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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For almost a year I have given the FOTD's a rating somewhere from 0 to 10 on my arbitrary scale of fractal worthiness. To this point the highest rating has been a 9, and the lowest, a 2. Since June 1, the rating of the FOTD's has been as follows: Rating 0 -- 0 Rating 1 -- 0 Rating 2 -- 0 Rating 3 -- 5 Rating 4 -- 7 Rating 5 -- 12 Rating 6 -- 13 Rating 7 -- 6 Rating 8 -- 1 Rating 9 -- 1 Rating 10 -- 0 As is true of most random distributions, most FOTD's have scored near the middle of the scale. As can be seen by plotting a graph, the distribution is a roughly drawn version of the well-known bell curve. With a larger sample the curve would become smoother. The sample lacks 0's 1's and 2's because I reject these poor quality fractals. It lacks 8's 9's and 10's because these exceptional fractals are quite difficult to create. Since June 1 the average rating has been 5.3, which shows that my rating judgement is honest, and that I do not practice grade inflation. However I do appreciate those who tell me that I occasionally under-rate my fractals. And while appreciating the kind comments, I never forget that beauty is in the eye of the beholder. And speaking of beauty, we have a FOTD to discuss. Today's image is a scene I found in the fractal created by the formula 10Z^(-6.67)+Z^(-0.667)+(1/C). This formula draws a grossly overblown thing which must be seen to be appreciated. Today's scene lies in a shallow valley near the extreme east edge of the parent fractal. The scene is that of the usual midget, in this case surrounded by holes of all shapes and sizes. Lots of holes is another feature of fractals created by adding negative powers of Z. The holes may be made larger by increasing imag(p3), which defines the escape radius, until the image becomes nothing but one big hole, in which case the inside fill must be set to something such as bof61 to create an image and resurrect the spirit of the vanished midget. At almost 1/4 hour, the parameter file is a slow one to calculate. The far wiser choice is to download the finished GIF image from: The fractal weather today finally settled down a bit. The partly cloudy skies, temperature of 86F (30C), and lack of thunder brought out the best in the fractal cats, who were more like their old selves as they chased each other around the yard. The fractal philosophy is still stagnated however, but the pressure to pontificate is still building, and when it breaks loose anything might happen. But the only thing that's going to happen right now is that I'm going to shut down the fractal shoppe and call it a night. Until tomorrow, take care, and fractals are good for the soul and spirit. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Holey_Midget { ; time=0:13:37.73 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.203986748470977/-0.038709771549937/118\
288.4/1/152.5 params=10/-6.67/1/-0.667/0/0 float=y
maxiter=1500 inside=0 logmap=103 periodicity=10
colors=000G0G<3>J0SK0VL0Y<3>P3j<2>S6mT7nW8o<3>fDsiEt\
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}
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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