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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: *Because today's FOTD is a special one, I have not given it a rating. If I were to rate it as a picture, it would rate a 3, but as I said, it is a special FOTD, one not subject to the normal quality standards. When discussing my FOTD's, I often refer to the parent fractal, a mysterious thing that exists unseen in the background, yet is the ground of being for the image on the screen. Well, today is the day we reveal that mysterious parent fractal that has lain behind so many recent FOTD images. The formula of this fractal is -1Z^(-11)-11Z^(-1.1)+(1/C). The fractal itself, a sprawling thing with its fan and its rings, is perhaps the most varied I have yet stumbled upon. On the near left side, a Mandel-shaped feature stands as the center of action, with the curious and bizarre fan-shaped feature just to its right. Rings decorate the ends of the many filaments, and the many holes are beyond description. Midgets lie everywhere in this fractal. In some areas, such as around the Mandel-shaped feature, they are easy to find; in other areas, such as the center of the fan and in the rings, they are quite difficult to locate; but in all areas the midgets do exist, hidden and waiting to be discovered. I show this fractal today because I will be searching through it for a few weeks, finding midgets and speaking of their parent fractal. When I refer to the parent fractal, today's FOTD is the fractal I am referring to. The parameter file is very fast, running in under one minute. But the download is equally fast. That download may be found at: The fractal weather was sunny all morning, but it turned cloudy in the afternoon, and rain is threatening tonight. The fractal cats, Thomas and Tippy, found the conditions ideal, spending the better part of the day lounging in the partial shade of the porch. The fractal philosophy stumbled along today, generally going nowhere. I have nothing to post at this time, though my philofractal mailbox holds a letter from JW, which I haven't read yet. When I do read it, it might give me the inspiration for a few words. For now, the day has ended, the FOTD has ended, and I'm shutting down Fractal Central for another day. Until tomorrow, take care, and see you then. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Parent_Fractal { ; time=0:00:57.18 -- SF5 on a P200
; Version 2000 Patchlevel 13
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip
center-mag=2.64923/1.99394/0.1527087/1/79.999
params=-1/-11/-11/-1.1/0/800 float=y maxiter=600
inside=0 logmap=yes periodicity=10
colors=000QW_<3>IXc<3>UTbXSb_RbaRb<3>eRleRnfRpgRshRu\
hRw<7>``X_aTZbQ<3>WfD<5>eoZgqbhrf<3>nxt<8>adS`bPZ_M<\
2>VUDUSARTC<3>EXLBYO8ZQ5_S2`U<3>1lW0nW0qW<2>0yX<3>RU\
JXNGZQH<4>edKggLhjM<3>nvO<3>ktRjtSitShsThsUiwahyZgzX\
<3>DOp6Ft6UV6c5KcHYUTkMdyTp<3>zVszWtzWtzXuzXu<3>V`PO\
aHQbL<3>YfZ_gaahecihejk<2>6mF<3>MqYQraUsfYtjMuT<3>Qy\
LRzKSzI<3>WzBXz9Yz7Zz5_z4<3>OzFLzHIzK<2>9zR<3>HzCJz9\
EzK<2>1zp<3>HzgLzePzcTza<8>WzjWzkWzl<3>Xzp<4>PzjNziM\
zh<3>Gzd<2>JznKzqJzn<5>IzYIzVIzS<3>IzH<3>dzfizlozrtz\
x<3>YzXSzRNzK<2>6z0<4>vzy
}
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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