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.

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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  1NE0F9074h6zX4jM3VB1FXTXOLOGEG878VzHKeBAL5alFS_BJO\
  79C3gBP`9LV7HP6EI4AC37689ACFBAAJ9XFEQBHK7BD356nzPf\
  qL_hHT_ELRAEI7793nZOaQIPHCC86UgZKTNAEBzPjeGVL8FDif\
  6NL68G348Z5BU49P37K26F24A135016gQ4XJ3MD1B6rkST6gL4\
  XE3M71BtQChK9YF7MA4B52Wb0RX0MR0IM0DG09B0450nzAYe6H\
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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=========================================