If an iterative function displays unpredictable, bounded behavior, it is called a Strange Attractor.  The Lorenz System is a famous example of this.  The Logistic Equation provides many simple examples, such as xn+1 = 3.6 * xn * (1-xn).  My favorite strange attractor is by Clifford Pickover (see his site), and is discussed in his book Chaos in Wonderland.

xn+1 = sin(yn*b) + c*sin(xn*b)
yn+1 = sin(xn*a) + d*sin(yn*a)
This attractor was included in a screen saver program by Chris Dueker, which you can download here.  Save it in your Windows/System folder, then access the Strange Attractor screen saver.  We found a particular nice set of points (-.944578, 2.303812, -1.372326, 1.454543) which produced a "double blinker" when set to two colors.  Here is a premade init file you can try, copy it into your Windows folder.  I tried to reproduce that here in Java, but the double blinker doesn't seem to work on my home computer.  While trying to force it to work, I found something new.  See my Applets page .

The program Rota is from Vladeta Jovovic from Belgrade, Yugoslavia.  Here's a demo of the program.  Basically, in a square grid, you can rotatepart of the grid, or take their negative.  It's a DOS program.

Chris Dueker also sent me an excellent program for visualizing four dimensional objects.  First, save the object known as the 600-cell to your hard drive. Here is his Windows program -- it will ask where the 600-cell data is stored.  A tesseract is here.

Jukka-Pekka Ikaheimonen has developed a new Zillions game.  If you have Zillions, then you can get Rollers.

The Tanuguchi Sliding Block Puzzle program is now available here (for free).  A new (to me) version of Fractint is available here (for free).  I converted this fractal to a PNG image (GIF also available) with StarOffice from Sun Microsystems (also free).  The whole website was built in Netscape Composer (free).  The image above was drawn in ISISdraw (free).  If you know of any good free programs, please contact me.

Michael Keller of World Game Review (an excellent magazine) has produced a new version of his Amazons computer game.  Go to the World Game Review site, and write to him about it.  There is a Zillions version of Amazons, but Zillions does poorly with territory games.  Michael Keller's version is much stronger.

IBM's VisualAge for Java is my choice for Java compilers.  I tried Borland's JBuilder, Symantec's VisualCafe, Microsoft's J++, and Sun's Java Developer's Kit, as well.  Due to ease of use, nice tutorials, and high support, I chose IBM over the others, after trying all five.

Mathematica is an incredible piece of software.  I use it constantly.

Tantrix is a set of 56 tiles that makes for both good games and good puzzles.

Gerry Quinn's Mathematical Games Page contains several nice programs, including JOUST, which I have found addictive.  It's a free program... you compete with a knight, destroying squares.