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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal image most certainly is a picture of a Minibrot. When I first saw it, I was tempted to state that the image is not a Minibrot because it is only a picture of a Minibrot, but then I realized that pictures of Minibrots are the real thing. A picture of a Minibrot, and indeed of any fractal, is the object itself. Today's picture is a picture that was produced without an object being photographed. It is as close to an actual Minibrot as one can possibly come. This, along with the fact that two days ago I posted an image that was not a picture of a minibrot, is why I named today's picture "This is a Minibrot". The formula that created the image is Z^(-0.6)+(Z^(-6)+(1/C), another unexpectedly simple expression, which in this case has produced a striking picture of a midget at the center of a fractal spiral. The parent fractal is a strangely twisted Mandel-shape, somewhat too large to fit on the default screen. An outzoom reveals the entire figure, which has a prominent bud at its east edge. From this bud a prominent tail shoots out, but this tail is not the normal infinitely deep filament, it is rather a broad area of fascinating intricacies, with an obvious 'S'-shaped curve at its center. I found today's midget deep down in this curve. The midget is better viewed than described. That veiwing may be accomplished by running the parameter file and waiting 8-1/2 minutes, or by going to the Usenet group: The fractal weather today was exciting to say the least, as the most violent thunder-storm of the year pelted the Fractal Central area with 2-inch (5cm) hailstones, torrential rain, spectacular lightning, and high winds. The wind and hail stripped so many leaves from the trees that the fractal lawn will need a raking. The fractal cats took shelter in the basement until the water started coming in. Then they dashed to the bedroom closet to weather the rest of the storm. They are just now venturing into the open. Surprisingly, there was no power failure, so the FOTD will go out on schedule. The fractosophy is still on a simmer, but the pressure to pontificate is building and the lid may blow at any time, releasing the wisdom of the ages for all the world to see. But that time has not yet quite arrived, so check here tomorrow at about this same time for possible enlightenment and certain amusement. Until then, take care, and be patient, for the best is yet to come. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
This_is_a_Minibrot { ; time=0:08:29.93 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.872362067538974/+1.227930592848623/2.7\
04756e+007/1/137.499 params=1/-0.6/1/-6/0/0 float=y
maxiter=1400 inside=0 logmap=137 periodicity=10
colors=000Kmk<15>EGGEEEECC<3>D45<3>CEKCGSCIWCL`CNcCP\
hCSmCUtCWw2SzCYwMbtWgselroqqyxp<16>yU_yTZyRYyPXyNWzL\
U<3>vPXvQYuRZtSZpT_mU`iV`cVWYSU<2>VKOUHRTFTVER`DVfCU\
lBXrA`s9du8g<3>y4bz3ax7_<6>oTQmWOl_N<2>hhIgkHhlF<3>l\
mBmnAnn9on8<12>NZWLYYIW_<3>BTg<10>7Se7Se6Sd<3>5Sd4Re\
5Sd<7>6ZZ6_Y6_X<2>6bV6cU4eW<6>FXOGWNIVM<3>OQH<3>UYDV\
_CXaBYcA_d9fe1<2>PkLFmT<3>TrN<3>UuHUvGUwF<2>UyBUsF<3\
>UwUUxYWya<8>mzWozWqzVszUuzUwzTxzTyzT<3>zzVzzVzzU<8>\
zzQzzQzzQ<2>zzOzzOzzM<2>zze
}
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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