By Theron Wirenga
It was a number of years ago, in August of 1985, when the cover of the Scientific
American caught my eye. The abstract image seemed somehow familiar but after further
examination I discovered it was an entirely new area of mathematics called fractals. A. K.
Dewdney's article in his Computer Recreations column entitled "A computer microscope zooms
in for a look at the most complex object in mathematics." fascinated me. This article was the first
exposure the general public had to Benoit Mandelbrot's fractal images and, perhaps more than
many other technical articles, launched a popular interest in fractal programming. Within a few
days of reading the article I had produced a black and white 50 pixel square image of the
Mandelbrot set on an IBM PC with an Intel 8088 CPU, an effort that took a several hours of
computing time as I recall.
As the 1980's progressed I purchased an IBM Model 50, which could display these
fractal images in 16 colors and on a 640 x 480 pixel screen. Later my fractals appeared in even
greater detail on an IBM Model 70 with 256 colors and a 1024 x 768 screen. During this time
most of my fractal programming was in Pascal, as Borland had produced an inexpensive Pascal
compiler that was a quantum leap in speed from the old BASIC interpreters. Later Borland
produced a C compiler as well and my fractal programs migrated to this language. Up until the
early 1990's all of these programs were written for the MS-DOS operating system. Computation
times for large Mandelbrot fractal images remained long, in many cases several hours and even
overnight. The introduction of math coprocessors in the Intel 486 CPU helped reduced
computation time and the Pentium family with its multiple pipes has finally brought the
rendering time down to reasonable levels.
As the Pentium CPU family was introduced I began writing my first Windows program
that produced a Mandelbrot fractal image. If you haven't figured it out by now, yes I'm a bit
enthralled with these images and continue to spend time writing even more involved programs
for their generation and display. Actually, I find it relaxing. Whenever work or other cares press
in I find myself at the computer watching a new Mandelbrot image painting its way across the
screen. It's my form of therapy.
Mandelbrot images aren't that hard to compute, you just need a computer because you
end up with millions and billions of multiplications to form an image. The core of the
computations for these images take up only a few lines of code and you can cut and paste this
code into any program fairly easily.
The Mandelbrot set is computed by operating on a fairly simple equation that contains
complex numbers of the form
[Continued]
