[Fractint] FOTD 04-08-06 (Well-Rooted Fractal [6])

3 Aug 2006

      FOTD -- August 04, 2006 (Rating 6)

Fractal visionaries and enthusiasts:

Today's 6-rated image is a scene in a remote valley of the 
Z^sqrt(2)+C as it appears 38 levels up the logarithmic ladder. 
I named the image "Well-Rooted Fractal" for no good reason.

The Z^sqrt(2) fractal is interesting because its midgets are 
unusually easy to find.  They first appear much like the midgets 
of the Mandelbrot set, hiding between two symmetrically placed 
elements.  Unfortunately, the patterns around the midgets in the 
square-root-of-two fractals have a tendency to all look the 
same.  The pattern around the barely-visible midget at the 
center of today's image lacks some of this 'sameness', but it is 
still similar to many other images.

The render time of 8 minutes is just the slightest bit on the 
slow side.  This slight bit of slowness may be avoided however 
by downloading the already-rendered image from the FOTD web site 
at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Another very hot day here at Fractal Central kept all thoughts 
of going outside from the heads of the fractal cats.  They spent 
the day watching birds and squirrels.  For me the day was about 
average.  If all remains average, the next FOTD will appear in 
24 hours.  Until then, take care, and I hear that fractal soup 
is delicious.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Well-RootedFractal { ; time=0:08:00.55--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=-0.6174173528\
  2187680/-0.20187002932680840/1.964483e+009/1/2.5/\
  3.90137333446116674e-007 params=1.414213562373/0/\
  38/0 float=y maxiter=5000 inside=0 periodicity=10
  colors=000fZmyN9wU7u`5tf3rm1qs0kf4fU8aHCX4GV88UC1W\
  M3YW4_e5`n6TaAMQEFDI81MIGJSVGaiDjwAlvGnuMpuSqtYstc\
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  GURIUTKUUMWUOTUQQUSNUUKXTI_THbTFeTEhTCkTBwT9zT8oax\
  g`p`_hUZ`NYTGXL9WD2W65jwGZnROf`DZeV`jlahh_feZdbXc_\
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  Ztcdr`jpXpnTulQvgNvcKw_HwVExRBxN8xJ5efraboYZmVWkRS\
  iOPgRNhULhWJhZHhaFhZMWbTd }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*floor(p/(2*PI))
  r=real(p2)-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=========================================