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Fractal of the Day
by Jim Muth
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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 distinct fractal themes in the image. Despite the ridiculous exponent, 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: 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 logmap=456
center-mag=-10.29306825/+0.0410706/163.76/1/142.5/0
params=1.009375/0/0/3500 passes=1 float=y inside=0
maxiter=16000 periodicity=10
colors=000KBULBUM9UN9UO8UP8UQ8TR6SS6TT4RU4RU4RU2PU\
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0fi0fi0fi1fj1fj1dj1dj2dl2dl0Kl0Km0Mo0Km0Kl0Il0Ij0I\
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=========================================
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times.
