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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a scene in the Z^(2.003)+C Mandeloid. This is the same fractal that holds the curious Julia rectangle that I sometimes use as an interesting FOTD object. But that rectangle exists at the ground level of the formula, which can be seen by setting the real(p1) parameter of today's MandelbrotBC1 formula to 2.003, and the real(p2) parameter to 3.14159... The actual parent fractal of today's image lies 1040 levels up the logarithmic hyper-spiral. Such an extreme height is necessary because the exponent of Z is so close to an integer value. This closeness causes the parent fractal to rotate and change very slowly as the value of real(p2) is raised. At a height of 1040, the parent fractal is rotated 180 degrees, a position that has the main stem, which has split into infinite flinders, facing east, and the East Valley, which has become smeared out, facing west. Interesting things happen at both locations. Today, we examine the things that happen on the east-facing main stem. I have chosen to explore the area immediately behind the large midget. In this area, we find what looks like a grid of railroad tracks, with midgets located where the switches would lie. Today's scene is located in the basin of attraction of a larger midget, which in turn is located in the basin of the largest midget on the main stem. And BTW, this large midget has been transformed into something that must be seen to be believed. To liven the image I have rendered it with the outside set to 'fmod' and the proximity set to the default 0.01. When editing the parameter file, I entered the proximity value by hand, though I doubt that this was necessary. While searching for a name, I was thinking of the mysteries of existence, which probably inspired the name "The Wheel of Life". The name is justified by the filimentary circular features surrounding the central midget. The rating of 7 combined with the render time of just under 4 minutes gives an overall value of 183. A good way to increase this value is to download the completed GIF image from Paul's web site at: Saturday was cloudy and chilly here at Fractal Central, with a high temperature of only freezing. The snow held off until nightfall, giving the duo of cats ample time to wander the yard in search of adventure. They found none, and peacefully retired to their beds at the end of the day. Today is starting most unpleasant, with an inch of slush on the ground and a cold rain falling. It's a good thing I have tuna in stock. My precognition now tells me that in 24 hours I will return with the next FOTD. So until then, take care, and either see the light or remain in the dark. The challenge is how to recognize the actual light. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Wheel_of_Life { ; time=0:03:15.46--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+1.74225596554302200/-0.004751357224868\
70/3.656832e+007/1/-25/7.36727087773808575e-006
params=2.003/0/1040/0 float=y maxiter=1500 inside=0
outside=fmod proximity=0.01 periodicity=10
colors=000RgaMjdGmfAph5rjBniHkiNghTdhZ`gdYgca`beVb\
iOamIapCSSqUUnWVkYXi_Yfa_dc`adb_fcXheVjfSlhQniNojL\
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ZxJ_yH_yFbxLdxQgxViw_lwdnwiounjrhdmbZhXTcRNZLHUFBP\
9AU88Z77d7sURmXTg_VbbYXd_ }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-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 20.0 PAR-FORMULA FILE==================================
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times.
