[Fractint] FOTD 31-10-11 (The peak [8])

31 Oct 2011

      FOTD -- October 31, 2011 (Rating 8)

Fractal visionaries and enthusiasts:

Today's image is an anti-bifurcation scene in the parent fractal 
that results when quadratic and order-11 Mandeloids are combined 
in the FinDivBrot-2 formula.  On the surface this parent is an 
everyday Mandelbrot set with everyday quadratic features, but in 
its depths it acquires Z^11 characteristics, with 10-lobed 
minibrots and all the other order-11 stuff.

The scene is located just off the main spike of the parent 
M-set, a short distance beyond the large minibrot, in a small 
quadratic minibrot that has morphed about 4/5 of the way to an 
order-11 shape.

The name "The Peak" tells that the central point contains not a 
hidden minibrot, but comes to a flat peak of low iteration.  
Instead of period doubling as the peak is approached, the 
fractal pattern experiences period halving, which is why the 
scene is one of anti-bifurcation.

The rating of an 8 includes 2 full points for the coloring, 
which is most of what the image has going for it.  When rendered 
with a different palette, the entire effect of the image falls 
apart.

The calculation time of 45 seconds on a 2000mhz machine is a 
good guesstimate.

The finished image may be viewed on the FOTD web site at:

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

The image is available in high definition at:

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

The original FOTD web site may be accessed at:

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

A mix of sun and clouds brought an average autumn day to Fractal 
Central Today.  The temperature of 46F +8C was slightly chilly, 
but not enough to keep the fractal cats from their watch post on 
the shelf by the southwest window.  Except for some bickering 
about unimportant things, the humans had an uneventful day.  The 
next FOTD will be posted in 24 hours.  Until then, take care, 
and rational skeptics know that ghosts exist only in the mind; 
those who have experienced ghosts know that they are real.  One 
of these certainties must be false, therefore, merely knowing 
that a fact is true does not make it actually true.

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

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

The_Peak           { ; time=0:00:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip float=y
  center-mag=-1.796068372208084/+0.00000000000489225\
  /4.953129e+012/1.0003 params=11/1e+050/0/0 inside=0
  maxiter=1500 periodicity=6 mathtolerance=0.05/1
  colors=000n5Gk4Fh4Ee4Dc3C`3BY3AW3AT29Q28O27L26I15G\
  15D14A13802501200nocklaij_ghZefXcdVabU__SYYQVWPTUN\
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  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyzzxzzwzzvzzuzz\
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  24512301100000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  000000000000000000000000000000IL0FJ0DG0BD09A068045\
  0220VH0TG0SF0RE0PE0OD0NC0LC0KB0JA0I90G90F80E70C70B\
  60A5094074063052032021010 }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

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