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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is another of those mysterious 'evaporated' fractals that is not there. It is not there that is if one thinks of a fractal as the border between trapped points and points that escape. All the points in today's image are trapped; the image consists of inside only. But the trapped points do different things in their confinement, and it is these differences that make today's image. The iterated formula mixes a portion of Z^(-6) with a somewhat smaller portion of Z^(-16) before adding (1/C). The midget at the center is the ghost of an actual midget, which can be returned to life by setting imag(p3) to zero. When this is done, the image reverts to a normal inside vs. outside fractal, which closely resembles the FOTD image, but without the fingers that inspired the name "Phantom Fingers". What rating to give the image was a puzzle. The first time I saw it, I admired the way it made a lot from nothing, and decided on a rating of 6. Then I stepped back and noticed the large drab flat areas, and thought it was worth only a 4. Unable to decide, I settled on a perfectly average 5, though a 4-1/2 might be more accurate. The parameter file is one of the all-time fastest, finishing in 30 seconds. It will take several times as long to download the GIF image from: The fractal weather (is there any other kind?) was perfect today. And perfect weather means contented cats. The cats showed their contentment by sleeping most of the afternoon, enjoying the sunshine and temperature of 66F 19C. Einstein once said that if quantum theory is correct, the world is crazy. Well, Einstein was right -- quantum theory *is* correct and the world is therefore crazy. This is weird enough, but we now know that the craziness is not limited to the atomic scale. It extends even to the objective world of everyday experience. At the atomic level, among other impossible things, a single object can be in many places at the same time. The only thing I can think of that is crazier than this is the ability of the human mind to see into the future, when common sense and everyday experience tell us that the future does not yet exist. The ability to see the future does exist, of this I am certain. But how could such a thing possibly operate, and what of the paradoxes it creates? To tackle these questions, I must start at the beginning. Before starting however, I must state that the things I shall say will be my personal opinion based upon personal experience with a good bit of speculation mixed in. I do not pretend that I will be doing science, therefore I will have no need to supply scientific proof. Likewise, no one who has not experienced precognition will be expected to accept its existence. My speculative ponderings will begin with tomorrow's Philofractal version of the FOTD. And when I speculate, my imagination knows no bounds. So check back tomorrow to see the story begin. You wouldn't want to miss the excitement. It's now time to get busy, give fractal Thomas some more food, and get some work done. Until tomorrow, take care, and I was ready to pray for peace, but I could not remember a single instance where praying for peace actually brought peace without the addition of military action. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Phantom_Fingers { ; time=0:00:30.59--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip
center-mag=-132.551/34.4115/12.30779/1/177.499
params=16/-6/6/-16/-0.89/1e+100 float=y maxiter=600
inside=bof61 symmetry=none periodicity=10
colors=000KPQFHPqzsVPn000PLgNJdKHa000FDVCBSEP3000C\
UBcUEBEILAXYDbi7glDfnIfqNfsTfvYfxbfyiZzpRzwJXvZ4vm\
5jj5Zg5Od5Ca51ZDQUJIVPAXV2YNB`GKb9TdJSbSS``RZiRXrR\
WiWba`hTenLjtDnzFhpGbfHXXIRNJLDKPHLTLMWPN_TOcXPf`e\
kFbiE_gEXeDVdDSbCP`CMZBKYBKZIK_OK`UKa_KbeUj`bqWkxS\
hrOemLbhI_cFXYCUT9RO6OJ3GGU8EsELfJSUOYHRRJUKLXEN`D\
XdCfgCocFh_HaWKVSMOOOHPNLQNPRNTSMXTM`UMdVMg`T`e_Uj\
fNolGifEcaCZXATS8ON6SKIWHU_EddGabK`aO_`SZ_WZZ_YYcX\
XgWWkWQncKpjEsr9uyLvmWvbgwSrwHquLptOosRnrUmqXlp_ko\
bjnedhcZbaTX_NRYHLWCGU3c15W77OD9GJtM`nKZhIYbHWXFVR\
DTLCSFAQ_S7WPASMDOJFLHIHEKDBNCQ5BKCAEJNZ1QZ8FOtELm\
DIgCF`BCVypBgaGRNLo8Gd9JV9LK9NREmODiMCeJBbHBZEAWC9\
SL5sF7cMd7K_AIVDGRFFMIDIKBDNlb0fY4`U8WQBQLFLHIFDMQ\
q_NjYLdWJYVGSTELSCFQtiVblcYe`TZZOTWJMUEFR`KFbWlYSh\
TOdOK`JGXECTAzaAqZAhXA_VARTAIR65U76T76S87S87R98Q98\
QA9PvY3lT8bOCTJHJELVdRPXQ
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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