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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Things got a little busy again today here at Fractal Central, which doubles as a graphic design shop when it's not busy being the fractal shoppe. With enough work to keep me hopping like a rabbit, I found little time to search for fractals, but in the brief time I found, I generated the sqrt(Z)+C Mandeloid. The default image of this expression drawn by the MandelbrotBC formula is quite interesting, with a spectacular main stem extending well beyond the default screen, and many promising side filaments. I did my searching along one of these side filaments. The midgets become quite difficult to locate when the exponent of Z is much less than two. In these cases, the filaments are the easiest places to find the midgets. As is the case with midgets in all low-order fractals, the midget in today's image is surrounded by sharp, almost dagger-like discontinuities, though the sharpness is somewhat offset by the mass of convoluted, twisting filaments. When I saw the convolutions, I named the picture "Convoluted Fractal" and gave it the honor of being a FOTD. The 7-minute render time is a bit excessive for an image that rates only a 5. Therefore, my advice is to go to the Usenet group: The fractal weather today was rainy in the morning, followed by a clearing in mid-afternoon. Despite the late sun and temperature of 66F (19C), the grass remained too wet for the fractal cats, who amused themselves indoors by sleeping and eating. My fractal philosophy remains suppressed, but may arise at any moment. Don't miss tomorrow's FOTD. If the philosophy rises between now and then, you'll want to be in on the action. And that's it for this evening fractal fans. Until next time, take care and fractals are just as real as we make them. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Convoluted_Fractal { ; time=0:07:13.72 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-0.84997772846451300/+0.37369015583381380\
/11165.74/1/140 params=1.414213762373/0/0/0 float=y
maxiter=15000 inside=0 logmap=130 periodicity=10
colors=000IEcICc<3>FCcHE_JFYKFUMGRNGPPHPQKMRLJTMHUOD\
WQBYS8YUB<3>YYIYZJY_MY`NY`PY`QZ`TZ`UZ`WZ`Y``_```````\
``abcabdacfacgacjadkbdlccmbao<3>cVrcTrcRsdQudOueNveK\
weJweGxfGyfDy<2>g9zhByiDwhEuiGrjHqjKokLllNjlOimQgoSe\
<2>qYbq``r`ZsbXscWudTveRvgPwhOxjL<2>ynG<4>zaIzZJzXJz\
ULzSLzOLzNMzJLzHLxIKwIKvIIuHI<3>pIHoIGlIGkIGjHE<2>fI\
DeIDdIBcHB`HB_IAZIAYI9WH8VH8UH8TI7QH6NG6KE5ID4<2>A92\
8817817916A06C07E0<3>7J06K05L07O09Q2BR3CT4FR5GT7<2>L\
UAMUBPUDQUESUFTTGVUIWUIZWJ<5>h`RjaTlcUmcVpdXqeYsfZuf\
`whaxhb<11>wpfwqgwrg<2>wthwthvtj<3>vvkvwkwxlwxlwylwz\
n<3>xzoxzoxzpxzpxznxzluziozg<3>VzXPzVIzS<2>MzMOzOQzP\
QzQ<2>UzSWzTXzV<4>bz_dz`dz`<3>jzflzgmzh<2>pzlqzmrzm<\
2>pzq
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
