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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The lateness of today's FOTD is due to a problem with Mindspring, my ISP. When the regular posting time arrived between 11pm and midnight last evening, I could not get connected. Oh well, as they say, nobody's perfect, expecially internet service providers. Things are better this morning. (I hope.) Today's image shows one of the things that happens when 0.7 part of the negative square root of 2 is subtracted from 0.7 part of the positive square root of 2. Actually, an infinity of things happen, but with limited time I can cover only one of them. To show that more than one thing happens, I will use the parent fractal of today's image as the source of tomorrow's image. The parent fractal resembles a grossly inflated and skewed figure 8. Today's scene is located in the vicinity of the east branch of the valley that separates the north and south lobes of the 8. This area resembles an eroded shoreline filled with Mandelbrot bays -- I think they are called radicals. The tiny midget at the center of today's image is located far out on a filament extending from the center of one of these bays. I have found that the overall nature of today's scene is quite common in fractals which combine more than one power of Z, so I could rate the image no higher than a 6. Yes, in the world of fractals, originality does count. I named the image "Negative Thinking" because it deserves a name. I can give no good reason for the exact name, other than a reaction to all the benefits of positive thinking we keep hearing about. Life is a mixture of good and bad events. Positive thinking is getting as much enjoyment as possible from the good things while minimizing the anger etc. from the bad things. Positive thinking sounds good in theory but it doesn't seem to work very well in practice. I suppose negative thinking would be the opposite. (Maybe negative thinking is what there is too much of in the middle east.) There is no problem with the render time of the included parameter file, which is under 6 minutes, and this is on my ancient fractal-dedicated computer with the exhaust fan that needs a slice of tissue attached to blow in the wind so that I can tell when the fan stops running and must be goosed to life again. And running the included parameter file may be avoided entirely by downloading the finished image from the FOTD web site at: The perfect weather here at Fractal Central on Friday went unappreciated by the new fractal cats, who spent the day indoors, chasing each other up and down the hallway, and getting into various other mischief. In my department, the work appears to be getting heavy. Hopefully, we will be able to keep it under control. The next FOTD is due to appear in 15 hours. If it fails to appear, you will know that the work was not kept under control. Until next time, take care, and when you need some positive thinking, think of fractals. I am positive they will ease your distress, or at least make you think your distress has been eased. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Negative_Thinking { ; time=0:05:49.33--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.17954814796951500/-0.092458505525142\
48/2.914394e+010/1/112.5/-0.0150162000124490908
params=0.7/-1.4142/-0.7/1.4142/0/0 float=y
maxiter=1800 inside=0 periodicity=10
colors=0001hMBfJLdGVcDdaAn_7xZ4feLQkaOfeMbhKZkJUnH\
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lQtiNrfKqcGo`DnYAlV7kS4iP }
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 PARAMETER FILE=========================================
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