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PC-SIG Diskette Library (Disk #2309)
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Information about “FRACTKAL”
FRACTKAL combines the best of a fractal generator and a kaleidoscope.
Similar to a kaleidoscope in that it can generate fractals at random,
this menu-driven program is great for the novice.
Finished fractals, generated by you or by FRACTKAL, can be saved as
PICT files and may brought up from disk at any time within the
program. The documentation is excellent and a short step-by-step
tutorial is offered.
While a higher-level user might find FRACTKAL's functions limiting, the
beginner can spend hours experimenting with custom-designing
fractals or seeing what the computer can come up with. All this,
without having to deal with the mind-boggling bells and whistles of the
more advanced fractal-generating programs.
FILE2309.TXT
Disk No: 2309
Disk Title: Fractkal
PC-SIG Version: S1
Program Title: Fractkal
Author Version: 2N
Author Registration: $15.00
Special Requirements: EGA
FRACTKAL combines the best of a fractal generator and a kaleidoscope, as
the name implies. It's similar to a kaleidoscope in that it can
generate fractals at random, which is great for the novice. (The program
is menu-driven and no mouse or other peripheral is required.)
Finished fractals, whether generated by you or by the program, can be
saved as PICT files and brought up from disk at any time within the
program.
The program's documentation is excellent and offers a short tutorial
that leads you step by step, with explanations of what terms and values
mean.
While a higher-level user would find FRACTKAL's functions limiting, the
beginner can spend hours experimenting with custom-designing fractals or
seeing what the computer can come up with. All this, without the
mind-boggling bells and whistles of the more advanced fractal-generating
programs.
PC-SIG
1030D East Duane Avenue
Sunnyvale Ca. 94086
(408) 730-9291
(c) Copyright 1989 PC-SIG, Inc.
FRACTKAL.DOC
* * * A FRACTAL KALEIDOSCOPE, VERSION 2N * * *
==================================
SYSTEM REQUIREMENTS:
These programs require an EGA graphics card, a color moni-
tor, a single floppy disk drive, and 192 kilobytes of random
access memory (more if you use terminate-and-stay-resident [TSR]
programs). FRACTK87 is identical with FRACTKAL, except that it
also requires an 8087 math co-processor.
FRACTK87 runs about seven times faster than FRACTKAL. Be-
cause the programs' main algorithm typically makes hundreds of
thousands of trigonometric calculations during a single run,
this speed difference can't be reduced significantly.
FAIR USAGE:
These programs are copyrighted, but we encourage you to
back them up and share them with your friends. We also encourage
you to register them, using the FRACTKAL.REG form (see page 6).
WHAT FRACTKAL AND FRACTK87 DO:
These programs help you design and display slowly-changing
pictures on your computer screen. Each picture is symmetrical
top to bottom and left to right, like the patterns shown by a
kaleidoscope whose mirrors are set at 90 degrees. Each picture
is also symmetrical in a deeper, more subtle, sense. For each is
composed of up to four fractals -- figures that look much the
same at any level of magnification.
You can easily create harmonious, flowing pictures whose
colors gradually change and which gradually become more and more
complex as time passes. By experimenting, you can refine your
designs until they are exactly as you want them, then save their
specifications to small disk files. Thereafter, you can rerun
your completed pictures whenever you wish. Because there are
more than 1,000,000,000,000,000,000,000,000,000,000 possible
pictures, you will probably be the first person ever to see the
ones that you create.
These pictures are suitable for unattended computer demos,
as aids to meditation (for which FRACTKAL's slower speed may be
valuable), and for simple aesthetic enjoyment. Their creation
and refinement can be challenging and engrossing.
CONTROLLED RANDOMNESS:
The programs' algorithms involve carefully limited amounts
of randomness. This has two consequences: (1) No matter how
long a particular display runs, it will never repeat itself;
instead, it gradually becomes more complex, and (2) Although
this may not be immediately obvious, no two repetitions of the
same specifications will ever yield quite the same display.
