Program: MandelBrot. Download here (20K) - Note: you will need MFC42.DLL to run this.
I think the result is one of my better programs! I am astounded by the actually mathematics of it more than the program itself. I am pleased with the program itself due to the huge magnification you can get too - a 17 digit percentage is a large number! I really find the concept of fractals incredible - I also have this nagging feeling that they will play a part in Artificial Intelligence, or Artificial Life, at some point in the near future. The simplicity (look at the Mandelbrot() function!) of the function itself, yet the immense and indeed infinite complexity it creates, seems to me to be one of the definite secrets of nature. The features of the program are simple. To zoom, click somewhere in the viewing scope, then somewhere else! The program will zoom in on the RECTANGLE bounded by those points. The Iterations edit box is the number of iterations that the program checks for per-pixel to determine whether the point is bounded or not. You will want to increase this quite a bit at high magnifications. I found that sometimes upon zooming in on a group of pixels, the result would be total black. This is not a bug in the program - simply increase the iterations and your wonderful shapes will appear! The "Equal Ratio" button, well, equalizes the ratios. Since you can select any rectangle for the viewing area, the shapes could get seriously distorted as magnification got greater. The ER button will change the Y-ratio to equal that of the X-ratio. You may lose the bottom part of the area you are viewing, but the viewing scope will look a lot better. Finally, Reset takes you back to where you were so you can start exploring all over again! Note that the title bar shows you the percentage magnification. For example, doubling the size of the fractal is equivalent to 200% zoom. Explore and have fun! Added greyscale! I got a book from the library on fractals a few days after creating the basic program. It really inspired me to try to create a colour or greyscale version of the program. Colour proved to be to difficult, so I settled for greyscale. It still produces infinitely more beautiful pictures to the first version. Also, I did find a small link between fractals and the world of ALife! Ever heard of Sierpinski's Sieve? It is a fractal that consists of an isoceles triangle which is split up into 4 small triangles, each 'upright' one of these is further split up, etc. Now, download CA Creator, enter in the rules DAAAAAAD, and see what happens. 
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"...and what does this have to do with Artificial Intelligence?" I hear you ask. Well, nothing really! I was reading Roger Penrose's The Emperor's New Mind (which IS about Artificial Intelligence - or the impossibility of) and he talked in great length about the Mandelbrot set. This really got me fascinated in the idea of fractals. So, that night I sat down and wrote a program in an hour that could draw the basic Mandelbrot set (what you see when it starts up). I spent a subsequent 3 hours adding zoom code and GUI tweaks.