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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is of a type that I rather enjoy exploring -- chaotic, yet filled with just enough patches of order and theme-sections to make it interesting. I named the image "Semi-Chaos" mostly as a description. The midget in today's image is of the order 1.618..., and, for a change, is not at the dead center of the frame. Actually, the midget is an added attraction, the main interest lying in the fragmentary elements scattered throughout the scene. Since I find only minor artistic merit in the image, and only a modicum of math interest, I could rate it no higher than a 4. But it's still worth a look, if only to see what a Z^1.618+C Mandeloid midget looks like. The MandelbrotBC formula, which is rather a committee project, once again did the work of rendering the image. The render was completed in 13-1/2 minutes on a 200mhz Pentium. The GIF image, already rendered, will soon be available on the Web at: The all-important fractal weather was quite pleasant today. The cats approved of the warm sunshine and temperature of 77F (25C), and showed their approval by sleeping on the porch most of the afternoon. While searching this evening for today's fractal, my mind drifted into heavy philosophical speculation, and I pondered about gravity and dark matter. The problem is that the outer parts of the galaxies are rotating too fast to be caused by the gravity created by the visible matter of the galaxies. To account for this discrepancy, astronomers have hypothesized that the galaxies are filled with large amounts of undetectable material they have named dark matter, and this unseen material is causing the excess gravitational acceleration. But this explanation is not satisfactory, since if the matter cannot be detected, it will be most difficult if not impossible to confirm its existence. There may be another possible way of accounting for the excess rotational velocity, and this is to assume that, like so many other natural phenomena, the Newtonian law of gravity is valid only within a limited range, which includes our scale of experience in everyday life, as well as the solar system. But perhaps, beyond this scale, gravity is quantized, and there is a minimum possible gravitational acceleration. If this is the case, then the outer parts of the galaxies would be subject to this minimum acceleration, which, being greater than the Newtonian laws of gravity would produce, would cause the excess velocities observed in the outer parts of the galaxies. I'll not speculate on how this might affect the ultimate fate of the universe. Since this alternate explanation is so obvious, it must have already been thought of by many astronomers, and probably discarded because it contains a fatal flaw. But it did supply me an hour or so of diversion while working on a dull routine job. Perhaps I'll continue this line of speculation on the Philofractal list in the next FOTD. I now see that it's post time, so until tomorrow, take care, and could the big bang turn into a big bust? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Semi-Chaos { ; time=0:13:37.34--SF5 on a P200
reset=2001 type=formula formulafile=semikaos.par
formulaname=MandelbrotBC passes=1
center-mag=-0.501937/-0.59952/582.5136/1/49.999
params=1.618034/0/122/0 float=y maxiter=30000
inside=0 logmap=145 periodicity=10
colors=00050U4DU2DU0FU0FU00U05U0AU0Fc5KmCPpKVnR_kY\
didiekndss`zy_zzWzzVzzSzzPzzNzzMzwKzsIzpHzlFzgCwdA\
u`9qY7pS5lP4kM2gH0eD0bA0`70Y20W00S00P00R00R00R00R0\
0R00R00R00R00R00R00R00R00R00R00R00S00S00S00S00S00S\
00S00S00S00S00S20S20S20S22S42S42V44V44V44V55V55V55\
V57V77V77V79V79V99V9AV9AV9AW44V57V79V9AV9CSADSCFSD\
HSDISFKRHNRHPRIRRKSRMVPMWPNYPP_PR`PRbNSeNVgNYiN`kN\
dlMgnMipMkqMls_qseuu`quYnuWguN`wP`wP_wP_wR_wRYyRYy\
SYySWySWyVWzVVzVVzWVzWSzWSzYSzYRzYRz_Rz_Pz_Pz`Pz`P\
z`NzbNzbNzbMzdMzdMzdKzeKzeKzeIzgIzgIzgHziHziHziFzk\
FzkFzkDzlDzlDzlCznCznCznAzpAzpAzs7zq9zqAzsCzsDzsFz\
sHzuIyuKuuMqwNpwPlwRiySeyVbyW`zYYz_Vz`Rz_Kz`MzbNzb\
PzdRzeSzeVzgVziWziYzk_zk`zlbzndzndzpezqgzqizskzslz\
unzwnzwpzyqzzszzuzzwzzwzzszzpzzlzzkzzizzgzzgzzgzzg\
zzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzz\
gzzgzzgzzgzzgzzgzzgzzgzzg
}
frm:MandelbrotBC { ; Formula by Andrew Coppin
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
