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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The world is composed of material, material is composed of chemicals, chemicals are composed of molecules, molecules are composed of atoms, atoms are composed of sub-atomic particles, sub-atomic particles are composed of superstrings twisting in 10 or more dimensions, superstrings are most likely composed of energy, which is the ability to do work and is expressed in numbers. Fractals are simply composed of numbers. With these simple facts, we begin today's FOTD. I named today's image "Rosalie Remembered" for a reason that will remain untold. The only certain thing is that speculation will lead to a wrong reason for the name. The formula that drew the tiny midget with an 8-lobed zipper around it is 5Z^(-2.6)+20Z^(-1.3)+(1/C), a totally whimsical expression that I stumbled upon by luck. The parent fractal is an oversized, barely recognizable Mandeloid with two areas of chaos extending NE and SE. In these chaotic areas, which appear not at all critical, lie two prominent though indescribable objects. Today's midget lies in the object in the NE chaotic area, and is one of the most unexpected midgets I have yet found. The run-time of the parameter file is a nominal 4 minutes. I leave it to the viewer to run the parameter file or wait 16 hours until the GIF image file is posted to: The GIF image may be downloaded within the hour from the WWW, where it will be posted to Paul Lee's web site at: The fractal weather today featured sunny skies and a return to winter, as a cold wind and temperature of 34F (1C) kept the fractal cats safe indoors all day. They displayed their dis-satisfaction by overeating. A few days ago I left off in the telling of the philosophical history of my life at the point where I had just rejected Catholicism and adopted Atheism. I made the leap because Atheism was to me the more sensible view -- a vast improvement over the dogmatic mystery things I had been taught in Catholic school. I gave up on religion when I saw that Atheism depends on no miracles or other impossible things; its truth is demonstrated simply by a careful observation of the world. And more importantly, Atheism is largely in agreement with science, which offers reproducible proof of its teachings. Why then, did I not remain an Atheist? Perhaps the most important fact was my inability as I grew older to convince myself of the truth of the basic philosophies of Atheism -- Materialism and Positivism. I never became convinced that the material universe is the one and only objective reality, nor was I convinced that the senses are the only means of obtaining knowledge of reality. Instead, I found myself straining to believe these things, in much the same manner as I had strained to believe the teachings of the Catholic Church. And this time it was the discoveries of science that had created my doubts. I came to realize that the human senses, even with their instrumental extensions, reveal but a tiny fragment of all that exists. And relativity shows that the tiny bit we can observe is so limited that intuitive common sense leads to wrong conclusions when it is applied to things far beyond the range of everyday experience. Even more disturbing, quantum mechanics calls into question the objective reality of the 'outer' world itself. And cosmology tells us that space, however real it may be, might be filled with things such as worm holes to alternate universes as well as to the past and future. Around this time I discovered the eastern religions, and how they agree with modern science. Scientific discoveries such as quantum mechanics are not at all troubling to those who follow the eastern religions, which for thousands of years have taught that the outer world is an illusion. Of course, many men of science declare this resemblance to be a mere coincidence, but they do so almost apologetically. Regardless, the resemblance does exist, and it remains a most curious coincidence. This resemblance, along with my inability to accept the philosophy upon which Atheism is founded, is in large part the cause of my doubts about Atheism. As a result of studying modern science and comparing it to eastern religions, my original *conviction* that no God exists was changed first to a *belief* that no God exists, then to an admission that I have no knowledge of whether a God exists, and finally to a feeling that the chances are in favor of something like a God. At the same time my conviction that no other worlds exist became a belief that in all likelihood other worlds do exist. Whether these other worlds are physical or spiritual, or if they are spiritual, whether our souls go there when we die, is an open question. As I see things at the present time of my life, Atheism, which says that God does not exist, could possibly be true, but Agnosticism, which says that we can have no direct sensory knowledge of God, is certainly true. I chose certainty before a possibility. Having come to the end of today's FOTD, I hear Tippy the tabby calling for his late snack. This means it's time to shut down the fractal shoppe, pack away the fractals, and prepare for tomorrow, when I'll do it all again. Until then, take care, and when a cat calls for food, you'd better feed him. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Rosalie_Remembered { ; time=0:04:02.16 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.920178727880141/+17.76183926661183/596\
723.6/1/-107.5 params=5/-2.6/20/-1.3/0/800 float=y
maxiter=1200 inside=0 logmap=67 periodicity=10
colors=000pXzrbzrgzktmsrzmulgwmiugXz`evVKwPYwI9tC2z5\
0q00z00n00z00k00w00i00m00f00d00_00T10S21K41L52A74595\
1A70C70EA0IE1LF5PIASKFVNKYPPbSTeTYhXbkYgo`krbou`js`g\
r`dp``p`Yo`Vm`Sm`Pk`Lj`Ij`Fh`Cg`9g`5e`2d`0d`0b`0``0`\
d0eg0hj0km0or0su0wx0zz0z<3>z1zz4zw5zr9zmCzhEwdHu_IrV\
LoQPmLQjHTgEVe_P_sIThPbYVjN_sCez1jz2jz4jz7hz<2>ChzEh\
zIezLdxQbpT`gX_Y`YQdXHgV7kT0oS0rQ0oP0kN0jL0<3>`F0YE0\
VC0TA0Q90P70L50K40H20F10I20K20N20P44S49T4FX4KY5P`5Vb\
5_e7dg7jj7ok7sm9ooAjpCepE`rFXsHTuIPuKKwLFxNAxN7zQC<3\
>zXVzY_z_dz`gzdk<2>zhz<3>zozumzgmkTmXFkH1k1<2>0k00k0\
1k04k07k1Ak4Ek5Hk9KkAHoFEpIArN7sQ4uV2wY0x`0ze0zh0zm0\
zp0zs0zoAzkLzgYzdhz`<3>YzPVzLTzKbzQjzXrzbmzbhzbezb`z\
bYzbTzbQzbLzbIzb9zzAzzCzx<3>Iz_KzTLzNNzHPzAQz4Sz0<2>\
SzNSzXSzdSzkSzuSzzSzzHzz5zo0zd0zV0z_0zb7zgFzjozxozz
}
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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