- 1 -
Tutorial
--------
Make backup (archival) copies of the following files:
FRACTKAL.DOC (this file), FRACTKAL or FRACTK87 (or both),
FRACTKAL.FRM, and EGAVGA.BGI. The latter is a support file
proprietary to Borland International.
CREATING OR CHANGING THE FRACTKAL.DAT FILE:
Next, copy EGAVGA.BGI and FRACTKAL or FRACTK87 (or both) to
the floppy disk or hard disk subdirectory which you plan to use
when running the program (hereafter, your home disk or direc-
tory). You might create a new hard disk directory called \FRK,
but a floppy disk will serve equally well (the program makes
little use of your disk drive so that using a floppy won't slow
it down much, and a single floppy disk will hold data for thou-
sands of pictures besides your program and its support files).
Next, go to your home disk or directory. If this is a
floppy disk, create a subdirectory to hold the data for your
pictures. (For instance, using a floppy disk in your A: drive,
at the A: level you might command MD \PIC. Your home disk is now
A:, but you will store picture data on A:\PIC. You should do
this because DOS limits the number of files that your root
directory will hold, but places no limits on subdirectories.)
Alternately, if you store program and support files on the hard
disk subdirectory C:\FRK, this could be both your home directory
and where you will store picture files.
Now you are ready to run either FRACTKAL or FRACTK87. The
program will identify itself, then will ask you for a path for
saving pictures. One option is merely to press Enter ( <--' ),
thereby electing to save these on your home disk or directory.
As we've seen, that works fine with a hard disk subdirectory,
but if you wish to save pictures to a floppy disk, be sure in-
stead to save them to the subdirectory that you created, rather
than to the floppy's root directory.
When telling the program about a subdirectory, be sure to
end your reply with a backslash (for instance, \PIC\, not \PIC).
The program will then create a 28 byte support file, called
FRACTKAL.DAT, on your home disk or subdirectory. It will never
ask you about paths again ... unless you change your mind.
WHAT TO DO IF YOU CHANGE YOUR MIND (for instance, if you
disobeyed the on-screen warning and didn't read this section
before you tried out the program): At the DOS level on your
home disk or directory, delete this support file (by typing DEL
FRACTKAL.DAT). The next time you run the program it will again
ask for path instructions, and you can respond correctly. Unfor-
tunately, you no longer will be able to rerun any pictures that
you saved before changing your mind. (We could have written the
program to avoid this loss, but only at the price of much disk
activity and consequent delay each time you rerun a picture.)
- 2 -
GENERATING A RANDOM PICTURE:
Next, the program will show you its main menu. Notice that
you can always return to DOS by entering 'Q' (or 'q' -- all
commands work with either upper- or lower-case letters).
The easiest way to make a picture is to let the computer do
all the work -- so for your first picture enter 'R' for a random
display. Your screen will blank, and usually will change color.
Most often you will immediately see a pattern begin to develop.
But this won't always happen: Your first foreground color could
(by chance) be the same as your background color; if so, you
won't see any pattern for a while. (There is one chance in 16 of
this happening, one in 256 of the first two foreground colors
being the same as the background, and only one in almost seventy
billion of all foreground colors being invisible this way.)
After a while, a second color and pattern usually will
appear, then a third and fourth. If you wait long enough, you
may see as many as ten different colors (though there is only a
small chance of this happening). Thereafter, your picture will
slowly fade, strengthen again, fade, strengthen ... gradually
becoming more and more complex.
SAVING YOUR PICTURE:
It's pure chance whether or not your picture is attractive.
If you like it, press (do NOT enter) "S" (or "s"). Your drive
will light and you will hear a beep, signifying that the program
saved your picture. (Thereafter, pressing "S" will have no
effect until you create your next picture.)
If you don't like your picture, or if you simply want to do
something else, press any key OTHER than "S" to end the display.
