Fractal visionaries and enthusiasts:

Due to an unexpectedly busy day on Friday, today's image is a quick and simple one, and the discussion is just as simple.

The image is named "The Golden Mallard".  On the surface it does resemble a duck floating serenely on an invisible body of water. (A lake transform might have been helpful in creating the water effect.)

Actually, the image is the parent fractal that is created when the formula Z^(1.05)+C is iterated 10-1/2 levels up the complex logarithmic hyperspiral with the 'recip' function applied.  (This function seems to work best with this formula, though I doubt that it is the most accurate.)

The calculation time of 41 seconds will pass quicker than a car at the Daytona Speedway.  But before this speed can be appreciated, the included parameter file must be set up and run.

A mix of sun and clouds and a temperature of 84F 29C made Friday a pleasant but rather warm day here at Fractal Central.  The fractal cats spent the day taking it as easy as possible without giving up the activity that goes with asking for food.  FL spent some of the time in the garden, caring for a sick rose bush.  (I did not realize gardening was so emotional.)

The next FOTD will be posted in 24 hours.  Until then, take care, and the next time you think a deep thought, try to determine how much the thought weighs.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

The_Golden_Mallard { ; time=0:00:41.30-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip
  center-mag=-1.58412/-0.336258/0.4444593/1/-20/0
  params=1.05/0/10.5/1500 float=y maxiter=3200
  inside=0 logmap=37 symmetry=none periodicity=6
  colors=00012K22K32L42L52M62M73M73N83N93O93OA3PA4PA\
  4PA4QA4QA4RA4RA5SA5SA5SB5TC5TD5UD6UE6VE6VE6VF6WF6W\
  F7XG7XG7YG7YG7YG7ZG8ZG8_G8_G8_G8`H8`H8aI9aI9bI9bI9\
  bJ9cJ9cJAdKAdKAeKAeKAeKAfKBfKBgKBgLBhLBhLBhLCiLCiL\
  CjLCjMCkMCkMDkMDlMDlMDmMDmNDnNEnNEnNEoNEoNEpNEpNEp\
  OFoOFoPGoPGoQHoQHoRIoRIoSJoSJnTKnTKnULnULnVMnVMnWN\
  nWNnXOmXOmYPmYPmZQmZQm_Rm_Rm`Sm`SmaTlaTlbUlbUlbUlc\
  VlcVldWldWleXkeXkfYkfYkgZkgZkh_kh_ki`ki`kjajjajkbj\
  kbjlcjlcjmdjmdjnejneiofiofipgipgiqhiqhiriiriiriiph\
  gnhfmhekhdjgchgbfgaeg`cf_bfZ`fY_fX`gY`hZ`hZ`i_`j``\
  ka`la`mb`nc`odbn_dmVelQfkRgjRhiRhiSihSjgSjgSkfTleT\
  mdTmdUncUocUocUpcVpcVpcWpcWpcXpcXpcYpcYpcZpcZpc_Nm\
  7Mm8Mm9LmALmBKmCKmDJmEJmFImGImHcmIcmJcmKcmLcmMcmOc\
  mNcmNmmNmmNmmNmmNmmNmmNmmNmmNmzMmzMmzMmzMmzMmzMmzM\
  mzMzzMzzMzzMzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzKzzKzz\
  KzzKzzKzzKzzKzzKzzKzzKzzz }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

END PARAMETER FILE=========================================