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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Our asymptotic approach to unity continues today as we investigate 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 resolution. 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: 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 logmap=455
center-mag=-26.71933195088172/+9.587738968748848/2\
.907681e+010/1.0234/-22.5/0 maxiter=2800 inside=255
params=1.025/0/43/3500 float=y periodicity=10
colors=000KbzKczKdzKezKfzKgzKhzKizKjzKkzKlzKmzKnzK\
ozKpzKqzKrzKszKszKrzKqzKpzKozKnzKmzKlzKkzKjzKizKhz\
KgzKkzKizKgzKezKczKazKazKYzHgzCUz2_z8QzEOzKOzPRpPQ\
nOPzNUzMOzLWzKNzJMzILzHLzGKzFVzEJzDIzCHzCCzFHzHMzK\
MzMRzOWzR`zTez_jzgozntzwyzzxzzwzzxzzyzvzzrzzmzzhzz\
czzZzzUzzPzzJzzHzzGzzEzzCzzBzz9zz8zzAvzBrzCmzDhzEc\
zDZzCUzRUTRUTRUSQUSQUSQURQURPURPUQPUQPUQOUPOUPOUPN\
UONUONUOzcOzcNzcNzcNzcMzcMzzMzzLzzLzzLzzKKKKJKKJKK\
JKJJKJIKJIKIIKIHKIHKHHKHHKHGKGGKGGKGFKFGKGGKGGKGHK\
HHKHHKHIKIIKIIKIJKJJKJJKJKKKKKKKKKLKLLXLLYLMYMMZMM\
_MNaNM`MM`MM_MM_MLZLLZLLYLLYLLYLKXKKXKKWKKWKJVKJVJ\
JVJJUJJUJITJITIISIISIHRIHRIHRHHQHHQHGPHGPHGOGGOGGO\
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=========================================
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