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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The rush ended right on schedule, giving me more time to search for fractals this afternoon. My search led me into the fractal created by the formula -199Z^(-1.567)+199Z^(-1.765)+(1/C). This parent fractal consists of a large chaotic ring extending west from a pair of roughly Mandelbrot-shaped center bays, with many small M-sets just inside the ring, and sub-rings attached by stems extending inward from the main ring. Today's midget lies in the WNW quadrant of the large ring, quite deep within one of these attaching stems. It is one of the more ornate midgets I've found recently, a fact that inspired the name "Ornate Fractal Scene". My first impulse was to rate the picture a 7, but when I stepped back a few feet, I decided on a rating of 6, which is still above average. The magnitude is large enough that the parameter file may not render at the proper magnitude at higher resolutions. For this reason, I have hand edited the command mathtolerance=/1 into the parameter file. The parameter file renders in a little over 14 minutes on a dated Pentium running at 200mhz. For fractal convenience, the file of the GIF image will be posted in 16 hours to the Usenet group: The weather today at Fractal Central turned most unpleasant, with light snow in the morning changing to sleet and a cold rain in the afternoon. The temperature of 34F (2C) and inclement weather kept the fractal cats indoors all day. But this time they behaved themselves like gentleman cats. Returning to where I left off two days ago in the FOTD, my religious education in Saint Martin's Catholic Elementary School turned out to be less effective than the nuns had hoped for. Not only did I graduate without planning to become a priest, I was so confused that I gave up on religion entirely, and decided to become an Atheist instead. The new philosophy was refreshing. I no longer had to accept all those unsatisfactory, "it's a mystery", or worse, those insulting, "sit down and shut up", answers to my sincere questions. I now could find answers that made sense. As I thought for myself, unhindered by the need to conform, the answers to questions I had long asked became clear. It became obvious that God hides Himself not so that we must use our faith to find Him, but rather He is unseen because He does not exist. It also became clear that science ignores things such as the soul and heaven because there is no evidence that these things exist either. I became interested in the history of the Catholic Church as told from a secular viewpoint by scholars with no doctrinal agenda to defend. I soon discovered that there was much the nuns had not told their students about the history of the church, and much more that they had told in a distorted way. I was not sorry that I had fallen from the faith. As the months progressed, I found myself starting to feel superior to those still burdened with the need to believe in the grown-up fairy tales known as religion. This may have been presumptuous, but in my mind I had let go of the crying towel. I had found the courage to face reality head-on, bravely accepting my isolation in an indifferent universe and my ultimate mortality. I found consolation in the simple fact of my present existence, which seemed the closest thing to a miracle I could imagine. I wondered why those who find no fear in their non-existence before birth hold such fear of returning to that state after death. I wondered how much better the world could be if all the resources wasted on the folly of religion were to be applied to improving the living conditions of mankind. I also found that Atheists are not evil people, but rather intelligent thinking people. I could understand why they sometimes become angry when annoyed by zealous proselytizing Christians. I wondered how religion, so obviously based on myth, superstition and wishful thinking, could possibly have endured so far into the age of scientific knowledge. I had reached the stage of novice Atheist. The mysteries of the world had begun to make a rudimentary kind of sense. True, the answers were not always pleasant, and there were still unanswered questions, but I realized that there will always be unanswered questions. If I had ended my quest right there, I likely could have become a full-blown Atheist and found acceptable peace of mind for the remainder of my life. But I did not end my quest, and those unanswered questions began growing, until they eventually became so important that they could no longer be ignored. In a near-future FOTD, I'll continue with the tale of why I ultimately rejected Atheism and became what I am. Very likely, if no surprise rush job comes in, the continuation will be tomorrow. When I get on a roll like this it's hard to stop. Well, I guess it's time to wrap things up here at Fractal Central and call it a night. The fractals are all put away, and I hear the gentleman cats getting into trouble downstairs, which is usually a sign they want food. Until next time, take care, and a fractal can cure boredom, but can it cure a fever? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
OrnateFractalScene { ; time=0:14:15.41 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.69758733918538800/+0.25365148700365960\
/4.640715e+010/1/-49.97/-0.03
params=-199/-1.567/199/-1.765/0/300 float=y
maxiter=1800 inside=0 logmap=283 symmetry=none
periodicity=10 mathtolerance=/1
colors=000498498<3>4FE4GG4IG<2>4MK8SMBYNGcPKiQNoSSjU\
WfX`b`dYchTemThqPkpMnmImjLkhDkgSjXRnN_sDuzEdvGmqGgmH\
ghHddJb`J_WKVQKSMMPHMMDNJ8NG4PD4PA4SG4TM8USGWWMXbTZg\
Z`mearkcxsdzykzzezz`zzUzzPvzJrzDoz7jz4iz4gz4fz7dz8dz\
BcyEbvG`sJ`qM_nNYkQWhTWeUVcXT``SXaTZ<3>aSNaSKaRH<2>a\
R8aR5aR4cV4d_4ec5eg5gl5hp7ju7jy7kz8mz8jz4mz8nzHpzQqu\
ZtogvipwcyzYzy_zw_yt_ps`hq`an`TmbMjbDhb5jY4gb4<2>cj5\
ao8`rAZuDXxGWzHUzKTzNUzMSzPPzSMzUJxWGsZDoaAjd7fe4bh<\
2>4Oq4Pp4Pp4Pp4Pn4Rn<2>4Rm4Rm4Tj7VhAWgD_dE`cHbaKdZNf\
XQgWSiUTfQUcMWbHW_DXY8ZV4ZS4ZP44R44J45L7ASBDYEHcHMjM\
QpP4sQTvSzcApb5gb4Xb4Kd4Pb4S_4UY4XV4aT5dR7gPAjMBnJEq\
IGtFJwDKzANz9Pz6Sz3Sz4Tz7UzCWzFWzJXzMZzR`zT`zWaz`czc\
dzgdzjezogzrhzskzuh<2>zyazzZzzW<3>zzNzzKzzHzzGzzDzzA\
zz4zz8<3>zzUzzZzzdzzjzznzzk<6>zzazzczz`zzZ
}
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.
