There are many programs to do this, and there are many Applets floating around the Internet. Of course I had to write one myself, so here it is. The source code is here. The algorithm I used for my app is the most commonly used. It works by calculating the values of C and checking if they diverge to infinity; if they do, then assign a color to the co-ordinate (x, y). The key here is the coloring, because that is what gives the pictures their distinctive look. Another algorithm that could be used is called Distance Estimator. This algorithm is also used in conjunction with a coloring algorithm and renders a more stunning result than the algorithm I've used here. The reason I know about Fractals  My fractal
page wouldn't be complete if I didn't mention why I know about these things,
so, for the sake of completeness, here it is: Back in 1990-1991, while I was still in high school, I used to go to the University of Waterloo's library for fun. While looking around I found the book The Fractal Geometry of Nature. It called my attention because of the cover--it had a picture of the Julia set. I picked it up and took it home. I read it cover to cover, not understanding all the mathematics, but I was hooked. During this time I had bought my second computer, a PC/AT 386 25 MHz, 640 KB RAM, 40 MB Hard drive with an EGA video card. I found out that these pictures were made by a computer and I figured that I should be able to draw them in my computer as well. During my research, I discovered that I needed a computer program to do what I wanted and that meant that I needed a programing language. I then bought Turbo C (by Borland) and the book Fractal Programming in C. I was able to code (copy) the samples in the book. Once compiled, I ran the programs and found out that it took around 8 hours to generate the simplest Mandelbrot set. Having discovered that my computer was too slow, I thought that a bigger computer would be much faster at rendering these things. And since I was at the University library already and I could dial into their systems to search for books, I got the idea that I could hack into the University computers to render my images. I didn't break into any computer (it was illegal then, and it is illegal now, so don't do it), but it was pretty fun exploring that side of computing. I guess security wasn't a big issue then, for I was able to find many public modems I could dial into. I continued coding and waiting hours to see what the images looked like. Once I began attending the University (for math), I didn't use the big UNIX computers to code fractals. I guess I had other things to do. |
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