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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: So it's the 10th anniversary of the FOTD. It's been the fastest 10 years in recorded history. Luckily, it was mentioned on the lists, for I had totally forgotten it. For the 10th anniversary we have a relatively plain fractal, which rates only a 4. This is slightly-below-average. I named the image "Alternate Critical" because its parent is the fractal that results when yesterday's formula is calculated with Z initialized to the alternate critical value of the function Z^(2.4)-Z^(2.6). A little calculation shows that the two critical points of this function are zero and 0.670176937. The MandAutoCritInZ formula automatically initializes Z to 0.670176937, so it was necessary to enter a value of negative 0.670176937 as the real(p4) parameter in order to re-initialize Z to the second critical point of zero. At the surface, the fractal that results when Z is set to zero is a virtual copy of yesterday's parent fractal, which somewhat resembles the cubic Mandelbrot set rotated 90 degrees. But it is not an exact copy. A quick examination of the surface reveals subtle differences, which quickly become major differences as one zooms down into the fractal. Today's image shows a scene located near a larger midget on a filament at the western end of the parent. The midget at the center is a curious one indeed. Apparently, it cannot decide whether to be a quadratic midget or something else. If it is trying to be a quadratic midget, it is doing a pretty poor job of it, since the expected powers-of-two series of elements that usually surrounds quadratic midgets is nowhere to be seen. Nothing is visible around the midget but a chaotic assemblage of cut-up pieces of fractal stuff. I can see a series of 2, 5, and 12 elements, which would seem to indicate a power around 2.5 -- the average of 2.4 and 2.6. As for the quality of the image, the less said the better. This is especially true when its inordinate calculation time is considered. I do not know how long the image would have taken on the fractal workhorse machine, a P200, but it took 16 minutes on the P4-2000. I will send it on ahead to Paul at the FOTD web site so that it will be posted ready for viewing as soon as this discussion appears. The FOTD web site may be accessed at: I'm out of time right now, but I'll explain the workings of all the MandelbrotMix formulas in tomorrow's discussion. Heavy clouds, showers of rain, and a chilly temperature of 48F 9C kept a damper on things here at Fractal Central on Thursday. The fractal cats' spirits were not dampened however. They managed to pull a stack of newspapers from the shelf and rip them to shreds all over the living room floor. After the mess they made, they hardly deserved their evening treat of tuna and cheddar cheese. My day was average, and as far as I can see, the days will remain average indefinitely. The next FOTD will appear in 24 hours. Until next time, take care, and where did all the numbers go? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Alternate_Critical { ; time=0:16:08.61-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=t
center-mag=-2.11102026345568200/+0.278394631139739\
60/7.97647e+009/1/-125/0.000234075480398991675
params=1/2.4/-1/2.6/0/0/-0.670176937/0 float=y
maxiter=50000 inside=0 periodicity=10
colors=0006KDALHELLILOMMSQMWROcSN`TMZULXVLVWKTXJQY\
IOZIM_HK`GIaFFbFDcEBVD9_C7e82mC5uF7wJ9zMBhPDiTFjWH\
kZJlbLleNmhPnlRooTvuTrsUorVlqWipXfnYcmZ`l_Yk`VjaSh\
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t2Eu2Eu2Du1Cv2Du2Eu2Fu3Ft3Gt3Ht4Kz4Uz4cz5mz5hs5cr5\
Zr6Ur6Pr6Oq7Oq7Pq7Qq8Qp8Rp8Sp9Sp9To9Uo9UoAVoAWnAXn\
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tWOsVOrVOqVOpUPoUPnUPmTPlTQkTQiSQhSQgSRfRReRRdRRcQ\
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KWLKWKKWJLWJMVKNVKOULPULQTMRTMRSNSSNTROUROVQPWQPXQ\
PYPQYPQZOR_ORziSzcSbMTcMTdLUdLUeKVfKVgKVhJWiJWzIXz\
UXkHYlHYmGZnGZoF_pF_qE`rE`uDbsEarE`qE`pE_nEZmEZlEY\
kEXjEXhEWgEVfEVeEUdETbETaES`ER_ERZEQXEPWEPVFOUFOSF\
NRFMQFMPFLOFKJQHIPIGNJFMK }
frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
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times.
