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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In the East Valley area of the Mandelbrot set there lives a herd of elephants. Each elephant stands astride its personal bud, guarding that bud from anything that might threaten it. In the cubic M-set two elephants guard each double bud. In the quartic set, there are three elephants per triple bud. And so it continues into infinity, the elephants eventually merging into a haze of undifferentiated elephant stuff. But what of the Z^(1.5)+C Mandeloid? In this set, the same trend continues. Half an elephant stands guarding each half-bud. I have no idea what happens to the elephants' rear ends, but the front parts are there, complete with curled trunks. It took the MandelbrotBC1 formula to show a level of the parent fractal where these half-elephants are not broken beyond recognition. Luckily, that level was found only 1.5 turns up the logarithmic hyper-spiral. I named the image "Half an Elephant", most likely because half an elephant is better than none. Of course, a half-elephant is not as good as a whole elephant, but that's another story. When the time to do the rating arrived, I pondered the image and decided on a rating of 6, which combined with the render time of 10.67 minutes gives an overall value of 56. The GIF image is available for near-instant download on Paul's web site at: The weather Saturday here at Fractal Central was very cold. All day, my digital thermometer hung around 10F -12C, which kept the cat duo confined very securely to the sources of heat. They needed only one minute on the porch to convince them that the outdoors was uninhabitable. In the evening, I presented them with a treat of tuna, which lifted their sullen spirits. Today, the regular work is pretty much caught up, but the fractal lady is thinking of a trip to look at 'antiques', (IMO, discarded junk), so I guess I'll tag along. But I'll be back in plenty of time to find the next FOTD fractal. Until that next fractal appears, take care, and look for the other half. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Half_an_Elephant { ; time=0:10:40.43--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor
center-mag=+0.15911535849239720/-0.002404932214412\
98/1541.738/1/22.5/4.45664338766249557e-013
params=1.5/0/1.5/0 float=y maxiter=15000
inside=255 logmap=39 periodicity=10
colors=000R9YS9YS9ZT9ZU9_V9_V9`W9`X9aY9aY9bZ9b_9c`\
9c`9da9db9ec9ec9fd9fe9gf9gg7gg8gf9geAgdBgcBgcCgbDg\
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PENPEMOELOELNEKNEKMEJMEILFILFHKFHKFGJFFJFFIFEIFEIF\
EIFEImSNoQPqNRpOQoPPnQPmROlSOkSNjTNiUMhVLgWLfWKeXK\
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`qtbrtcssetsfurhvriwpfxocymazlZzkWziUzhRzgOzeMzgJz\
iIzkHzmHzoGzqGzsGzuFzwFzxFzyEzzEzzDzzDzzDzzCzzCzzC\
zzBzzBzzAzzLzzMzzNzzOzzOzzPzzQzzQzzRzzSzzTzzTzzUzz\
VzzUzzVzzVzzWzzWzzXzzXPPm }
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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