IFRACS.EXE

                                  Alfred D'Attore

        ("Upgrading" this software, I inadvertently introduced some bugs.
                           I believe they are now gone.)

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**       This software is mathematics-intensive.  It requires 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++, are for the most part
"Iterated Function Systems" as described by Michael Barnsley in his book
"Fractals Everywhere."  Once IFRACS.EXE is decompressed; further decompres-
sion is accomplished by "installation."  Merely command --

            Install Origin Drive Space Destination Drive

            Install C: C: is perfectly acceptable

The programs will be copied to the destination drive in the subdirectory
"IFRACS," and expanded therein.  Command "FRACS," and a MENU will appear.
actuating the Space Bar and the letter "p" controls the program.  The Space
Bar yields a new picture.  Lower case "p" fits the picture to the screen.
The Esc key exits the program.  Thereafter, when at the C: prompt, and you
wish to run it once more; merely command --

cd ifracs

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

FRACS

and you will be presented with the MENU.

Option 1, (one), will lead to Fractals selected at random; primarily iterated
function systems, (although some representative samples of other fractals will
appear).  Actuating the Space bar and lower case "p" controls the graphics.
The Space bar will yield a new picture.  Lower case "p" fits the picture to
the screen.  For "Hopalong" fractals, the user should wait until the picture
is fully formed.  The Esc key exits the program.

Option 2 and 3 are fractals of the more othodox type.  In both cases, the
first screen display is optimized for speed.  Both presentations 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.  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 presentations require a bit time to form and even more to inves-
tigate, all screens are formed 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 "ZAP10.CPP" is one of Iterated Function Systems contained in FRACS.EXE.
This one is particularly simple:

z = az + b

where a, b, and z are complex numbers. "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.  If ZAP10.CPP is compiled using the Borland Turbo C++ editing
and compiling environment, the program should run unmodified.

"ZAP.EXE" also contains a variation of the equation given above, to wit --

z = az + e^b, (or z = az + "e" to the power of "b").

This small change so expands the scope of the IFS as to require "containment."
At times, the output overflows the screen; or alternately, becomes so small as
to appear as little more than a dot.  Hit lower case "p," however, and the
fractal will fit itself to the screen.

All programs provide 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.


                                 * * * * *


The definitive program is, of course, "Fractint."  But among Iterated Function
Systems, I believe David Canright's "FREDEX," is the best.  It is written
entirely in "C" and is as fast as any fractal software ever gets.  The author
was good enough to supply me with his source code.  Unfortunately, it was a
very 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.
Besides, I wanted to try my hand.

IFRACS.EXE is "freeware."  It can be reproduced and distributed 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
                                     USA