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PC-SIG Diskette Library (Disk #2309)

[PCjs Machine "ibm5170"]

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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.


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     
The program's documentation is excellent and offers a short tutorial    
that leads you step by step, with explanations of what terms and values 
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
1030D East Duane Avenue                                                 
Sunnyvale  Ca. 94086                                                    
(408) 730-9291                                                          
(c) Copyright 1989 PC-SIG, Inc.                                         


                *  *  *  A FRACTAL KALEIDOSCOPE, VERSION 2N  *  *  *


               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).


               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.


               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 -


               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.


               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 -


               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.


               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.


               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).


               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 

                                       - 4 -


               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.


               Here are a dozen sets of picture specifications that I find 
          attractive. Colors left blank mean to use the default colors.     

                 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 |
                 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 -

                 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|
                 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!


               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 

               h. Testing whether a real number response to a prompt is 

               i. Checking that your printer is turned on and ready to 

                                       - 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 -


║                <<<<  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