The program will ask you whether you are done generating random
displays. If you enter "Y" (or "y"), it will return you to the
main menu. If you answer "N" (or "n"), it will create a new
picture for you.
For this tutorial, create random pictures until you get at
least one that you like well enough to keep. The program will
save the first of these under the name SPEC1.FRK, where SPEC
stands for "specifications", the second as SPEC2.FRK, and so
forth up to SPEC9999.FRK. Each such data file uses only 50 bytes
of disk space. DO NOT RENAME THESE DATA FILES, or the program
won't be able to rerun their pictures.
RERUNNING A PICTURE:
This time when you're back at the main menu, enter "O" (or
"o") to run a display that you have saved. The program will ask
you to choose by number which picture you want to see. (If you
hadn't saved any pictures it would tell you so.) Rerun any one
that you wish. As mentioned earlier, if you had photographed
this display both times it appeared, you might notice slight
differences between the two photos.
- 3 -
If you saved a picture but then later erased its SPEC file,
or if you saved it on one floppy disk but had another disk in
your drive, the program would "know" that you had saved a pic-
ture with its number, but wouldn't be able to rerun it (and
would tell you so).
DESIGNING A NEW PICTURE:
Thus far, we have used the program's automatic features.
Now let's be creative: From the main menu, enter "N" (or "n")
to design a new picture.
1. The First Two Windows: The program will ask some ques-
tions which, unprepared, you might find puzzling. Here's some
background: The program generates displays one point at a time
(though it immediately echoes each point to three symmetrical
places, to simulate a kaleidoscope). Each new point moves from
the previous point's location in a random manner.
This randomness is controlled by two factors: a "radial
index," which determines how far the point moves toward the
center or the upper right corner of the screen, and a "rotation
index," which determines the point's movement around the center.
The radial index affects two characteristics of the fractal
patterns that you will create: the higher that index, (a) the
bushier (more spread out) those patterns will be and (b) usual-
ly, though not always, the closer to the center of the screen
those patterns will extend. The first window asks you to enter a
single radial index for all four of your display's patterns.
Its rotation index determines the characteristic shape of a
final fractal pattern. Since each picture uses four patterns,
the next window asks you to enter four rotation indexes.
2. The Color Windows: Next, the program asks you whether
you want to use its default colors in your picture. These are a
set of colors that many find to be harmonious. Using them also
saves time when you're fine-tuning radial and rotation indexes
by trying out their displays. Answer "Y" (or "y") for now.
As with random displays, if you like the picture that you
get, press "S" (or "s") to save it. Pressing any other key will
clear the display; the program will then ask whether you want
to create another display.
Answer "Y" (or "y"). This time, after entering your radial
and rotation indexes, reject the program's default colors (enter
"N" or "n"). The program will show you a color chart and ask you
to choose your picture's background color. Once you have done
so, it will ask you for nine foreground colors; these may re-
peat each other, and may repeat the background color. After you
have chosen your ninth foreground color, the display will begin
automatically.
- 4 -
TRYING OUT INDIVIDUAL FRACTAL PATTERNS:
The best way to learn how to use this program is to play
with it. It contains a built-in tool for such experimentation:
The main-menu option to try out individual fractal patterns. At
the main menu, press "I" (or "i"). The program will ask you for
a radial (bushiness) index, then for a single rotation index,
after which it will display a single fractal and its three sym-
metrical reflections. When this display is complete it will
beep, and pressing any key will return you to a request for a
new radial index.
Try 1 for bushiness (radial index) and -9 for the test
fractal (rotation index). Even though the resulting display
shows only one fractal pattern, it's in four colors. The dark
blue sub-pattern is the original fractal, the other colors are
its reflections.
The self-similar symmetry of a fractal pattern is obvious
here. For instance, the portion of the dark blue sub-pattern
near the upper left of the screen is a larger version of the
portion in the upper center, which in turn is echoed by succes-
sively smaller versions as the sub-pattern moves toward the
upper right corner.
