FRACTALS.1

                                        by

                                  Alfred D'Attore

                            (Upgrade of previous edition)

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**   These programs are all mathematics-intensive.  They require a very    **
**       fast computer for satisfactory results.  While not strictly       **
**   necessary, a mathematics coprocessor is also desirable.  The screen   **
**     can be normal VGA, 640 by 480 pixels, 16 colors; the most common    **
**                                 monitor extent                          **
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The included programs, written in Borland Turbo C++ and Microsoft QuickBasic,
are for the most part "Iterated Function Systems" as described by Michael
Barnsley in his book "Fractals Everywhere."  They were written primarily as an
intellectual exercise to further this author's understanding.  They turned out
so well, however, that I decided to put them on a self-installing disk and
place them in the public domain.

All programs are of the "stand-alone" type; that is, merely typing the name of
the program will start them.  Using the installation disk, command --

            "Install B: C:," for example,

and the programs will be installed on the C: drive in the directory "IFRACS."
Command "FRACS," (a good place to start), and actuating the Space Bar and the
letter "p" controls the program.  The Space Bar yields a new picture.  The
letter "p" fits the picture to the screen. The Esc key exits the program.

Thereafter, when at the C: prompt, and you wish to run these programs once
more; merely command --

cd ifracs

and you will be in the "ifracs" directory.  Then command any program --

FRACS              (for example)

and you're off and running, once more.

Two programs, "MANDEL.EXE" and "COSH.EXE," are fractals of the more orthodox
type.  Both feature a "Zoom" capability.  That is, pressing the Page up key
will bring a rectangle into view.  Page up decreases its size; Page down
increases it.  The cursor keys can be used to move it in the indicated
directions.  Pick any area of the picture; hit the Enter key, (Return), and
then the Space Bar once more, and a new picture will form, exactly as
outlined within your rectangle, but -- of course -- greatly enlarged.  As
above, press Esc to exit the programs.

Since both these programs require considerable time to form, the picture goes
to the screen in "thirds;" that is, one vertical line out of three at a time.
If you permit, a full picture will result; the next two time periods "filling
in" the fractal.  You need not wait, however, to "zoom" in.  You can "zoom" at
any time.

The "ZAP" group of programs are Iterated Function Systems of a somewhat
different but particularly simple variety:

z = az + b

where a, b, and z are complex numbers.  Note in ZAP10.CPP, (resembling one of
the source programs in the "ZAP" group and listed herein in ASCII), "a" has an
absolute value that is always less than 1.00.  As far as I can determine, this
is the only requirement for proper operation.  When ZAP10.CPP is compiled using
the Borland Turbo C++ editing and compiling environment, the program should
run unmodified.

Five programs, HEXAGON.EXE, TRIANGLE.EXE, TREE.EXE, LEAF.EXE, and DRAGON.EXE
have little or no variability built in.  They were written solely to examine
the affine maps provided in Prof. Barnsley's text and to experiment a bit.
They are included for interest.  Exit at any time using the Esc key.

Last, there is "copying" these fractals to standard image files for storage.
This software provides the capability to store images as PCX files.  At any
time, (preferably when the fractal is fully formed), hitting the TAB key,
unshifted, will start the process.  The bottom blurb will disappear and the
question, "Input filename ?" will appear in its place.  Give the image a name
of eight letters or less, (no extension), and hit RETURN.  A "beep" will
announce when the image is stored.  Afterwhich, the user can proceed exactly
as before.  Hit the SPACE bar, for example, and a new image will form.
"Storage" is possible with all programs except the five named above in the
preceeding paragraph.

There are many "fractal" programs.  The best, I believe, is "Fractint," a joint
venture by a number of experts in this field.  Of the Iterated Function Systems
type, David Canright's "FRED," is by far the best.  It is written entirely in C
and is as fast as any of these fractal programs ever get.  Both program groups
are in the public domain.  They can be obtained from any information system,
(most notably CompuServe), or from one of the shareware houses.

Mr. Canright was good enough to supply me with his source code.  Unfortunately,
it was quite a sophisticated package, and my knowledge of "C" was not yet at
that level to permit understanding.  It was actually easier to write my own
programs.  (It was better for learning, too.)

Feel free to reproduce and distribute this disk at will.  Comments and/or
questions are welcome and may be addressed to me at --

                         1300 South Farm View Drive
                               Apartment B-21
                            Dover, Delaware 19904