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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Another average day brings another average fractal, this one from 3.1415926535898 turns up the complex logarithmic spiral of the formula Z^1.75+C. Yes, I realize that the number of turns is almost equal to pi, but it is not exactly equal. Pi equals 3.14159265358979, and the 0.00000000000001 difference makes a world of difference in the appearance of the finished fractal. The difference must be seen to be fully appreciated. The parent fractal is a Mandeloid with X-axis symmetry, rotated 180 degrees from the normal position. Curiously, the Z^1.75 Mandeloid is the only one that has such symmetry at this point on the log spiral. Today's scene is located on the bud side of the west branch of the valley of a large distorted bud on the northern shore of the main bay of the parent. I named the image "Imperfect Minibrot" because the exponent of Z, which is 1.75, is a fractional value and therefore produces imperfect broken images. The imperfections abound in today's image, perhaps the most notable being the 7 elements that surround the imperfect midget at the center. Not only are these elements broken, but 7 is a strange number that doesn't belong in polite fractals. The next ring inward holds about 12 elements, but not exactly 12 elements, which is not surprising, since 1.75 times 7 equals 12.25. So much imperfection can only make a fractal that is average or below, thus the rating of an average 5. The render time of 19 minutes is admittedly slow, but can be avoided by downloading the finished GIF image file from: Thursday's weather was the best of the summer here at Fractal Central. (Have I said that before?) Deep blue skies flecked with angel-hair cirrus clouds, low humidity, and a temperature of 86F 30C brought out the best in the dynamic cats, who spent most of the afternoon in the holly thicket, wishing they were kittens again. Today is starting fair enough, but rain is possible later this afternoon. It remains to be seen how the duo will adjust. I'll adjust quite well -- once the work is finished, that is. Until next FOTD in 24 hours, take care, and have you tried the fractal miracle diet? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Imperfect_Minibrot { ; time=0:19:01.63--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-0.146140556417671/+0.6352473582880382/\
7857607 params=1.75/0/3.1415926535898/0 float=y
maxiter=12000 inside=0 periodicity=10
colors=000K6lMAjODiPHhRKfTOeURdWVbYYaZa``dZbhYckXd\
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YGRPDOGBL7AMDANJa6FW6QQ6a
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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