[Fractint] FOTD 26-07-08 (The Forest Floor [8])

26 Jul 2008

      FOTD -- July 26, 2008 (Rating 8)

Fractal visionaries and enthusiasts:

Our asymptotic approach to unity continues today as we investi-
gate the fractal that results when the formula Z^(1.025)+C is 
calculated 43 levels up the complex logarithmic hyperspiral with 
no function applied.  Actually, I am not certain which, if any, 
function is the 'correct' one to use with the MandelbrotBC3 
formula, or even if there actually is a correct way to deal with 
the infinity of 'correct' solutions to the multi-valued complex-
logarithm.

Today's parent fractal is an oversized parabolic-shaped thing 
with the focus of the parabola on the east-southeast side.  This 
parent requires a bailout radius of 3600 to give it room to 
spread to its full extent.  An area of chaos appears at its 
northwest extremity, with today's scene located in this chaos.

There is a minibrot at the center of the image, but don't waste 
time trying to reach it.  It lies far beyond the limit of resolu-
tion.  At the magnitude of the actual image, the picture reminds 
me of a scene in a forest, looking upward from the forest floor 
toward a mighty fir tree.  I named the image "The Forest Floor".

If I had more time, I might have made the fir tree likeness more 
convincing.  As it is, even with its flaws, the image rates an 
8, which is pretty good as fractals go.

The calculation time of just under 6 minutes can be eliminated 
by viewing the already-calculated image on the FOTD web site at:

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

Tomorrow's FOTD will be posted in 24 hours.  Just for the fun of 
it, I'll reduce the exponent to 1.00625 to see if I can find 
anything.  But with an expression whose graph is virtually a 
straight line, I can guarantee no success.  Regardless, until 
then, take care, and stay on the straight and narrow fractal 
path.

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

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

The_Forest_Floor   { ; time=0:05:55.52-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=ident float=y
  center-mag=-26.71933195088172/+9.587738968748848/\
  2.907681e+010/1.0234/-22.5/0 params=1.025/0/43/3500
  maxiter=2800 inside=255 logmap=455 periodicity=10
  colors=000KbzKczKdzKezKfzKgzKhzKizKjzKkzKlzKmzKnzK\
  ozKpzKqzKrzKszKszKrzKqzKpzKozKnzKmzKlzKkzKjzKizKhz\
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  MzMRzOWzR`zTez_jzgozntzwyzzxzzwzzxzzyzvzzrzzmzzhzz\
  czzZzzUzzPzzJzzHzzGzzEzzCzzBzz9zz8zzAvzBrzCmzDhzEc\
  zDZzCUzRUTRUTRUSQUSQUSQURQURPURPUQPUQPUQOUPOUPOUPN\
  UONUONUOzcOzcNzcNzcNzcMzcMzzMzzLzzLzzLzzKKKKJKKJKK\
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  GFNGFNFFMFFMFELFELFEKEEKEEKEDJEDJEDIDDIDCHDCHDCHDC\
  GCCGCBFCBFCBECBEBADBADBADBACBACA9BA9BA9AA9A99A9899\
  89988988877877876876876765765764764753653653652652\
  6415415405405405516516527 }

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