FOTD 23-08-12 (Square Root Reciprocal [6])

23 Aug 2012

      FOTD -- August 23, 2012 (Rating 6)

Fractal visionaries and enthusiasts:

To produce today's little masterwork, I took the expression 
Z^(sqrt(2))+C and calculated it 0.707106781 levels up the 
logarithmic hyperspiral.  (The hyperspiral is another name for 
the hyperladded.)  By no strange coincidence, 0.707106781 is the 
reciprocal of 1.4142135624, the square root of 2.

The resulting parent fractal is a monster with more convolutions 
than a street map of Tokyo.  Today's image lies in the Seahorse 
Valley area of the parent, though one would never guess it by 
looking at the parent.  Rarely have I seen such an obscure 
Seahorse Valley.

The rating of a 6 is a sign that I am not very impressed with 
the image.  We have seen too many similar images over the past 
15 years of the FOTD.

The name "Square Root Reciprocal" describes the expression that 
created the image.

The calculation time of 3-1/4 minutes is slow, though still 
faster than yesterday's.  Visit the web sites for a speedier way 
to view the image.

View the finished image at:

      <http://www.crosscanpuzzles.com/Archives.html>

A high-definition rendering is at:

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

The back images are at:

       <http://www.Nahee.com/FOTD/>

A near perfect day passed by peacefully here at Fractal Central 
today.  The fractal cats heartily approved of the near cloudless 
skies and temperature of 84F 29C.  The humans went through the 
day with nothing exceptional to report.  The next FOTD will be 
posted in more than an hour but not as much as a week.  Until 
whenever that might be, take care, and it seems we're becoming 
so frantic to stay healthy that we have forgotten how to live.

Jim Muth
jimmuth@earthlink.net

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

Sqrt_reciprocal    { ; time=0:03:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=cosxx passes=1
  center-mag=+0.8559664295/-0.0636040039/13101/1/\
  50/0 params=1.4142135624/0/0.707106781/0 float=y
  maxiter=3750 inside=0 logmap=146 periodicity=6
  colors=000JBKIAII9HH8FG8EF7CE6AE59D57C46B34B33C43C\
  53C63C73C83C93GA6KB9OCCSDEWEH_EKcFNgGPkHSoIVsIXoHW\
  lGVhFUeEUaDTZDSVCRSBRPAQL9PI9OE8OB7N76M45L15L4BS6G\
  Y8McARiCQoRPjQKeQFaPAYPAUQCPRELSGHTHITJJULKVMLWONW\
  QzXRzYTzZVz_Wz_Yz`_za`zbbzbdzcezdgzeizejzZdzTZzMUz\
  GOzAJzAIzAIzAHzAHzAGzAGsAFsAFsAFrAErAEqADqADqACzAC\
  z99zACzAEzBHzBJzCLzCOzDQzDSzEVzEXz9PzCUzEZzGbVJgaL\
  lhFqpJpoNpoQpoUooXoo`ondnngnnknnqppnnnklmhjlehkbgj\
  `eiYchVagS`fPZeMXzKVzHUzESzBQz8Oz7Rz4Mz6Nz7Oz8Pz9Q\
  zBRzCRzDSzETzGUzHVzIVzJWzLXzMYzNZzOZzQ_nR`oSapTbqY\
  etUbqR`nOYkLWzHTzERzBOz4Lz6Mz8MzAMzCMmDMmFMmHMmJMm\
  LMmMMmOMmQMmSMmUMmVMmXMmZMm`MmbMmzMEzMDzMCzMBzIBzK\
  AzMAzO9zQ9zS8zU8pWmrYms_mtamvcmwecxgcyiczgczeczdcz\
  bcz`czczzczzczzczzczzczzczzczzcbzcezcgzcjzclzcozcq\
  zcszmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\
  zzmzzmzzmzzmzzmzzmzzmzzmz }

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=========================================

Jim Muth

Sebastien Helie

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