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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yes, I realize that I'm late with today's FOTD, but it's still before 8am of February 3rd here at Fractal Central, so I'm still technically on time. Sometimes when exploring in the infinite world of fractals, I come upon a scene truly unexpected. Today's image is one of those scenes. The formula that drew the image is Z^1.5+C -- about as simple an expression as one could find. True, I used the MandelbrotBC formula, which draws the more remote parts of the infinite complex-log spiral, but the entire spiral is all basically the same image. The unexpected feature is the decoration surrounding the order-1.5 midget. The circular features scattered through the image are unlike anything I have seen, and far from the fragmented chaos that would be expected in a fractal with an exponent of Z equal to 1.5. When I saw the horde of circular depressions, I immediately realized how unexpected such objects are in such fractals, and named the picture "Unexpected Fractal". The rating is a marginal 7. The midget in the image lies near the shore of a larger midget, which in turn lies near a secondary bud of the parent fractal. The image takes over 50 minutes to render from the parameter file. Luckily for those with limited time, the completed GIF image file will soon be posted to: The fractal weather today was partly sunny and quite pleasant, with a temperature of 49F (9.5C) that let the fractal cats have a good romp in the yard. At 4pm a squall of rain and snow moved in, dropping the temperature to near freezing, but by that time the cats had completed their day's adventure. It's now time to reconfigure the fractal shoppe, and turn it into a more conventional work shop. Until 18 hours from now, when I'll return with another fractal and quite likely some philosophy, take care, and don't feel concern when the FOTD is a bit late. It's just that those extra good images sometimes take a little longer to find and render. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Unexpected_Fractal { ; time=0:50:50.72 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotBC passes=1 center-mag=+0.6463\
5330784977680/-0.85505467314147980/923397/1/-19.999
params=1.5/0/6/0 float=y maxiter=75000
inside=0 logmap=1050 periodicity=10
colors=000PVuTTsWRr_PqcOpfNojKm<3>xEhq9mk6q<2>gAsfCs\
fDu<2>cHvaIwaJw`Lx<2>YPyYQzWRz<3>TWzVZzY_z_ay`cycdxe\
fwggwhhvkkumluposqprsqrvsqxupyvp<3>Tz6ZmAdaGjQKpEPu0\
Vv2U<3>xGUxJUyNUyPUyTUzWUz_UzaU<3>zpVzoUzoUwoTuoTroT\
omRlmRjmRfmQ<5>QlOOlOKkNIkNGkNCkL9kL6oJ7kL8hN9fPAdQC\
aTD_UEWWGUYHR_IP`JNcKKdLIeNKdNLcOOaOP`PQ_PTZQUYQWYRY\
WRZVT`UTaTUdRUeQYgKUfQ<3>KdkIdpGcvCZzDez<2>DzuDzsCzq\
<2>CojCdhC`fAYdAT`AOZ<2>A9O73NA3KE2JI3KK6LO7NR8OV9PY\
CQ`DRdERgERjGRmGRqGRuGRwHRzHR<3>zHQzHPzIP<4>zONzPNzQ\
L<6>zZJz_Iz`IzaJ<3>zfEzgDzhCzjA<3>zo7zp6zq5zr3zs3zu7\
zv9zwCzxGzyI<10>zzkzzmzzpzzs<2>zzzzzwzzszzqzzmzzk<3>\
zzZzzWzzTzzQzzWzzY<3>zzZzz_zz_zza<5>zzwzzv
}
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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