Let's now experiment with bushiness. Try (4, -9) instead of
(1, -9); the pattern will be similar to the previous one, but
thicker and more detailed. Try (7, -9) then (10, -9), and see
what happens. This particular pattern is one that moves a little
closer toward the center of the screen as the radial index in-
creases, but which still leaves the center pretty bare.
PICTURES THAT YOU MIGHT WANT TO TRY:
Here are a dozen sets of picture specifications that I find
attractive. Colors left blank mean to use the default colors.
Indexes:
Bushiness | 5.6 | 7.6 | 7.6 | 7 | 3.5 | 3.5 |
Fractal 1 | 0.1 | 0.1 | 0.1 | 7 | 32 | 32 |
Fractal 2 | 0.3 | 0.3 | 0.3 | 7 | 34 | 34 |
Fractal 3 | 0.5 | 0.5 | 0.5 | 7 | -34 | -34 |
Fractal 4 | 0.7 | 0.7 | 0.7 | 7 | -1 | -1 |
Colors:
Background | 0 | 0 | E | | 0 | 7 |
Foreground 1 | 1 | 1 | 1 | | 5 | 5 |
Foreground 2 | 3 | 3 | 3 | | C | C |
Foreground 3 | 9 | 9 | 9 | | D | D |
Foreground 4 | B | B | B | | 4 | 4 |
Foreground 5 | 6 | 6 | 6 | | 0 | 0 |
Foreground 6 | 1 | 1 | 1 | | 3 | 3 |
Foreground 7 | 3 | 3 | 3 | | 9 | 9 |
Foreground 8 | 9 | 9 | 9 | | B | B |
Foreground 9 | B | B | B | | 1 | 1 |
- 5 -
Indexes:
Bushiness | 4.7 | 4.7 | 5.7 | 5.7 | 10 | 5.8 |
Fractal 1 |-0.25|-0.25|-0.25|-0.25| 10 | -27 |
Fractal 2 | 0.5 | 0.5 | 0.5 | 0.5 | 10 |-27.5|
Fractal 3 | -11 | -11 | -11 | -11 | 10 | 27 |
Fractal 4 | 11 | 11 | 11 | 11 | 10 | 27.5|
Colors:
Background | E | B | E | B | | 3 |
Foreground 1 | 0 | 0 | 0 | 0 | | 4 |
Foreground 2 | 7 | 7 | 7 | 7 | | 0 |
Foreground 3 | 8 | 8 | 8 | 8 | | 5 |
Foreground 4 | F | F | F | F | | 1 |
Foreground 5 | 6 | 6 | 6 | 6 | | 8 |
Foreground 6 | 0 | 0 | 0 | 0 | | D |
Foreground 7 | 7 | 7 | 7 | 7 | | 0 |
Foreground 8 | 8 | 8 | 8 | 8 | | B |
Foreground 9 | F | F | F | F | | 8 |
This completes the tutorial. Enjoy the program!
Registration
------------
If you do enjoy it, you should register it. This program
represents many hours of work; we can continue to enhance it,
and to develop other shareware products, only if you support it
and the shareware concept. There are two ways to do so:
$15 Registration:
----------------
For $15, you will receive a disk that contains:
1. The most recent version of the program (specify FRACTKAL
or FRACTK87). It will include the following additional features:
a. Instead of being limited to a single radial (bushiness)
factor for all four fractal patterns, you will be able to
specify a different bushiness for each pattern. This will allow
you to create a wider variety of pictures.
b. In testing individual fractal patterns, whenever you
find one that you like you will be able to save it (and up to
three more) for automatic inclusion in your next picture. This
will avoid re-keying these specifications.
c. During any display, you will be able to freeze and
unfreeze it (stop and restart its changing) by pressing the "F"
key. This will make it possible to linger over effects that
appear and disappear.
