As part of the Dynamical Systems and Technology Project, we have developed several JAVA Applets for use in exploring the topics of chaos and fractals. These applets are designed to accompany the four booklets in the series A Toolkit of Dynamics Activities, published by Key Curriculum Press.

Applets associated with the book Fractals include:

The chaos game. Yes, this is a game. Try to beat the computer by hitting specific targets via the moves of an iterated function system. This game allows students to understand the construction of the Sierpinski triangle via the chaos game.

Fractalina. This applet allows you to set up the vertices, compression ratios, and rotations associated to an iterated function system and then compute and view the resulting fractal.
If you have black and white monitors, be sure that you choose the appropriate colors for the points from the Color Selection button inside the applet so that you will be able to see the picture!

Fractanimate. This applet allows you to string together a collection of fractal images generated by Fractalina into a movie. We encourage you to become quite familiar with Fractalina before trying to use this applet.

Applets associated with the book Chaos include:

Linear Web. This applet allows you to see the results of iteration of linear functions of the form Ax + B in three different ways: as a list of the orbit, as a web diagram (graphical iteration), and as a time series graph.

Nonlinear Web. This applet allows you to see the results of iteration of nonlinear functions such as the quadratic function x² + c, the logistic function kx(1 - x), and many others. You can iterate step-by-step or view the entire web diagram.

Target Practice. This applet allows you to practice graphical iteration in the setting of a game. We give you a target (a particular "itinerary"); your job is to find an orbit graphically that has this itinerary.

Cycle Practice. This applet is a more advanced version of Target Practice. Your job in this game is to find a cycle (not just an orbit) with a given itinerary. Be sure to master Target Practice first before attempting this game.

Orbit Diagram. This applet allows you to draw the orbit diagram (or bifurcation diagram) for a variety of families of functions. You may also magnify various portions of these complicated sets.

Applets associated with the book The Mandelbrot and Julia Sets include the following. These applets are also part of the Mandelbrot Set Explorer, an interactive tutorial associated with this book.

The Mandelbrot Set Iterator. This applet allows you to choose a c-value in the Mandelbrot set and then view the corresponding fate of the orbit of 0.

The Mandelbrot Set. This applet allows you to choose a point in the Mandelbrot set and then view the corresponding Julia sets.

The Mandelbrot Movie Maker. This applet allows you to choose a path in the Mandelbrot set and then compute and view the corresponding Julia sets along this path in movie format.

Applets associated with the book Iteration include:

Towers of Hanoi. This applet allows you to play the classic game called the Towers of Hanoi.

For comments and suggestions write to Robert L. Devaney at bob@bu.edu