; Date: Thu, 12 Apr 2007 22:47:10 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 13-04-07 (Alternate Critical [4]) ; ; Id: <1.5.4.16.20070412225102.0def23d6@pop.mindspring.com> ; --------- ; ; FOTD -- April 13, 2007 (Rating 4) ; ; 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 re- ; veals 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\ bPgcMfdJeeGdeFcfFbfFbfEagEagE`gE`hD_hDZhDZiCYiCYiC\ XjCXjBWjBWkBVkAUkAUlATlATl9Sm9Sm9Rm9Rm8Qn8Pn8Pn7Oo\ 7Oo7No7Np6Mp6Lp6Lq5Kq5Kq5Jr5Jr4Ir4Is4Hs3Gs3Gt3Ft3F\ t2Eu2Eu2Du1Cv2Du2Eu2Fu3Ft3Gt3Ht4Kz4Uz4cz5mz5hs5cr5\ Zr6Ur6Pr6Oq7Oq7Pq7Qq8Qp8Rp8Sp9Sp9To9Uo9UoAVoAWnAXn\ BXnBYnBZmCZmC_mC`mD`lDalDbl3kfDblNVrYMyXNwXNvWNuWN\ tWOsVOrVOqVOpUPoUPnUPmTPlTQkTQiSQhSQgSRfRReRRdRRcQ\ SbQSaPS`PS_PTZOTYOTWOTVNUUNUTNUSMURMVQMVPLVOLVNLWM\ 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========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint