[Fractint] FOTD 21-09-11 (Crack in the World [7])

22 Sep 2011

      FOTD -- September 21, 2011 (Rating 7)

Fractal visionaries and enthusiasts:

Today's image is named "Crack in the World", meaning the world 
of fractals.  The name points out that the scene is located very 
near the negative X-axis of its parent fractal, where everything 
is broken apart.  This parent was created when I calculated the 
expression Z^(2.01)+C at a level 11 turns up the logarithmic 
hyper-spiral with the 'floor' function applied.  (Actually, I 
think the 'floor' function gives the most accurate values of the 
multi-valued complex logarithm, but it would take a better 
mathematician than me to figure it all out.) 

The parent fractal is a distorted Mandelbrot set rotated about 
15 degrees clockwise, so that the southern branch of Seahorse 
Valley intersects the negative X-axis.  Today's scene is located 
near this point of intersection.

With its inward-jutting low-iteration elements, the image 
appears as though it is very near the bailout cut-off point.  
Actually, it is very near the X-axis, which serves as a cut-off 
point in the image.

The rating of a 7 is perfectly average.

The calculation time of 5 minutes is a bit slower than I would 
have preferred, but still brief enough to make the calculation 
no more than a minor annoyance.

All the calculation problems may be avoided by viewing and 
hopefully enjoying the finished image on the official FOTD web 
site at:

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

And check the high-definition version at:

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

The classic FOTD site may be accessed at:

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

Heavy clouds kept an all-day damper on things here at Fractal 
Central today.  The temperature of 73F 23C was pleasant enough, 
at least for the fractal cats, who approved of the lack of rain 
as they enjoyed the outdoors from indoors.

My day was uneventful, which makes dull reading but a pleasant 
experience.  FL had a more active day with black-spot infested 
roses.  The next FOTD will be posted in 24 hours.  Until then, 
take care, and be ever alert for charlatans.

Jim Muth
jimmuth@earthlink.net

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

Crack_in_the_World { ; time=0:05:02.53-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=floor
  center-mag=-0.8068576369195436/+0.0000047645303079\
  /2.951255e+008/1/-67.5/0 params=2.01/0/11/0 float=y
  maxiter=7200 inside=0 periodicity=6
  colors=000424CCzlwzzzzGK8R0OK0ID0C606vtgjhZZYQNMHB\
  B899AG02EjjFbiFViGNhHFgH8gNBjTDmYFoRGmLHlFIj9Ji3AA\
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  qL_hHT_ELRAEI7793nZOaQIPHCC86UgZKTNAEBzPjeGVL8FDif\
  6NL68G348Z5BU49P37K26F24A135016gQ4XJ3MD1B6rkST6gL4\
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  XYQPPJGHD886`07R05I03901IrEFhBC_99R76I4392c3sX2iQ2\
  `K1SD1I609OEQKBLG9HC7D848 }

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