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.

** Important Notice:**
Security has been greatly enhanced recently on the web for java
applets like those on this page. Because of this, you may have
problems accessing these applets. If so, you can remedy this as
follows (for Mac users --- a similar procedure should work for
PC users, but I don't know the details).

Here is how to correct problems with access to these applets:

- Go to system preferences in the Apple menu
- Click on java
- Click on see the security tab
- Click on edit site list
- Add " http://math.bu.edu/DYSYS/applets " to this list, or add the address of specific applets
- Click OK and exit securely

Applets associated with the book Fractals include:

**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. On some browsers, apparently the numbers that you enter in this
program show up as white-on-white, so the numbers do not appear on the screen.
If this is the case, you can just
highlight the appropriate window to see the numbers. Someday I'll figure out
how to fix this....

**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:

**Nonlinear Web**. This applet allows you to see the results of
iteration of nonlinear functions such as the quadratic function
**x ^{2} + c**, the logistic function

**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 Quadratic Map Applet**. This applet allows
you to view simultaneously
the Mandelbrot set, a Julia set, and the fate of any orbit in or
around the Julia set. You can also use this program to make animations of
various Julia sets derived from moving along different paths in the Mandelbrot
set.

** The following applets are somewhat older and some do not run on Macs
using OS X (and some other machines).
**

**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/Julia Set Applet**. (Old Version.) This applet allows
you to view simultaneously
the Mandelbrot set, a Julia set, and the fate of any orbit in or
around the Julia set.

**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 for computing the parameter planes and Julia sets for other complex functions. These applets are really a research tool for me and my students, but we place them here so other people can see the interesting parameter planes and Julia sets that arise from iteration of certain non-quadratic complex functions in the complex plane.

**Quartic polynomials**. This applet deals with maps
of the form **Cz ^{2}( 2 - z^{2})**.

**The complex exponential function**.

More applets to come soon. Maybe...

Applets associated with the book Iteration include:

**The Function Iterator**. This applet allows you to iterate a
number of different functions, including
the quadratic functions **x ^{2} + c**,
the logistic family

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