/****************************************************************************
 * This formula file or any formula file derived from it cannot be used for
 * commercial purposes or to create hard copy output without the explicit
 * consent of the original author.
 ****************************************************************************/

fractal {

   // Establish the mapping between complex coordinates
   // and display coordinates

   mapping {
      (-1.06998963680096360000,
       0.01989089626422963600,
       -1.02434378669220180000,
       0.03744682379349050000) => (1280,490)
   }















   formula {
     
      z = current;
      zold = [0, 0];

      $xmax = 0;
      $xmin = 0;
      $xtot = 0;
      $ymax = 0;
      $ymin = 0;
      $ytot = 0;
      $mmax = 0;
      $mmin = 0;
      $mtot = 0;
     
      $stop = 0;
      $tolerance = 1e-10;

      while($stop == 0 && $count < 20)
      {
         if(abs(real(z) - real(zold)) <= $tolerance &&
            abs(imag(z) - imag(zold)) <= $tolerance)
         {
            $stop = 1;
         }
         else
         {                        
            f_z  = pow(sin(z), 3) - cos(z);
            fp_z = 3 * pow(sin(z), 2) + sin(z);

            zold = z;
            z    = z - fp_z / f_z;
                       
            value = log(z);
            $x = real(value);
            $y = imag(value);
            $m = mag(value);

            $xtot = $xtot + $x;
            $ytot = $ytot + $y;
            $mtot = $mtot + $m;

            $xmax = max($xmax, $x);
            $xmin = min($xmin, $x);

            $ymax = max($ymax, $y);
            $ymin = min($ymin, $y);

            $mmax = max($mmax, $m);
            $mmin = min($mmin, $m);
         }
      }

      $r = 0;
      $g = 0;
      $b = 0;

      if($count > 0)
      {
         $r = (($xtot / $count) - $xmin) / ($xmax - $xmin);
         $g = (($mtot / $count) - $mmin) / ($mmax - $mmin);
         $b = (($ytot / $count) - $ymin) / ($ymax - $ymin);

         // some constants ...

         $pi    = 3.14159265358979323846;
         $twopi = 2 * $pi;

         // adjust these to taste ... they should be: 0 <= value <= 255

         $rStart = 255;
         $gStart = 255;
         $bStart = 255;

         // adjust these to taste ... they should be: 0 <= value <= 2

         $rStep = 1;
         $gStep = 1;
         $bStep = 1;

         // Calculate the colors ...

         $r = -cos($twopi * $r);
         $g = -cos($twopi * $g);
         $b = -cos($twopi * $b);

         $r = $r * 127 + 127;
         $g = $g * 127 + 127;
         $b = $b * 127 + 127;

         $r = $r * $rStep + $rStart;
         $g = $g * $gStep + $gStart;
         $b = $b * $bStep + $bStart;

         $r = $r / 360;
         $g = $g / 360;
         $b = $b / 360;

         $r = sin($pi * $r);
         $g = sin($pi * $g);
         $b = sin($pi * $b);

         $r = $r * 128 + 127;
         $g = $g * 128 + 127;
         $b = $b * 128 + 127;      
         
      }

      set_color($r, $g, $b);
   }
}














