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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we return to the image quality that makes fractals worth the effort. The rating of an 8 is the highest in some time. Hopefully, this is a sign of things to come. To create the parent fractal, I mixed together Z^(-1.77) and Z^(-7.71), added (1/C) and let the mixture iterate for 1200 cycles. The resulting fractal is beyond description, an oversized thing consisting of numerous bays, valleys, long looping filaments, scattered bits and pieces, a curious almost-midget, as well as assorted other items of interest. The east side of the main bay is decorated with a prominent valley, which at first glance might be taken to be an East Valley. From the center of this valley extends a zig-zag filament strung with dewdrop-like nodes. Today's scene lies rather deep in one of these nodes. Surprisingly, the area has almost none of the typical 'East Valley' features. The standard equal-iteration-band rendering gives a good-enough image, but the evaporated version of the scene is better. It is this evaporated version that I used as today's FOTD. I made the totally-inside material visible by using the bof61 inside fill. Other fills might work equally well, but I have not yet tried any of them. When searching for a name, I noticed the hyperbolic elements and named the image "Iterative Hyperbolae". When figured into the 6-minute render time, the rating of an 8 gives an overall value of 135. What the overall value might be when the image is downloaded is up to the individual to decide. The download is available at: Rain fell all day here at Fractal Central on Monday, while the temperature reached only 59F 15C. The cats did not approve and showed their disapproval by flipping into their sulking modes. A treat of tuna in the evening helped a bit, but a dish of fish cannot make up for a missed afternoon in the yard. Today looks somewhat better, so we'll see how it goes. For me it's a day of work before fun. Until next FOTD fractal, take care, and be at ease. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
IterativeHyperbole { ; time=0:05:55.50--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.40024400180910400/-0.000531620471100\
73/3.385291e+010/1/15/0.000876059279207246078
params=1/-1.77/0.23/-7.71/0/1e+100 float=y
maxiter=1200 inside=bof61 periodicity=10
colors=0000V`0b_0jY0rW0mQ0iL7dGC_BIW5OS2qty`nfLjP`\
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0k_0fT7bMDZGKTAQP3YL0cH0jO0dV0``2Yf4Tm8OtBKzFGzHCr\
Y7fk2Vz0Tt5SmFQfMP_WPVcMPVKLMIGDGC5F80PAD_BSjCftDu\
pFqmGmjHigHdcI``KYZLTWLQPOWKQ_DTd8Wi2Zn0`r0cwitCfq\
GdpKcnObmS80m50j35g0Dd0Lc }
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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