailed outlines of various topics, including the foundations of arithmetic,
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 Newton Basins  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Newton's method for finding solutions to equations leads to some fantastic images when applied to complex functions. This program colors the complex plane according to where an initial guess will eventually take you, and gives each solution a different
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 Nonlinear Dynamics (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
Links to sites on nonlinear dynamics, chaos and turbulence studies, complex systems and visualization, continued fractions and chaos, dynamical systems and technology, dynamics and stability of systems, with indications of level and type of resource offered.
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 Nonlinear Science FAQ  James D. Meiss
The Frequently Asked Questions document for the newsgroup sci.nonlinear.
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 On Beyond Newton: from Simple Rules to Stability, Fluctuation, and Chaos (Serendip: Complex Systems)  Bryn Mawr College
An interactive exhibit on homeostasis/autonomy/chaos centered around population dynamics. The phenomenon of rules giving rise to not only order but also disorder, and, beyond that, to previously unknown forms of order, is the terrain currently being explored
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 On the Area of the Mandelbrot Set (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
One can upper bound this area by filling the area around the set by disks, or lower bound it by counting pixels; strangely, Stan Isaacs notes, these two methods do not seem to give the same answer. From the newsgroup alt.fractals.
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 Pages Mathématiques  Lycée de Vienne SaintRomainEnGal (académie Grenoble)
Une série de cours de mathématiques: Géométrie du triangle; Transformations; Géométrie des cercles; Barycentres; Coniques et courbes; Solides; Statistiques; Fractales; Géométrie non euclidienne;
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 PaperFoldingFractals  Joel Castellanos, Rice University
A classroom teaching or personal learning software tool for Windows that can be an introductory lesson to fractals. Simple, stepbystep processes of paper folding can give rise to infinite verities of fractals. The user learns what fractals are and how
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 Papers Online: Advanced Chaos  The Chaos Group, Univ. of Maryland at College Park
An online collection of published articles and preprints on advanced chaos theory, covering the topics of: Control and Targeting, Dimensions, Fractal Basin Boundaries, General Chaos, Quantum Chaos, Riddled Basins, and Shadowing.
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 Pascal's Fractals  Ivars Peterson (MathLand)
It's possible to convert Pascal's triangle into eyecatching geometric forms. For example, one can replace the odd coefficients with 1 and even coefficients with 0. Continuing the pattern for many rows reveals an everenlarging host of triangles, of varying
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 Pascal Triangle Applet  Sergey Butkevich
An applet that graphically presents Pascal's triangle modulo an integer number p; i.e. it computes the binomial coefficients. It can draw triangles with up to 650 rows with a p value between 2 and 30,000 (though it's not very clear above 15,000). The
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 Pattern Exploration: Integrating Math and Science for the Middle School  Martin Logan et al.
Download PDFs of lesson plans from units such as The PascalSierpinski Connection, Branching Patterns in Trees, Lessons in Paper Folding, Fractal Wallhanging, Patterns in Nature, Scaling and Dimension, and more. With accompanying Java applets and Cabri
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 Peanut Software for Windows  Rick Parris
Abstracts and links for downloading free mathematics software: Wingeom (highprecision geometric constructions); Winplot (generalpurpose plotting utility); Winstats (scatter plots, curve fitting, histograms, statistical data, and standard theoretical
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 Periodic Points of Quadratic Polynomials  Cut the Knot!, Alexander Bogomolny
The main purpose of the Mandelbrot set is to index Julia sets corresponding to various values of the parameter c... iterations inside M evolve differently depending on the value of c. (You may explore some iterations via the applet supplied.) An interactive
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 Permadi.com  F. Permadi
Java and Flash applets: logic games, drawing and patternmaking programs, Conway's Life, and more arcadestyle offerings. Also includes tutorials in using Flash and a graphics gallery.
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 Peter Winton's Radical Home Page
Math topics include puzzles, a gallery of fractals, and Visual Basic programs to download (count the grains of rice on a chessboard, or graph different curves).
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 Plane Graphic Calculator  J. E. Lillge
A Java calculator that can plot graphs of mathematical functions. Intended primarily as an educational aid to understanding the geometric interpretation of mathematical functions, it also supports complex numbers, vectors, and parametrically defined functions.
