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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Sensible people see a fractal, say ho-hum, and forget about the thing. Others, not quite as sensible, discover fractals and are surprised at their variety, then experiment with them for maybe a month or two, and eventually grow bored and move on to more sensible and productive endeavors. Those like myself, who have gone beyond the need to act with common sense, become obsessed with the endless intricacies and spend years, perhaps a lifetime, exploring the limitless varieties of the things numbers do. And like those fractal fans, some fractals make no sense at all. (Maybe all fractals make no sense, but that's another story.) Today's image is an example of a senseless, illogical and thoroughly irrational fractal. For some reason known only to who or whatever is in charge of the things numbers do, the midget in today's image lies exactly on the shoreline of its parent, with its east (bottom) half surrounded by the expected outside material, but its west (top) half existing invisibly in the potential inside material that forms the upper half of the image. Since invisible things are hard to see, I made the invisible visible by coloring the inside with the <fmod> option, with the proximity set to 0.085. The result is one of the more unusual midgets in the FOTD series. The real(p3) parameter is the one that works the mischief. It is critical, and must be set just right to get the half-and-half effect. I named the image "Mandelbrot Network" because of the delicate network-like elements in the top half of the image. Because of the unusual nature of the image, I raised the rating one point from a 6 to a 7. I suppose it's worth the rating. The render time of 2 to 3 minutes is quite reasonable for an image with so much inside area colored with the <fmod> option. And as always, those who would rather not render may find the finished image posted to Paul's web site at: For the benefit of those who concern themselves with the weather in far corners of the earth, the fractal weather Wednesday here at Fractal Central, which is located not far from 39,21N 76,32W, was hotter than a firecracker, with blazing sun and a temperature of 104F 40C. In response, the fractal cats spent the day under the air conditioning vent, stretched to near twice their normal length. Today promises to be just as hot if not hotter, but it's the Independence Day holiday here in the USA, the day when fireworks displays are everywhere, (except where they have been banned because of fear of terrorism), and it's supposed to be hot on the Fourth of July, as the day is usually called. I might wander over to the local fireworks display this evening; or I might not. I haven't decided. In either case, I'll have another glorious FOTD in two days on July 6. Until then, take care, and I'll bet there's snow falling in the New Zealand Alps. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Mandelbrot_Network { ; time=0:02:50.60-SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.523994586278288/0/121.9547/1/90/-1.2\
3373533611470521e-014 params=1/0.35/-1/0.3/32.175/0
float=y maxiter=500 inside=fmod proximity=0.085
logmap=yes periodicity=10
colors=0008PdAPcCPaEOaGO_INZKNXMMWOMURLSTKRVJPXIOZ\
HM`GKbGJdFHfEGiEEkDDmCBoC9qB8sA6uA5v93x81y92y93x93\
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BXIBXHBXHBXHAWHAWHAWGAWGAWGAWGAWGBVHCVIBUJAUKAUKAU\
KAUKAUKAUKAUKAUKAUKAUKAUK }
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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