Precision Software Appli…tions Silver Collection 1/Precision Software Applications Silver Collection Volume One (PSM) (1993).iso/windows/games/norner.exe/NORNER.DOC

Text File | 1990-11-16 | 5KB | 127 lines

This is the readme file for the NORNER, a WINAPP that creates custom
fractals.  The NORNER was written by Garry J. Vass, 72307,3311.  The
archive should contain NORNER.EXE and NORNER.DOC (this file).  The
complete source and make is in another archive, NSRC.ARC.

QUICK START

     1.  WIN NORNER.
     2.  (P)lot, (G)o
     3.  Select an area with your mouse
     4.  Para(M)eters, (S)peed.  Change speed to every pixel
     5.  Go to step 2.


INTRODUCTION

  What is "norning"?  It is from the infinitive, "to norn",
  which is derived from the Teutonic mythological figures
  "die Nornen".  These are usually interpreted as three women
  who endlessly weave the strands of fate (the Greek counterparts
  are Atropos, Lachesis, and Clotho).  If the strands of fate
  should ever break, the Gotterdammerung (i.e., twilight of the
  Gods) will quickly follow.  In the Greek pantheon, Clotho
  gathers the strands, Lachesis weaves the threads, and Atropos
  cuts the threads.  Get the idea?

  In a much more mundane context, "norning" is taken to mean
  the activity of "weaving fractals".  Norners do this for fun,
  for a living, for art, or for science, but in one way or another,
  beautiful shapes and color inflections get created.


         "Norners do it with complexity!"


  The father of all Norners is Beniot Mandelbrot, an enthusiastic
  Frenchman who uncovered the process while examining the price
  movements of cotton futures.  The father of all popular Norning
  programs is FRACTINT, a truly astonishing piece of work.


USAGE NOTES

     1.  The program defaults to a "far away" zoom of the Mandelbrot
         set where every fifth pixel is plotted.  Zooming is accomplished
         with the mouse.  Click and hold the mouse button in the upper
         left of your zoom area and drag the mouse such that a rectangle
         is formed.

     2.  Use the "Go" command on the menu to see the zoomed area blown
         up to the client dimensions.

     3.  As the fractal becomes more interesting, use the "Speed" command
         to sharpen the resolution.  Complex fractals take a while to
         plot, speed is not my primary concern at this point.  If the
         speed is set to something other than one, use to "Fill" menu
         to toggle the Dot/Block mode.

     4.  Use the keyboard to interrupt the plot.

     5.  Use the "Transforms" command to alter the characteristics of
         your fractal.  IMPORTANT NOTE:  Be judicious in selecting
         your transforms for two reasons:

             a.  Many complex operations are time consumming and
                 usually add little to the outcome.  If you want
                 something in the middle of the fractal, add a
                 sin/cos function.  If you want an elaborate edge,
                 try raising Z to the sixth power.

             b.  Overloading the equation may generate huge numbers
                 that cause over/underflow.  This is usually followed
                 by a spectacular system crash.  The surest way to
                 initiate a spectacular crash (i.e., cold start needed)
                 is to build a transform like,

                     Z^2 + Z^3 + Z^4 + Z^5 + Z^6 + Z^7 + Z^8... and so on.

                 Caveats galore.

     6.  Use the "Iterations" menu to select an iteration count.  The default
         is 12.  This parameter controls how colorful the fractal is.  It has
         increasing returns to about 100 and diminishing returns at higher
         values.

     7.  If a fractal "doesn't look right", remember that it sizes itself
         into the client area, which may or may not be proportioned just
         right for the image you are seeking.

     8.  If you like to hack around...
          If you have the SDK...
            If you hook the Timer such that the NORNER plots, say, 50
             points on every timer message, then yields...
                If you do some hot-shot SDK calls just right...
                    Guess what?
                       You get a WINAPP that sits quietly in the
                       background and paints a fractal over your
                       WALLPAPER!!

HOW IS A FRACTAL GENERATED?

   For each point in the fractal, the NORNER uses the following
   approach:

       1.  Scale the constant term "C" to the real and imaginary
           boundary points.
       2.  Set the variable term "Z" equal to "C".
       3.  If the absolute value of "Z" is greater than 2,
           go to step 7.
       4.  If the number of iterations has been exceeded,
           go to step 7.
       5.  Apply the transform.  In the case of the Mandelbrot,
           this is "New Z" = "Last Z" times "Last Z" plus "C".
       6.  Increase the iteration count and go to step 3.
       7.  Select a color for the point.
               If no iterations were done, select white.
               If 1, 9, 17, etc iterations were done, select black.
               If 2, 10, 18, etc iterations were done, select blue.
               If 3, 11, 19, etc iterations were done, select green.
               and so on...
       8.  Move to the next point and go to step 1.


Garry J. Vass
72307,3311