[Fractint] FOTD 27-07-08 (The Limbo Factor [6])

26 Jul 2008

      FOTD -- July 27, 2008 (Rating 6)

Fractal visionaries and enthusiasts:

In today's image I tried to go down to an exponential level only 
half as far from unity as yesterday's exponent of 1.0125.  But I 
could find nothing of interest in the fractals with an exponent 
of 1.00625, so I tried an exponent of 1.009375, which is 3/4 as 
far from unity as yesterday's 'forest floor' image.

The searching down there was difficult, minibrots were nowhere 
to be found, but I finally found an interesting patch of chaos 
in the Z^(1.009375)+C Mandeloid fractal right at ground level of 
the complex hyper-ladder.  Today's image shows a small sample of 
that interesting chaos.

To me, the most amazing thing with the image is that the graph 
of its generating expression is virtually a straight line.  But 
even such a tiny departure from straightness can do unexpectedly 
intricate things when iterated a sufficient number of times.

In today's image we have areas of near total chaos, areas that 
are totally featureless, as well as areas of fractal patterns 
that repeat at ever smaller scales.  There are also several dis-
tinct fractal themes in the image.  Despite the ridiculous expo-
nent, today's fractal image is as fractal as any fractal could 
be.

I named today's image "The Limbo Factor".  After all, the point 
of the Limbo is to go as low as possible.  Then I rated it at a 
6.  My inability to find a minibrot in the parent fractal cost 
the image at least one whole rating point.

The calculation time of under 4 minutes on a computer running at 
2000mhz is reasonably brief.  And the trip to the FOTD web site 
at:

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

to view the finished image there can be equally brief, if not 
briefer.

The next FOTD will be posted in 24 hours.  Until then, take 
care, and view the world through fractal-colored glasses.

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

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

The_Limbo_Factor   { ; time=0:04:54.34-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-10.29306825/+0.0410706/163.76/1/142.5/0
  params=1.009375/0/0/3500 float=y maxiter=16000
  inside=0 logmap=456 periodicity=10
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  i0Hi1Hg1Ff2Ff2Fd4Dd4Db6Ba }

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=========================================