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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's quickie fractal was found with so little effort that I could hardly give it a rating. Before I entered the parameters I knew that the parent fractal would be a Mandelbrot set rotated 180 degrees, with a prominent spike extending from its East Valley as well as from its west end. And I knew that a strange little Mandeloid would lie on this extra spike. This strange little Mandeloid has a string of 5 extra bays extending from its west end, and curiously, the largest of these bays lie farthest from the main body of the Mandeloid. Today's scene lies rather deep in the southern branch of the valley separating the fourth and fifth bays, which are the two largest. I named today's image "Mysterious Hexabrot" because the pattern around the minibrot consists unexpectedly of 6 lobes rather than the usual 4. I am finding this particular oddity more and more often in my travels through the fractal backwoods. I have no idea what it means, though I imagine that some mathematical genius somewhere on earth has already answered the question. The only thing not super quick about the image is its calculation time of just under 4 minutes on the nuclear P4-2000mhz machine. The tired old P200 unit, which is still in fractal service, would take about 25 minutes to do the job. Taking all this time into consideration, I recommend viewing the finished image on the FOTD web site at: But because of the unusual post time of this FOTD, I would give Paul a couple hours to calculate the image and post it on the web site. Brilliant sun and autumnal temperatures in the 50's F, or around 13C, prevailed at Fractal Central on Saturday, making it a most pleasant day to be outdoors. While F.L. and I were outdoors, the fractal cats were having an equally pleasant day indoors. But they still demanded an extra treat when we returned in the evening. The next FOTD will appear on schedule in 12 hours or so. Until then, take care, and we will never solve all the mysteries of existence until we discover them. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
MysteriousHexabrot { ; time=0:03:55.08-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident inside=0
center-mag=-1.9597975605951/-0.0184877289191/4.841\
299e+008/1/-45/0.00032688 params=1/2/-0.2/3/0/0/0/0
float=y maxiter=10000 periodicity=10
colors=000Q`C2ttLwxczzuzzpyxkvrgtlbqeZo_UlUPiNLgHG\
dBCb5B_CAYIAWO9UV9S`8Qf8OlARnBUoDWpEZqF`rHcsIftKhu\
LkvMmwOpxPsyRuzSxzTzzUtwVmrWhmWciX`dYZ_ZWVZTR_RM`P\
H_MDZIBWJEQOGOSJQXLR`NTeQUiSWnUXrXZwZ_z`YybWwdUvfS\
thRsjPqlNpnLnpKmrIktGjvEhxDgyKeomLkhPicThZXgU`fZNS\
XQUWTWVVYTY_S_aRbcxUKsWNoXQjZTf_Vb`YYb`UccfUuY_mMv\
cE6zGCxIItKOpMUlO_h4ChFRfLZuM`qNanObkPch6n`9laCkbF\
icIhcLfdOeekkvmpjiniflhbjg_igWgfTeekupepm`ljVhgvXI\
mZOQEkNEqJLlFShBYdBVaBS_BPYBMWBJUBGSBDQDJRFORHTRJZ\
RLcRNiROoRTuVXzZbsahlcneetZgzTiW`X2hKSdcbm`_kaYjbW\
hcUgdSeeut5xOzsRwnTtiWqdYn_`kVbhMQRNTUOVWOYZP_`Qbc\
X2_`feZeeXeeWeeUdeTdeRde2as6bq9boDcmGckKdiDq9HpAKp\
BOpBRpQ9AS9BU9CW9DY9E_9Fa9Gc9HeCLfFOfISfLWgOZgRbhU\
fhWihTkgRlgPmgMngKogIqgFrgDsgBtg9ugCrdFobIl_LiYNgW\
TcTY_RbXPhTMmQKrMIwJGaMEGODKRJNTPQVVQWTQWSQXQQXPQY\
OQYMQYLQZKQZIQ_HQ_GQ`EQ`D }
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.
