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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I have seen a rumor on the Fractint list recently that the upcoming FOTD CD will be a musical one. I would like to put this rumor to rest. There will be no music on the CD, neither fractal music nor otherwise. Fractals make great visual images. They can even be used to select words from a dictionary and place them in an arrangement that will simulate bad poetry. But fractals do not make music that I have the patience to sit, concentrate on, listen to for hours, and be inspired by. When turned into sound, fractals do make very interesting background noise however, though I do not consider this cacophony to be music. Today's lowly 2-rated fractal is little better than 'fractal music', and it represents the end of my adventures with the experimental MandelbrotMix3 formula. The experiment has been a failure. The image shows why. This fractal is typical of those created by the formula. The image tries too hard. It has so much of everything that it ends up having a lot of nothing. It is so busy with competing themes that it has no single theme to serve as a center of attention. In frustration, I named the image "A Boring Lesson". In addition, the formula is exasperatingly slow, and requires the user to calculate a critical starting point manually. The outcome of all this is that the formula has been consigned to the trash bin of forgotten formulae. I have satisfied myself that, just as the Z^2 Mandeloid creates the richest fractal, so does mixing only 2 powers of Z create the richest mixed images. I leave it to the reader to decide whether a 2-rated image is worth the 50 minutes required to render it from the parameter file. Those who decide that the image is not worth nearly an hour of computer time may download the finished image from one of the following two web sites: The fractal weather Wednesday here at Fractal Central was sunny but blustery and cold. In response, the mood of the fractal cats was also blustery. They passed much of the day on their shelf by the window, watching a flock of blackbirds scrounging for morsels in the yard and intermittently complaining about the cold. It's now time to finish the modicum of real work so that I can return to the preparation of the FOTD CD. Until a few days from now, take care and see you soon. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Boring_Lesson { ; time=0:50:49.74--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3 function=ident passes=1
center-mag=+1.564290873945641/+2.097972456507608/2\
.125008e+007/1/177.5/-7.57875697517812474e-006
params=0.01/4/-0.2/2/2/-1/-2/-3/1.4306355202818/0
float=y maxiter=1500 inside=0 logmap=188
colors=030qUtsUttUsuSsvSsxSsyVtzXtzYtzatzbtzdtzfuz\
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}
frm:MandelbrotMix3 {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END 20.0 PAR-FORMULA FILE==================================
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times.
