|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: In the FOTD discussions I often mention parent fractals. But in my quest for ever more spectacular midgets, rarely do I give these parent fractals the attention they deserve. In a way, it is an oversight. Ignoring the parent fractals is like exploring the midgets of the Mandelbrot set while ignoring the whole set itself. These rarely seen and undeservedly ignored parent fractals have in them all the features of the M-set. In addition to the midgets, they hold buds, filaments, stars, spirals, valleys, and often features that do not exist in the M-set, such as disconnected features, areas laced with holes like a swiss cheese, and phantom features that exist invisibly in the flat inside areas. Well, today we take a step toward giving these unsung fractals the recognition they deserve. It is only a small step, but it is a step. Today's image is not a scene in a fractal -- it is the entire fractal. In fact, requiring several out zooms to fit on the screen, it includes the greatest surface extent ever to appear in a FOTD. How far does the bloated fractal extend beyond the borders of the screen? I have no idea. The fractal may be infinite. The effect of the image is one of a vast space filled with floating bits of fractal debris. At the center, a pair of joined twin M-sets lie partially covered with this debris. Many fragmentary M-sets fill the surrounding area, though none are intact. These open areas are sometimes difficult to see, but can be revealed by toggling in and out of color-cycling mode. Despite the overall chaotic nature of the fractal, embryonic themes can be found trying to get started. Perhaps the most obvious theme is that of butterfly shapes in the upper right part of the frame, but other less obvious themes exist throughout the image. Actually, this particular parent fractal has an overall non-critical appearance, and is therefore unlikely to have any impressive midgets lying within it. Its only impact comes from its surface appearance. I named the image "The Parent Fractal" for obvious reasons. I rated it at a 4 mainly because it is a disorganized weakly-composed affair with too many competing centers of attention. But even so, it's worth a look. The parameter file renders in 12 minutes, perhaps a bit too slowly for an image that rates only a 4. To avoid impatience, the completed image may be downloaded from the FOTD sites on the W.W.Web. These sites may be found at: The fractal weather today seemed more like spring than late Autumn, which made the fractal cats happy. They really enjoyed the spring-like sun and temperature of 61F 16C. But it's been 38 days since the last rain, and things are getting quite dry around here. Hopefully, the forecast of week-end rain will work out. Regardless of the possibly wet outdoor conditions, the indoor conditions will remain in the cat-pleasing dry range all week-end. As for me, I've got a bit of work to do and some fractals to find. Until tomorrow, take care, and think noble thoughts. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Parent_Fractal { ; time=0:12:23.04--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=8.52651e-014/-9.9476e-014/0.009186404/1\
/180 params=1/-0.85/1/-1.85/-7.264/525 float=y
maxiter=12000 inside=0 logmap=yes periodicity=15
colors=000CEOCEOCDPCDPCDQCCQCCRCBRCBSCBSCAzCApCAsC\
9nC9nC9jC8iC8dC8ar7Xo7Xm2Zk5Yh7Xe9WcBV`DUZFUMHTOJS\
QLRUNQTPPPRPXTOZVN`YMb_LdaKfcKheJigIkiHmkGomFqoFsq\
EusDwuCywBzyBxwCwuCvtDurDtqEroEqnFplFokGniGlhGkfHj\
eHicIhbIf`Je_JdYKcXKbVL`UL_SLZRMYPMXONVMNULOTJOSIP\
RGPODOPEPQFPRFPRGQSHQTHQTIRUIRVJRWKRWKSXLSYMSYMTZN\
T_NT_OT`PUaPUbQUbQVcRVdSVdSWeTWfUWgUWgVXhVXiWXiXYj\
XYkYYkYYkYYg_TbaOZcJUeEMg7Qf9TeBWdDZcEacGdbKgaPj`U\
j`Zj_ciZhhYmhYmhXmhXmhXmhXmhXmjXhiXcjX`iX`iXaiXbiX\
chWdhWegWffWgeWhdWhbWiaWj`Wk_WlZWmYWnWVoVVpUVpTVqS\
VrRVsPVtOVuNVvMVwLVxKVyLWzMWzMXzNXzNYzOYzOYzPZzQZz\
Q_zR_zR_zS`zS`zTazTazUbzVbzVbzWczWczXdzXdzYdzZezZe\
z_fz_fz`gz`gzagzahzbhzcizcizdizdjzejzekzfkzelzfmzf\
mzfmzfmzfmzfmzfmzfmzfmzfmzfmzfmzgmzhmzimzjmzkmzlmz\
mmznmzomzpmzqmzrmzsmztmzumzvmzwmzxmzymzzmzzmzzmzzm\
zzmzzmzzmzzmzzmzzmzzmzzmz
}
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==================================
|
times.
