Dynamical Systems and Technology Project

Dancing Triangles

## The Dynamical Systems and Technology Project at Boston University

Zooming Sierpinski

This project is a National Science Foundation sponsored 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. At this point, there are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iteration, fractals, iterated function systems (the chaos game), and the Mandelbrot and Julia sets.

### JAVA Applets for chaos and fractals

Play the chaos game; explore iterated function systems; and make fractal movies, like the Dancing Triangles and Zooming Sierpinski above, all at your own computer. These applets are now up and running!

### The Mandelbrot Set Explorer

 This is an interactive site designed to teach the mathematics behind the Mandelbrot and Julia sets. It consists of a series of tours in which you will discover some of the incredibly interesting and beautiful mathematics behind these images. The site is designed to be used by readers of The Mandelbrot and Julia Sets, published by Key Curriculum Press. This site is under construction, so I welcome any comments you have.

### Chaos, Fractals, and Tom Stoppard's Play Arcadia

 An interactive paper describing some of the mathematical ideas behind Tom Stoppard's wonderful play, Arcadia, including how young Thomasina, then sixteen years old, discovered back in 1800 the equations for images from nature such as fractal ferns (as shown unfolding on the left) as well as the basic principles of chaotic dynamics. And how, 200 years later, the mathematical biologist Valentine finally uncovered Thomasina's amazing discoveries.

### Mathematics Field Days

The fourteenth annual Mathematics Field Day for New England area high school students will be held at Boston University on Tuesday, October 19 and again on Tuesday, October 26, 2004. Thanks to the over 1,000 students and teachers who attended last year. We'll be back again in late October with the 14th annual Field Day. See you then!Hope to see you again this year! As in previous years, we expect these events to fill up fairly quickly. Contact Cynthia Brossman at cab@bu.edu if you and your students wish to attend. While you're waiting for the Field Day, have a crack at The Fractal Quiz!!!

We have organized several Field Days at sites in California, Maine, and Connecticut in recent years and plan to hold additional events in the future. Let us know if you are interested in hosting such an event.

### Dynamic Spreadsheets for Use in Algebra, Geometry, and Calculus

At this site you may download several spreadsheets used by Professor Devaney to explain such concepts as the Babylonian Method for finding square roots, Newton's Method, the chaos game, the logistic population model, and other topics.

### Fractal Movies

For high school teachers and students, field day participants, and readers of Fractals.

### Interactive Papers on Dynamical Systems

Including The Fractal Geometry of the Mandelbrot Set, Chaos in the Classroom, and more (mainly for high school students and teachers).

### The Center of Excellence for Learning in Education, Science, and Technology (CELEST)

This Center brings together leading scientists, educators, and technologists from Boston University, Brandeis University, MIT, and the University of Pennsylvania to study learning systems. There is much overlap between the activities and goals of the Dynamical Systems and Technology Project and CELEST.

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