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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal combines 0.4 negative portions of Z^(1.5) with 6 portions of Z^(-0.5) before adding C. When the parameters are entered into the formula, the default image looks most unpromising, consisting of nothing more than a few flat equal-iteration bands. But an out-zoom reveals a quite interesting display of distorted Mandeloids and pseudo-Mandeloids lying off the screen to the north and west. Today's scene is located in a disconnected area of interest in the interior of the northern valley of the very large bud of the eastern Mandeloid. I named the image "Fire-Wheel" after the broken ring of fiery red elements surrounding the midget at the center. The rating of a 5 seems fair enough. And the render time of 15 minutes gives the image an overall value of 33. The most convenient way to see the image is to download it from the FOTD web site at: At the end of the most recent philosophical discussion, I had rejected the Catholic church and its doctrines, which to me were no longer believable. Presuming that I was an Atheist, I felt proud that I had the intelligence and courage to see and accept the world as it really is. When I passed a church, I felt somehow above the people who went there. I did not need the pie-in-the-sky fantasies that they needed to make them feel good. I did not need to dream of an imaginary god who loves and cares for people regardless of what they might have done, but forgets his loving care and turns into a vengeful despot the moment they die. I did not need to delude myself into believing that I will somehow remain conscious after I die, and then be reunited in heaven with those who have died before me. My observations of the world, my knowledge of science, and my common sense told me that things such as God and immortal souls are no more than fantasies carried over from the past, which many people still need to help them cope with the hardships of life. For a while, the world seemed to make good common sense, even if it appeared not nearly as consoling as the Catholic doctrine had taught. But as time passed, my initial enthusiasm for Atheism began to falter. It left too many questions unanswered. I was no longer as certain of its materialistic view as I once was. Atheism eventually appeared to me as just another unprovable doctrine. I became hung up on the fact that Atheists have no demonstrable proof that there is no God. They merely point out that science has found natural explanations for so many once-mysterious things that it is now more reasonable to believe that a natural explanation will eventually be found for most, if not all, of the remaining unsolved problems, making a supernatural element unnecessary. If no god is needed, the Atheist doctrine says, and no signs of such a god exist, as observation shows, why then believe in one? At the same time, my puzzlement about existence increased. I started wondering in particular about the likelihood of my own existence. Why had one particular human infant (myself) been so different from all other conscious entities that had ever come into existence not only on earth but throughout the universe? Why had that one infant and none other been me? According to Atheism, there is no reason. It is all an accident. My own conscious existence seemed to be an extremely fortunate accident indeed. But how fortunate? As the months passed, my confusion continued to increase. If the universe is infinite, I thought, then the number of possible different conscious entities must also be infinite, and the chance of my particular self-awareness ever coming into existence would be one divided by infinity, or zero. My existence was impossible, yet there I was, right there and then, and nowhere else in the infinity of time and space. Is it not curious, I also wondered, that the universe just happens to be now experiencing the very same and the only infinitesimal span of time in which I will exist. And then the situation grew even more puzzling. According to relativity, there is no universal present moment of time, just as there is no universal point of space. Time is not an independent field of some sort spread evenly throughout the three-dimensional universe; it is more accurately seen as the fourth dimension of space perceived sequentially rather than simultaneously. The time throughout the universe is unique for each different observer. This means it is wrong to suppose that the entire universe is now experiencing the tiny span of time in which I will exist. This span of time is but a narrow slice of the four-dimensional space-time continuum, which extends beyond our intuitive sense of sequential time. The phrases 'before birth' and 'after death' no longer appeared to be absolutes. They needed to be re-defined. This certainly did not mean that a conscious creating entity known as God does exist after all, nor did it mean that I have an immortal soul that will leave my body and live on in a spirit world when I die, but it does mean that, behind the scenes, the vast expanse of the universe is put together far differently from the way we intuitively imagine it to be. Clearly, I needed (and likely still do need) to do much more thinking. And this was just the beginning of the philosophical ponderings that turned me from Atheism. To be continued soon . . . With cloudy skies, drizzle, and a temperature of only 45F 7C, Thursday left much to be desired in the cat department here at Fractal Central. Just a single glance out the door and a wet paw or two convinced the duo that the day would be far more pleasant if they passed the time indoors on their shelf by the window. A generous treat of tuna eased their disappointment. Conditions this morning are somewhat improved. It should be a better day for the duo. For me, the work is normal and I already have two more FOTD's in storage. I'll keep storing extra ones until I have a week's supply on file and ready to go if the work becomes too heavy to write a new FOTD each day. The next FOTD, along with more philosophy, will appear in a few days. Until that golden moment arrives, take care, and keep thinking. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Fire-Wheel { ; time=0:15:07.59--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.77174139347286160/+7.555493521532266\
00/330120.1/1/97.5/2.15404465632451636e-007
params=-0.4/1.5/6/-0.5/0/525 float=y maxiter=1800
inside=0 logmap=246 periodicity=10
colors=0000RA0SA0TA0TA5UB8UFAUICTMETPGTSITWKSZSkYR\
iZRhZQgZQfZQd_Pc_Pb_Pa_O_`OZ`NY`NX`NVaMUaMTaqlLfeR\
WZXakXZgYWdZUa_RY`OVaBKmCLhDLZEMUEMUFNZGNbGOfHOj7S\
m6Qg6Oc6MaZJNzH4yQ7xZ9wgBvpDvyFqvGmtGhqGdoG`mGWjGS\
hHNeHJcHFaHAZH6XH2VH5QO8MVAHaDDhF9nQZIPVOORUNO_MKd\
LHjKDpKAuKFqKJnKOjKSgKWdK``KdYKhVHjLElCBm3Ch5Cd6C_\
8CW9DSADNCDJDDFEHEFLEGOEGSEHVEIZEIbDJeDKiDKlDLpDMs\
DMmILhMLcQLYVKTZKObKJfKKdNLcQMbTM`WN_ZOZaPXdPWfQVi\
RTlSSoSRrTPuUOxUNzuwNrrMpmLniLkdKi`JgWJeSIbNH`JHZE\
GXAGVEIUHJTKLSNMRQNPTPOWQN_SMbTLeUJhWIkXHnZGq_Ft`J\
sXNrTRqPUqMYpIaoEdoBniBwdBrWOmO`iGlYJgNMbCPYDQZEQZ\
FQZFQ_GR_HR_HR_IR`JR`KSoKSaLTaLSaMSaW71SEEPLQU0mT0\
mScpRcmQckPchOcfNccUHLTJNSKPRLRQMSQNUPOWOPXNQZMR`u\
7icIe9yiAzhBzgCzgDzfEzfFzeGzeGzdHzdIzcJzcKzbLzbMza\
Kz`Lza4z_Dz`jzoezl`ziWzfWzciz4fz8dzBbzE`zHZzKWzNUz\
QSzTQzWOzZmzlizjfziczh`zg }
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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times.
