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Fractal of the Day
by Jim Muth
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Patient Fractal enthusiasts and visionaries: After a three-day hiatus, there's nothing like a fractal named "Fractal on Hiatus". Actually, it's the three-day lapse between FOTD's that inspired the title, rather than anything to do with the image. Today's image was created when I mixed Z^0.9 and Z^(-0.9), and did a bit of probing into the resulting fractal. I gave more effort than my usual 10 minutes to the coloring of this one, and the result probably reflects the extra effort. Actually, I've been putting so little artistic effort into coloring my FOTD fractals that I'm almost embarrassed to be posting them to a list devoted to the artistic aspect of fractals. Today's image requires a not-so-speedy six minutes or so to render -- long enough to make a download worth the effort. The image may be picked up and downloaded from Usenet at: The fractal weather today was crisp and fall-like, with blue sky, brisk north winds, and a temperature of 60F (15.5C), which was perfect for fractals. When I left off four days ago, I was ready to reveal my thoughts about why each of us is ourself and not some other self. I had just commented on the indirectness of our awareness of other awarenesses, and how easily pseudo-awarenesses can be created by our minds in dreams. To begin to find the answer, we turn to science. The goal of science is to unify, though often it is first necessary to break apart and analyze the thing being investigated. Using this method, we have unified space and time, energy and matter, the electromagnetic force and the weak force, waves and particles. The ultimate goal is to unite everything, which obviously includes the nature of self-awareness, into a single theory, which would be simple enough for the average person to comprehend. This idea of a unified theory of everything is at the present time a distant hope, but it is the inspiration for my tentative solution to the impossible problem of why I am myself. To begin, I have rejected all simplistic, materialistic approaches such as claiming that consciousness does not exist, or is nothing more than the behavior of the body. Then I have remembered that all my previously answered big questions were based upon an apparently common-sense but wrong assumption. In this case, the wrong assumption could be only that other awarenesses than mine actually exist. After much thought, I have come to the tentative conclusion that the conscious principle animating those other bodies is an unconscious part of my consciousness, just as my consciousness is an unconscious part of every conscious entity in the universe. Not only is the world I observe around me a part of myself, the living minds in that world are also a part of myself, and I am a part of everything. And this statement is true for every person on earth. We see now that I am myself because it could not possibly be any other way. A new aspect of the same mind, which is my mind and the mind of every other person on earth, reappears in a different form with each new birth. What we do to others we literally do to ourselves. (Whether we will actually ever experience those 'other' minds is another question for perhaps another FOTD.) If you wish to call this universal mind "God", I would almost agree; being an agnostic, I cannot make that final leap. But in the end, I am always amazed at how often rational science leads to the realm of the metaphysical and mystical. In a day or so, when I've recovered my full strength, we'll tackle the next big question -- Where was I before I was born and where will I be after I die? That's it for this evening, fractal fans. Until next time, take care, and never forget that all people are siblings, (the politically correct version of all men are brothers). Jim Muth jamth@mindspring.com |
START FORMULA==============================================
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 FORMULA================================================
START PARAMETER FILE=======================================
Fractal_on_Hiatus { ; t=0:06:43.76 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.03283717737713847/-3.3089797447112830\
0/9.783103e+011/1/42.49/0.009
params=-10/-0.9/10/0.9/-0.8/0 float=y maxiter=1500
bailout=25 inside=0 logmap=148
symmetry=none periodicity=10
colors=00000D<7>00C00C00C<5>00D00D00D<4>02E02E02E<3\
>04F34F<3>00F00F24E<8>D_BFcBGgA<3>Lt9Mw94yA8wCBtE<3\
>OeMSaOVYP<3>gUXkTZnS`qSa<22>ukuvluvmv<3>vpy<15>fMf\
eKedId<3>aB`<2>3zY<11>TdcWbdY`d<3>eUf<3>UafSdfPffMh\
fJjfHlf<8>BdrBdsAct<3>8`y<3>VUc_TYeRT<2>uND<4>oIHnH\
ImGJ<3>iDL<2>CU6<7>bgNeiPhkR<2>rpXuqZwrb<3>wvq<5>ww\
nwwmwwm<3>wwk<3>wwpwwqwws<2>wwvwwwwwv<3>wwcwwZwwVww\
QwwM<3>wwZ<4>wwRwwQwwO<2>wwKwwJwwKwwD
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Fractal_on_Hiatus { ; t=0:06:43.76 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.03283717737713847/-3.3089797447112830\
0/9.783103e+011/1/42.49/0.009
params=-10/-0.9/10/0.9/-0.8/0 float=y maxiter=1500
bailout=25 inside=0 logmap=148
symmetry=none periodicity=10
colors=00000D<7>00C00C00C<5>00D00D00D<4>02E02E02E<3\
>04F34F<3>00F00F24E<8>D_BFcBGgA<3>Lt9Mw94yA8wCBtE<3\
>OeMSaOVYP<3>gUXkTZnS`qSa<22>ukuvluvmv<3>vpy<15>fMf\
eKedId<3>aB`<2>3zY<11>TdcWbdY`d<3>eUf<3>UafSdfPffMh\
fJjfHlf<8>BdrBdsAct<3>8`y<3>VUc_TYeRT<2>uND<4>oIHnH\
ImGJ<3>iDL<2>CU6<7>bgNeiPhkR<2>rpXuqZwrb<3>wvq<5>ww\
nwwmwwm<3>wwk<3>wwpwwqwws<2>wwvwwwwwv<3>wwcwwZwwVww\
QwwM<3>wwZ<4>wwRwwQwwO<2>wwKwwJwwKwwD
}
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 19.6 PAR-FORMULA FILE==================================
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times.
