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

There are numerous java applets at this site for exploring topics involving chaos and fractals. For example, you can play the chaos game, make fractal movies (like the two above), and explore other iterated function systems. You can investigate the orbit diagrams of numerous real dynamical systems. And you can plot the Julia sets and (the analogue of) the Mandelbrot set for many different families of complex functions.

### 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.

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

 This is 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 the 1800s 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.

### 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.

### 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).