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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's image, things get stranger yet. Now, the midget itself has been infected by whatever is happening in this part of the fractal world. What we have in the image is a quadratic midget that has begun to morph into a midget of the sixth order. The five lobes of sixth-order midgets are already taking shape. The smaller satellite midgets however still retain the familiar Mandelbrot outline. Check the westernmost extremity of the large midget, on the X-axis where the stem branches out. You will find a perfect Mandelbrot bud there. Then check the smaller outlying midgets. Some of these are irregular holes with a decidedly non-critical appearance, but others are perfect mini-Mandelbrot sets. Finally, notice the 6,36,216... series of elements leading to the central midget -- a sure sign of an emerging sixth-order midget. What's happening here is crazy enough, but we have not yet seen the worst of it. Stay tuned over the next few days for even stranger fractal wonders. Since today's image has only limited artistic worth, I have rated it at a 4, which is a little below average, but not low enough to make the 1-1/4 minute render time too much to ask. Thanks to the short render time, the overall value registers an impressive 323. Perhaps the fastest way to see the image is to download it from the FOTD web site at: Fine early spring weather on Thursday made the fractal cats happy. The warm sun and temperature of 68F 20C was just what the duo was waiting for. They spent the entire afternoon in the yard, doing what old-age cats do best -- sleeping. When they came inside, the treat of tuna completed their day. This morning is starting even warmer. Another good day seems to be coming. I have several hours work to accomplish, then it's back to the fractal screen. Until next FOTD, take care, and who knows what is possible in the world of fractals? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
What_is_it { ; time=0:01:14.37--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.509759593836255/0/351.2859/1/180
params=1/3/0.355/4/0/0 float=y maxiter=900 inside=0
logmap=15 symmetry=xaxis periodicity=10
colors=000LB9L96L84OC6RF7UI9XLA_OBbRDeUEhYFk`HncIq\
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zfzzczz`zzXzzUzzRzzOzzLzzIzzFzzCzz9zzAzzBzzBzzCzzC\
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HzzPzzWzzbzzjzzqzzxzzuzzrzzozzlzzjzzgzzdzzazzZzzXz\
zUzzRzzOzzMzzOzzPzzQzzRzzPzzNzzLzzJzzHzzFzzEzzCzzB\
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zzbzz`zzVzzQzzUzzXzz_zzczzfzzizzmzzpzzszzozzkzzgzz\
dzz`zzXzzOzzLzzJzzGzzEzzB }
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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