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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I have before me the May '04 issue of 'Scientific American' magazine, which arrived in the mail yesterday. This magazine features articles of scientific interest that have been watered down and stripped of most mathematics so that they can be understood by the average educated person. The cover story is titled 'The Time Before Time', and proposes that time did not start with the so-called 'big bang', but might stretch backward forever into the past. If this is so, then time will never end. If an end to time were possible, it would already have happened, and we would not be here wondering about the start and end of time. There is something strange about time. In a way it is even more strange than space. To imagine a limit to time is as impossible as imagining it going on forever. I suspect that something is wrong with the questions we ask about time. Perhaps, instead of wondering whether time is limited or limitless, we should be wondering whether time is truly as objective as we assume. Our universe is four-dimensional. We know this. But why do we perceive one of the dimensions in such a different way? I have no answers, only ideas without proof, which some will agree with and others disagree with. But one thing certain is that the task of rendering of today's image has a very short extent in the space-time dimension -- 12-million miles to be almost exact. This distance seems long only because we compare it to our immediate surroundings. When compared to the size of our galaxy, 12-million miles is like an atom in a baseball. I could rate today's image no higher than a 6. It is more a demonstration of the outside=real option than a fractal discovery. The parent fractal is an indescribable thing created by combining Z^(-2) with Z^(-4) and adding (1/C). Today's image lies on a filament at the northwest edge of this parent. I named the image "Fractoid" a nonsense word that has a nice sound to it. Perhaps the best feature of the image is its very short render time of one minute, which raises the overall value to a huge 566. This value will not be lost if the image is downloaded from: Tuesday was fair enough here at Fractal Central. The cats did not notice the blue skies and puffy white clouds, though they did enjoy the sun and temperature of 66F 19C. A rain squall arose in the evening, but by then the duo was safely indoors. Today is starting sunny but chilly. For me the day is starting with work to be done. Only then can I tackle the world of fractals. Until next time, take care, and never forget that FOTD accuracy is not guaranteed. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Fractoid { ; time=0:01:04.10--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-2.10780498607015700/+0.387334621764656\
80/3984544/1/-145/5.90356517361084743e-006
params=1/-2/0.5/-4/0/0 float=y maxiter=300 inside=0
outside=real periodicity=10
colors=000UM8zQ9zUAzYCzaDzeEwaHuYKrUMpRPmNRkJUiGWk\
KZlN`nQboUdqXgr_isckufmvipxmryptzsvvpusmupkumhujfu\
fcucau`ZuYWtVUtRRtOPtLMtIKtFHtCFtFIpILlKOiNQePTaSW\
ZUYVX`R_cOafKdhGfkDin9kp6gm9dkB`hDYfFVcHRaKOZMKXOH\
UQESSHRVJQXLPZNO`QNcSMeULgWLiXPfYSdZVb_Z`_aY`dWahU\
bkSbmQVmLNmGGmB8m61m1KmDbmPtm_om`kn`gp`cr`ZtaVvaRx\
aNwaKwSIwIGw8EwACwBBwC9wD7wE6wF7wG7wH8wH8wI9wI9wJ9\
wKAwKAwLBwLBwMBwMEwJHwGJwILwKNwMPwORwQTwRVuTWsVYqX\
_oZan_coaepcgreisgjthkrglqgmofnnfolepkeqidrhdsfcte\
cucbvbbw`ax_ayY`yX`rZck`edbhYdjRelSfjSfhTgfTgdUgbU\
h`VhZViXWhVWgTXfRXePXdO_cVbc`dcfbcd`cbZc`Xc_VcYTcW\
ScVQcTOcRMcQKcOIcMHcLLcKOcJRcIVcIYcH`cGccFgcFjcEmc\
DpcDgcHZcKRcNIcR9bU1eX3eW5eW7eV9eVBeVDeUFeUGeUFdRE\
dPDdNDdKCcIBcGAcDAcB9b98b67b47b28d49e5Af6Bg8Bh9CiA\
DjBEkDFlEFmFGnHHoIIpJIqKJhOK`SLaWMb_NccOcgQceRcdTc\
bUc`_cJXcHVcFScCQcANc8Lc6 }
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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