[Fractint] FOTD 21-02-13 (In the Phantom [8])

22 Feb 2013

      FOTD -- February 21, 2013 (Rating 8)

Fractal visionaries and enthusiasts:

Today's image is a scene in yesterday's 'phantom' parent 
fractal, which was revealed by switching the value of initial Z 
of the Feb. 18 image to the second critical value of the 
generating function, which is -1.  The location is near a larger 
minibrot in a tiny valley on the western shore line of the large 
western bay of today's parent.

Today's parent fractal, which appeared as yesterday's FOTD, is 
quite unusual.  It is filled with minibrots, but the minibrots 
are not the expected quadratic variety as they are in the other 
parent fractal of today's function.  Instead, as is illustrated 
in today's image, they appear to be of an order somewhere around 
2.5.  Actually, today's entire parent is strange, and deserves a 
more careful examination, which I will do in the next few days.

The rating of an 8 is divided half-and-half between mathematical 
interest and fractal artistic value.  The name "In the Phantom" 
describes the location of today's scene -- in a fractal that 
first appeared as a buried 'phantom' fractal in the background 
of the image for February 18.

The calculation time of 6-1/2 minutes is slow.  Checking the web 
sites can cut the wait to seconds.

The finished image is posted at:

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

Variations in hi-def are at:

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

The back images are at:

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

A mix of sun and clouds, complete with a few flakes of snow, 
made today a typical sample of midwinter weather here at Fractal 
Central.  The temperature of 34F +1C was almost exactly average 
for the day.  The fractal cat spent several hours on the shelf 
in the southwest window, trying to enjoy the off-and-on sun, 
while the humans passed the day working.  The next FOTD will be 
posted, that much is certain.  The only question is exactly when 
it will be posted.  Until whenever, take care, and have fun.

Jim Muth
jimmuth@earthlink.net

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

In_the_Phantom     { ; time=0:06:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=cosxx inside=1
  center-mag=-1.759337223588773/+0.04880086507460096\
  /1.244e+010/1/-97.5/0 params=-2/2.3/1/4.6/-0.02/0/\
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  gzEfz6ozAjzDfzHbzhlzfhzed }

frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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