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Text File
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1987-02-03
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4KB
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84 lines
Images from the Mandelbrot Set
Each dot on each picture represents a complex number. The Mandelbrot set
consists of the complex numbers c for which the sequence
2 2 2 2 2 2
{c, c +c, (c +c) + c, [(c +c) +c] +c, . . . }
does not approach infinity. In these pictures, points in the Mandelbrot
set are represented by black. A colored area represents a set of numbers
for which the sequence diverges after a certain number of steps. Color
assignments are arbitrary and differ from one picture to another.
One of these pictures shows an area containing the whole Mandelbrot set.
The others show magnified portions. The amount of magnification is limited
by the accuracy of the computer's arithmetic and the time available.
The boundary of the Mandelbrot set is a fractal curve. The number of
dimensions is somewhere between one and two. Many fractal curves are
self-similar: they consist of parts which are exact miniatures of the
whole. The Mandelbrot set has infinitely many parts which resemble the
whole, but they are all different.
See the August 1985 issue of Scientific American.
Instructions:
1. Make a working copy of the program. Copy the files on the distribution
disk to a system disk (formatted with the /S parameter). You may make as
many copies as you wish and distribute them for other people to use
provided you do not modify the program or documentation.
2. To start the program, enter MBS followed by a file name such as WORLD.MAP.
WORLD.MAP is a file containing an overview of the Mandelbrot set. If you
enter the name of a file that does not already exist, the program will
create that file and another file of the same name but with an .EDG
extension, containing information about the picture. If you enter the name
of a file that already exists, the .EDG file must also be in the same
directory.
You may put a number after the file name on the command line, which
determines the maximum number of iterations for each pixel. The default
parameter is 2, which is the smallest number the program will accept. The
maximum number of iterations is 42 times the square of the parameter plus
the lower bound.
3. If the file has already been created, the picture will appear on the
screen. This will take a while if the picture has not been computed yet,
in which case it will appear one byte at a time as it is computed, which
usually takes a long time.
If the file has not been created yet, the program will ask for the edge
coordinates of the picture.
If you want to interrupt the program while it is making a picture, press
control C and it will save up to the last completed line.
4. When the picture is done, you can change the color set by pressing C.
(Does not work with EGA.)
5. If the picture is done, you can select a new picture. Press S (for
smaller) several times, then press the down key. Lines will appear. Use
the cursor keys, S, and B (for bigger) to move the lines until they are
above and below the area you want in the new picture. Then press the
return key. The program will ask for a file name for the new picture.
If you don't want to select a new picture, press the return key and the
program will stop.
6. If you like this program or think you would like it if it ran much faster
or if you could change it, and if you have 8087 capability or a C compiler,
send $39.95 (check or money order) to
Odhner Corporation
RD1 Box 28A Perkiomenville Rd.
Perkiomenville, PA 18074
and we will send you (Postpaid in USA) the ultra-fast 8087 version and the
C (DeSmet) source code and assembly language enhancement. (PA residents
please add 6% tax.) The C program compiled for 8087 runs many times faster
than the plain 8086 version. The assembly language enhancement makes it go
more than twice as many times faster.