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 A Playground of Thoughts  Takasugi Shinji
Takasugi's "Number Systems of the World" lists dozens of languages; how to count from zero to one hundred in each; and the mathematical meaning of the expressions for each numeral. For example, the French say "93" with quatrevingttreize, which means
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 Polynomiography  Bahman Kalantari
Polynomiography is the "art and science of visualization in approximation of zeros of polynomials. This visualization is via fractal and nonfractal images created based on the mathematical convergence properties of iteration functions." The galleries
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 Primordial Soup Kitchen  David Griffeath, Dept. of Mathematics, Univ. of Wisconsin
Research on the selforganization of random cellular automata. Griffeath produces colorful computer graphics that illustrate the ability of local parallel update rules to generate spatial structure from disordered initial states. His Welcome offers access
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 Project Interactivate  Shodor Education Foundation, Inc.
Interactive middle school lessons on number and operations, geometry and measurement, functions and algebra, and probability and statistics. They feature: online activities (illustrative Java applets including: Venn diagrams; clock arithmetic; Pythagorean
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 The Published Data of Robert Munafo  Robert Munafo
Mathematical data includes MuEncy, The Encyclopedia of the Mandelbrot Set (History, Exploring, Area, Algorithms, Naming, etc), properties of specific numbers, such as 2.68542 . . . and 143, and very large numbers and ways to write them. Programs include
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 The Pythagorean Theorem and the Maya Long Count  Charles Wm. Johnson; Science in Ancient Artwork 
Various essays dealing with the possible extension of the Pythagorean Theorem to the third power in relation to the mathematical and geometrical appearance of the Maya long count fractals within progressive series of right triangles. It would appear that
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 Query Interface to the Contents of the Mathematics Archives  University of Tennessee, Knoxville (UTK)
Search software, abstracts and reviews; teaching materials, etc. by keyword.
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 Random (Blog)  Neil Bickford
Bickford writes "about mathematics, cellular automata, programming, Rube Goldberg Machines, and overall randomness." Posts of the selfdescribed "mathematician/programmer/scientist," dating back to May, 2009  when Bickford was 11 years old  have included
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 Recursos de Matemáticas en Internet  Flavio P.
Información buscable, dividida en categorías que contienen enlaces comentados: altas, actividades, actualización, apuntes, buscadores, congresos, debate, enlaces, Escher, fractales, historia, lista general, Olimpiadas, publicaciones,
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 Redecorator Fractal Wallpaper Manager  Seraline P/L, Sydney, Australia.
A wallpaper manager, or randomizer, and image creator for Windows 95/98/NT/2000. Redecorator can change your desktop wallpaper as often as you like, creating seamless tiles and fractals.
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 Research Experiences for Undergraduates (REU) Program in Mathematics  Cornell University
During the summers of 1996, 1997, and 1998 undergraduates worked on research projects under the direction of Cornell University Mathematics Department members: Analysis on Fractals; Dynamical Systems.
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 Rivendell Educational Archive  Leigh Denault
An educational archive of materials in botany, history, math, science, drama, literature, philosophy, and art. Math resources include mathematician biographies, a fractal image gallery, and a bibliography.
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 Sacred Geometry  Bruce Rawles
"In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form
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 sci.fractals FAQ (Frequently Asked Questions)  Shirriff, Stepp
A archived FAQ from sci.fractals, a Usenet newsgroup about fractals; mathematics, and software, aimed at being a reference about fractals, including answers to commonly asked questions, archive listings of fractal software, images, papers that can be
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 Search Ask Dr. Math Archives  The Math Forum
Search by keyword K12 math questions answered by volunteer 'math doctors' in the U.S. and abroad.
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 Seattle Fractals Digital Art  Doug Harrington
A fractal art site featuring highresolution digital fractal art prints for sale, and fractal art Windows 95/98/NT/2000 screensavers.
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 SelfContacting Fractal Trees  Don West, Department of Mathematics, SUNY Plattsburgh
Two very different forms of Mandelbrot and Frame's equation for tip contact, pointing out some gaps in logic and errors in statements, with proofs, or at least outlines, of the author's assertions.
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 Selfsimilarity  Robert L. Devaney; Dept. of Mathematics, Boston University
A section from the paper "Chaos in the Classroom," describing selfsimilarity, with the example of the Sierpinski triangle.
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 Serendip  Bryn Mawr College
An expanding forum and a continually developing set of resources for exploring and supporting intellectual and social change in education, social organization, and for making sense of life, organized into: Brain and Behavior, Complex Systems, Biology,
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 Shapari and Curvay  Spelunk Computing
Windows software designed to allow children to produce abstract and fractal patterns from simple shapes and operations. Shapari offers 5 levels of difficulty, allowing children to challenge their visualization abilities by matching computer generated
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 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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