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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's modest effort rates only a humble 2 on my scale of worth. I had originally rated it a 5, but then I realized that a better image lies closer in toward the midget. This realization caused me to consider today's image flawed, and as a result I dropped its rating to 2 and named it "A Flawed Fractal". But it is flawed only in comparison to what it might have been, and in fact might turn out to be in a soon-to-appear FOTD. The formula is once again a combination of various portions of Z^(-1.1) and Z^(-11) plus 1/C. Minor variations of this formula produce images of the most interesting kind, with midgets of an even more interesting nature lurking within. The parameter file takes an exasperatingly long time to render even on a Pentium machine. But relief is as near as the internet, where the GIF file has been posted to Usenet at: The fractal weather today was perfect -- the first day in several weeks that I heard no thunder and saw no rain. The deep blue sky, puffy clouds, dry atmosphere, and temperature of 83F (28C) brought out both the neighborhood lawn mowers and the fractal cats. The great conditions also brought out the philosophy in me. Having just completed the program magazine for the 2000 Kung-Fu Competition, I pondered the nature of the martial-art discipline known as Kung-Fu. After working closely with the organizers for several weeks, I have come to realize that the art of Kung-Fu involves as much spiritual discipline as physical prowess. In fact, when studying the art, one learns how to direct and focus a spiritual energy known as Qi, or sometimes Chi. The more skeptical among us tell that such energy does not exist, that those who claim to be using Qi energy are actually skillfully using well-known natural laws of physics. When I mentioned this to one of the Kung-Fu masters, he merely laughed. "Who knows more about Qi energy?" he replied. "Those who have worked with it all their lives or those who do not yet know that it exists?" Then he gave me a brief demonstration of the energy in action. The tingly heat I felt could have been the power of suggestion, or a natural physiological effect, or it could have been Qi energy. Since the Kung-Fu master knew more about the topic than I, and he claimed that the heat was caused by an actual spiritual energy, I must take the word of the expert. I find it a bit incredible that Kung-Fu students would devote so much effort to working with something that does not exist, and after hundreds of years have still not discovered that it does not exist. As for me, I'm undecided whether it exists, but I have no doubt that 'Qi' is a good scrabble word. And of course, I'll be here again in 24 hours with another fractal, this next one guaranteed to rate higher than today's. And I'll also have some more words of wisdom. Until then, take care, and fractals are forever. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Flawed_Fractal { ; time=0:25:31.92 -- SF5 0n a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.01733612521571942/+1.594853495298927/1.\
182371e+010/1/125.003 params=-11/-1.1/-1/-11/-1.975/0
float=y maxiter=6000 inside=0 logmap=149 periodicity=9
colors=000R62T62<3>gQQjVWn_a<2>xns<3>kskhtjeuh<2>Xxb\
UyaTwc<8>TnoTmqTlr<2>TivThwUet<4>UWjVUgVSe<3>VKY<3>c\
YMe`JhcG<3>pp5<7>md_mccmag<3>lXv<3>jpmjtkkrl<7>lfple\
qmcq<2>m_smZsk_r<3>ebqdcqbdqaeq`eq<6>XMrXJrWGr<3>V5r\
k2c<8>eHOeJMdLK<3>bRE<3>HZZB`c6bh<3>FlkHokJqlLsl<3>R\
PXTITUAPV3M<9>eaTfeUghV<2>jsXkvXjuY<5>dt_ct`bs`<3>_s\
a<2>huZkuYlna<3>nRqnLtoLt<3>qMtqNtrNtrNt<3>oQqVjXnRp\
<17>_eaZf`Zf`<3>VjXyNB<3>`fTHxq<13>RncRnbSma<3>VjYGb\
N
}
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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times.