- 6 -
d. After running any display, you will be able to view its
specifications on the screen or print them on your printer. This
will be especially helpful in understanding randomly-generated
displays and in modifying pictures that you saved earlier.
e. After running any display, you will be able to repeat
it, either unchanged or with some parameters the same and others
different. This will greatly reduce tedious re-keying when
refining pictures.
2. An updated FRACTKAL.DOC manual (on disk), with a tutor-
ial that explains these and other program enhancements.
3. Data files for generating several displays that I find
particularly attractive.
4. News of forthcoming Quantrill Software products.
5. A small bonus graphics program.
$35 Registration:
----------------
You will receive all of the foregoing, plus:
1. The complete Turbo Pascal 4.0 code for this program.
Almost all of this is written in plain-vanilla Borland Pascal;
the comments contain references for the few exceptions. Here are
some of the carefully tested procedures, functions and other
programming techniques that you can add to your programming
repertoire. Some are elementary, others not:
a. Displaying and printing records.
b. Testing whether files and paths exist before trying to
use them.
c. Allowing users to designate paths for saving files.
d. Saving records to disk files.
e. Recalling them from disk.
f. Allowing users to exit gracefully from your program at
any point during its execution.
g. Testing whether a character response to a prompt is
"legal".
h. Testing whether a real number response to a prompt is
"legal".
i. Checking that your printer is turned on and ready to
print.
- 7 -
j. Displaying a menu of colors.
k. Changing graphics background colors without messing up
your foreground colors.
l. Turning the cursor on and off without the cosmetic flaw
of the way that Borland recommends.
m. Restoring the screen to its original state after using a
window, and at the end of a program.
n. Partly correcting for the non-random nature of Turbo
Pascal's Randomize.
o. Drawing on-screen boxes within windows.
p. Designing easy-to-use menus within these boxes.
q. Generating this program's sign-on display.
2. Complete Turbo Pascal 4.0 code for the small bonus
graphics program.
3. A small bonus utility that calculates how to center on-
screen boxes.
4. Complete Turbo Pascal 4.0 code for this utility.
If possible, print out and use FRACTAL.REG to register. In
any event, be sure to request either FRACTKAL or FRACTK87.
Our Philosophy
--------------
Many recreational and decorative graphics programs are
available to PC users. Quantrill Software seeks to develop ones
that have two relatively rare characteristics:
1. They encourage active user involvement in designing and
modifying displays, instead of the passive user role typical of
"mindless" graphics programs.
2. They generate complex, aesthetically "deep" displays,
instead of the usual simple patterns.
In addition, of course, we are concerned to develop pro-
grams that are as easy and convenient as possible for you to
use, and eagerly welcome your comments and suggestions.
Art Thomas, Proprietor
QUANTRILL SOFTWARE
1642 Indiana
Lawrence, KS 66044
- 8 -
GO.TXT
╔═════════════════════════════════════════════════════════════════════════╗
║ <<<< PC-SIG Disk #2309 FRACTKAL >>>> ║
╠═════════════════════════════════════════════════════════════════════════╣
║ ║
║ To print documentation and tutorial, type: ║
║ COPY FRACTKAL.DOC PRN (press Enter) ║
║ ║
╚═════════════════════════════════════════════════════════════════════════╝
(c) Copyright 1990, PC-SIG Inc.
Directory of PC-SIG Library Disk #2309
Volume in drive A has no label
Directory of A:\
EGAVGA BGI 5139 11-02-87 4:00a
FRACTK87 EXE 56320 5-12-89 4:41p
FRACTKAL DOC 23936 10-11-88 10:29a
FRACTKAL EXE 56256 5-12-89 4:41p
FRACTKAL REG 1536 5-12-89 5:08p
GO TXT 650 1-01-80 5:57a
GO BAT 40 1-01-80 6:00a
FILE2309 TXT 2665 8-28-90 3:18p
8 file(s) 146542 bytes
11776 bytes free