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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: Today's fractal has no midget. This is because there are no midgets in the Mandeloid fractals formed by exponents of Z between zero and one. In fact, there are almost no fractals in this range. Z^0.7 gives an empty circle; (-Z)^0.7 adds a few flat bands inside the circle. It is only when Z^0.7 and (-Z)^0.7 are added together that an adequate fractal appears. No midgets exist in the entire parent fractal of today's FOTD. The number of lobes on a Mandeloid midget is one less than the exponent of Z in the generating formula. Z^3 produces a Mandeloid with 2 lobes, while Z^2 gives one lobe. Following this sequence, an exponent of 0.7, such as in today's formula, should produce midgets with -0.3 lobes. Since such midgets are impossible, no midgets are in these fractals. But midget or not, today's picture is an interesting one, displaying as it does just one of the infinite patterns possible in the world of fractals. After studying the picture for several minutes, I got the impression that I was looking at an emulsion of order and chaos. I therefore named the picture "Emulsion". I could just as easily have named it something like "Amoebae" or "Ice Floes", but the first name that comes to mind is usually the one I stick with. At over 4 minutes, the parameter file is just slow enough to make a download the better choice. That download may be found at: The fractal weather today was the antithesis of yesterday's glorious day, as a mass of cold, damp air came in off the North Atlantic, and with its low clouds and mist, drove away the sunshine. The temperature of 45F (7C) was just too chilly for the fractal cats, who still remember the day in the sun they enjoyed yesterday. Such gloomy weather, however, is perfect for pondering things such as human spirituality. This afternoon, I actually managed to get in a little pondering. As I recall, when I last discussed this topic, I had not yet defined my view of spirituality. I did mention the things that I feel are not true spirituality. I told that in my opinion spirituality is far more than having a deep but blind faith in the doctrines of a particular religion and following the rules of that religion. I also told that doing good deeds, caring about others, having high moral standards, and exhibiting law-abiding behavior that conforms to the cultural norm, while desirable in themselves, are but a small part of spirituality. I went on to tell how, when one contemplates the vastness of the universe and the incredible order of the natural world, that person will often be overcome with emotions of awe and wonder. But these are mere natural human emotions, having little to do with spirituality. What then remains that might be called spirituality? Our present form of science can offer no answer, for science has failed to develop the means to investigate the spiritual aspect of existence. This failure is usually justified by the claim that to attempt an investigation of spiritual reality would be a wasted effort, since in all likelihood nothing is there to investigate. Having found no answer in the field of science, we might turn to religion. Here, our luck is a little better. The world's religions do offer answers, but there are hundreds of religious denominations, each with a different version of the truth. With so many denominations claiming to teach the truth, how are we to know which denomination actually teaches the truth, or even if such a thing as as absolute religious truth even exists? IMO, the only solution to this dilemma is to take a consensus of all the world's religious beliefs, and see which doctrines are held by the greatest number of religious denominations. When the various beliefs are averaged in this manner, the dogmatic doctrines that are held by only a limited number of religions fall out of prominence, leaving only the core beliefs that are held by all religions. Even a belief in the existence of a being known as God is not held by all religions, but one belief is held by virtually every religion on earth, and this belief is that a person's physical existence on earth represents only a small part of that person's total being. This is the most universal teaching of the world's religions, and also where the split between science and religion originates. Religion claims that a person is more than his body; science claims that a person is defined by his physical body and its behavior alone. If an individual extends beyond the spacetime limits of his physical body, then that extended part of the individual's existence must lie beyond the range of the physical senses. If it did not, there would be no mystery. One aspect of the spiritual nature of man therefore comprises the transcendent nature of the spiritual parts of both the individual and the universe. Perhaps the greatest philosophical debate of all time concerns the nature of mind vs. the nature of matter. This dichotomy appears in many forms. Body-soul, mind-matter, subjective-objective, real-imaginary. As it is currently argued, the question of which is real -- mind or matter -- will never be answered, for mind and matter are different aspects of the same thing. Therefore, another aspect of spirituality is the direct realization that subjective experience and objective experience are in fact two different aspects of the same thing. The most incredible result of this view of the subjective and objective worlds is that the individual must be considered as one with the universe. This does not mean that the individual exists as an object in the universe; it means that each and every individual *is* the universe. At the spiritual level, the universe and the individual are one and the same. It follows of necessity that at the spiritual level all individuals are one and the same. What we do to others, we do to ourselves. This realization of the unity of all individual beings with the universe is yet another aspect of spirituality. At this time I'll cut it short. The main point of today's discussion is that true spirituality requires a transcendent reality. Without this, there is no spirituality. An understanding of the principles of science does not necessarily require a rejection of the idea of real spiritual worlds. Since science does not concern itself with the spiritual, no proof need be given of spiritual reality. I've got far more to say on the topic of spirituality. I'll return again tomorrow with perhaps more enlightenment or, (depending on one's point of view), perhaps more nonsense. With the fractal cats worrying me for their late snack, it's time to shutter the fractal shoppe and call it a night. Until next time, take care, and perhaps a fractal is as close to the spiritual as one can reach through the senses alone. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Emulsion { ; time=0:04:43.30 SF5 on a P200
; Version 2000 Patchlevel 8
reset=2000 type=formula formulafile=plusmin.frm
formulaname=MandelPMnew passes=1
center-mag=-7.40285102940337700/-0.32273404088181770\
/177.6565/1/-62.5 params=2.39/0.7/0/0/0/0
float=y maxiter=3000 bailout=25 inside=0
symmetry=xaxis periodicity=10
colors=000g_W<45>jjsjjsjjt<2>kkukkvkmv<2>kpxkrxkqyzt\
ykozwpzjlyrmxhjwokwgivjhuegu<38>DDVCCUCCT<2>99R99RAA\
S<22>SDTTETUET<2>WETXETWDS<35>aJWaJWaKW<3>aKWdNYdNYb\
KX<12>cMYdNYdNY<3>dNYA9G5AH<20>OHQPHRQIR<3>UJTeWOeWO\
<14>g_W
}
frm:MandelPMnew {; Jim Muth
z=p2+10^(-100),
c=pixel+(p3)
a=real(p1)+1, b=imag(p1):
z=a*((-z)^b+z^b)+c,
|z| <= 250
}
END 20.0 PAR-FORMULA FILE==================================
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