[Fractint] FOTD 13-12-08 (Two Into Fifteen [6])

12 Dec 2008

      FOTD -- December 13, 2008 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image shows what happens when a fractal with a positive 
exponent of Z (in this case 2) starts to change into a fractal 
with a negative exponent of Z (in this case minus 15).  As the 
real(p2) parameter of 0.0000001 shows, a very small departure 
from zero makes a great change in the appearance of the result-
ing fractal.  Curiously, the image is also quite sensitive to 
the bailout radius.

The original Mandelbrot set is still present at the center of 
the image, but the 16 points of the minus 15 Mandeloid are 
already fully formed, symmetrically surrounding the Z^2 figure.

I named the image "Two Into Fifteen" because it shows a Mandel-
brot set already well on the way to being a Z^(-15) Mandeloid.  
There are almost certainly many interesting minibrots deep in 
today's image, which is actually its own parent fractal.  I 
might search out a few of them in upcoming FOTD's.

As for a rating, I decided on a 6.  I really put too little 
effort into the coloring to rate the image higher.

Even with the passes set to 1, the image is extremely fast, 
finishing in a mere 15 seconds.

The already finished image is posted to the FOTD web site at:

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

Friday dawned with wet snow falling here at Fractal Central, but 
with the temperature around 34F +1C, it melted almost as fast as 
it fell.  A little sun peeked through the breaking clouds in the 
afternoon, too little too late to make the fractal cats happy.

My day was rather busy, though not as hectic as it would have 
been if problems had come up.  The next FOTD is due to be posted 
in 24 hours.  A lot of graphics work remains to be finished 
however, so there is no guarantee that the FOTD will appear as 
scheduled.  Until next time, take care, and shun disappointment.

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

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

Two_Into_Fifteen   { ; time=0:00:15.42-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=DivideBrot6 passes=1
  center-mag=-0.03296/0/0.295 params=-15/19/1e-007/17
  float=y maxiter=1000 inside=0 logmap=yes
  symmetry=xaxis periodicity=10
  colors=000FoctThhKzmx0hzzHcdHUYHKSJMPKONLQLNSIOUGP\
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  _mz_mz_mz_izTfzNczHczGbz7 }

frm:DivideBrot6   { ; Jim Muth
z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2,
d=real(p2)+0.00000000000000000001, f=imag(p2)+16:
z=z^(a)/(z^(-b)+d)+c
|z| < f }

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