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Fractal of the Day
by Jim Muth
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Fractal visionaries: The weather today was so dull that I can barely remember it. Oh yes, it was partly cloudy with a temperature of 60F 15.5C and a south wind at 12kph. Regardless, it was a perfect day for scrounging in fractal land for that one perfect fractal that might exist among the infinity of infinities of fractals that might exist. Unfortunately, tonight has become totally overcast, and the meteor storm, if it happens, (which I doubt), will be invisible from fractal central. But I'll be up around 5am just in case a hole opens in the clouds and the meteors are there. The fractal I found was created by the next in my series of 12 MandNewt formulas, MandNewt10. This formula, as well as numbers 11 and 12, has six variable parameters. Since the six parameters are limited to real numbers, the resulting fractals always have X-axis symmetry. In some cases, the extra variable parameters are redundant, simply increasing or decreasing the values of other parameters, but overall the result is totally unpredictable, which is the way I like my fractals. I named the picture "The Omega Point" because as I studied it, I wondered if there could possibly be a last fractal. Actually, that's the way I name most of my fractal pictures -- I stare at them until a name comes into my head. The picture is a lot like my "Fractoland" picture of several days ago, though I'm not blaming this one on Dr. J. The picture has vague buds half obscured by bits and pieces of ectoplasmic fractal material, and areas of chaos offset by organized areas of quasi-order. But this image has at least a hint of order amid the most chaotic disorder. The spiral occupying most of the top third has no corresponding feature in the earlier picture. This spiral reminds me somewhat of the images produced by the Barnsley formulas. The GIF file has been posted with data intact to: In one of the day's e-mails, (there were over 50), I saw immortality mentioned. That set me to thinking about the possibility of living forever. Would it be desirable or would it be a torment of the worst imaginable kind? Most would agree that it would be desirable to live longer lives. After all, the way it is now, by the time we learn the lessons of an entire life and get wise, it's too late to do much with our wisdom but pass it on to the young who will ignore it anyway. And then the same will happen to them. No wonder mankind seems to be stuck in a rut, spinning its wheels. But what about eternal life. Eternity is forever -- time without end -- unimaginable infinity. In my young years I used to frighten myself trying to imagine how long time without end would be. I never pictured it. Would anyone want to live this long? I don't know about forever, but I would like to be around until I had seen every possible fractal. (I guess that *is* forever.) So what if in 100 years or so, some great scientist or metascientist discovers a way to grant immortality to mankind at a cost all could afford? Aparently, this would mean that those unlucky ones who had already died would be lost forever but those lucky enough to be alive at the time, or not yet born, would be immortal. Well, this would be grossly unfair to those who had already died -- including me. I would demand to be among the immortal so that I could see my fractals. Now before anyone laughs, remember that at the present time we exist after an eternity of never having existed. How much easier must it be to exist a second time after having already existed once. Any science which could not accomplish that simple task would be hardly worthy of being called by the honorable word "science". And now I suspect that the honorable thing to do would be to wrap this up and see if I can get it posted. Until next time, when I shall likely be a bit more settled, take care, and remember that no matter how far you search, you will never find the last fractal. Jim Muth jamth@mindspring.com |
START FORMULA================================================
MandNewt10 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-b)*z-g
j=c*z^d+g
z=z-e*h/j,
f <= |h|
}
END FORMULA==================================================
START PARAMETER FILE=========================================
The_Omega_Point { ; 80min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=mandnewt.frm
formulaname=MandNewt10 passes=1
center-mag=-0.735227/1.28731/1.153329/1/-75
params=3.524/1.979/-3.263/1.769/0.733/0.736 float=y
maxiter=12000 bailout=25 inside=0 logmap=yes
symmetry=xaxis periodicity=0
colors=000A8L<2>97O87PA9R87P71O64N53M42L35P74TB3XF6W\
Ec_DgZ<10>1TN<19>jBclBcmCd<36>pMnpMnqLm<46>sLNsLMrKL\
<63>tjU<5>Qo8Lp4Fo0<37>cvMcwMdwNexOexO<2>hyQ
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
The_Omega_Point { ; 80min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=mandnewt.frm
formulaname=MandNewt10 passes=1
center-mag=-0.735227/1.28731/1.153329/1/-75
params=3.524/1.979/-3.263/1.769/0.733/0.736 float=y
maxiter=12000 bailout=25 inside=0 logmap=yes
symmetry=xaxis periodicity=0
colors=000A8L<2>97O87PA9R87P71O64N53M42L35P74TB3XF6W\
Ec_DgZ<10>1TN<19>jBclBcmCd<36>pMnpMnqLm<46>sLNsLMrKL\
<63>tjU<5>Qo8Lp4Fo0<37>cvMcwMdwNexOexO<2>hyQ
}
frm:MandNewt10 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-b)*z-g
j=c*z^d+g
z=z-e*h/j,
f <= |h|
}
END 19.6 PARAMETER-FORMULA FILE==============================
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