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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: WARNING -- I went beyond the topic in today's discussion, as I occasionally do. The discussion is rambling and rather philosophical. Those who have a 'knee-jerk' reaction to philosophy or mysticism should move on directly to the image and spare their knees. Depending on where the observer is located, today is either the shortest or longest day of the year. For those living on the equator however, where all days are 12 hours long, it is just another 12-hour day, though it is still one of the two days of the year with the lowest maximum sun angle. On a special astronomical day such as today, fractals are just as real or unreal as on any other day. The position of the sun has no connection to the world of fractals. This much everyone can agree on. But do other universes exist where such a connection might be possible? After all, the name of today's image is "Otherworld Fractal", and I gave it this name because it is unlike anything that might be seen in our familiar version of the 'real' world. In the naive days of my youth, I was certain that there is only one real world and that world was the one I had learned to construct from the images I observed through my senses. Those who thought otherwise were confused and superstitious. True, I realized that my senses could detect only a tiny part of that real world, but there was still only one real outer world, and that world was the ultimate reality, which was out there whether anyone was around to observe it or not. That was when I was young and naive. I am no longer young, though I am still rather naive, (aren't we all), but I am not so naive as to believe that anything such as an ultimate reality can exist unless one is referring to the idea known as God. When one truly knows God, all questions about creation and existence become non-questions. When one asks why God created the universe, or where God came from, or even what happens to people after they die, then that person does not truly know the nature of reality. When one asks, or even wonders about such things, that person is displaying his ignorance about both himself and the world he assumes he exists in. When one flees from such questions into the comfortable and easy-to-comprehend world of Atheism, that person is merely showing the arrogance that conceals his fear of the unknown. I know this because I was once there. When one realizes that God is an idea, yet uses this fact as evidence that there is no God, that person is closer to the truth. When one realizes that the physical universe is also an idea, that person is closer still. . . . . . . to be continued . . . perhaps . . . Just imagine it -- all this off-topic stuff came about because I had the thought that today's image is a scene that could never be observed anywhere in the universe as we know it. But it very easily could exist in the world of fractals, especially the world created by the formula Z^(1.1)+C. The rating of a 6 is about what the image is worth. Its overall value could be anything, but calculates at a 90. The most convenient way to see the otherworldly image is to download it from the FOTD web site at: With a temperature of only 19F -7C, Monday was far too cold here at Fractal Central for the dynamic duo to go outside. But they spent several hours on their shelf by the window, watching the chilled starlings huddle around openings of the neighborhood chimneys to keep warm. A surprisingly small serving of tuna was needed in the evening to make the duo happy. This morning is starting less cold, but still far from warm. We'll see how the duo adjusts. For me it looks like another in the nearly endless string of similar days of work before fractals. The next FOTD will appear right here in 24 hours. Until then, take care, and be of good cheer at this time of year. Save the mysteries for next year. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Otherworld_Fractal { ; time=0:06:40.57--SF6 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1
center-mag=-2.14292936172586400/+0.027868278465541\
99/374.3557/1/7.5/5.92893789619353129e-012
params=1.1/0/-28.3/0 float=y maxiter=500
inside=255 logmap=77 periodicity=10
colors=000K3HL4IM4JN5KO5LP6MQ6NR7OS4PT7QU9RVCSWETX\
GUYJVZLW_OU`QTaSTbVTcXSd_SeaSfcRgfPhhOikNjmMkoKnrJ\
qtIvyIswHqvHntGlsGirFgpFfoEdnEclDakD`jCZhCYgAXfFVd\
KUcPSbURaZP`cO_cNZcLZcKZcIZcHZcFZcEZcBZcCZcDZcEZcF\
ZcFZcGZcHZcIZdIZeJZfKZgLZhLZiMZjNZkOZlPZmPZnQZoRZp\
SZqSZrTZsUZtVZuVZvWZzXZxYZyZZzZZz_Zz`ZzaZzaZzbZzcZ\
zd_zd_ze_zf_zg_zh_zi_zh_zg_zg_zf_ze_zd_zd_zc_zb_za\
_za_z`_z__zZ_zZ_zY_zX_zX_zW_zV_zU_zU_zT_zS_zR_zR`z\
Q_zP`zO`zO`zN`zM`zL`zL`zK`zJ`zJ_zI_zH_zG_zG_zF_zE_\
zD_zD_zC_zB_zA_zA_z9_z8_z7_z7_z6_z5_z3Zz4_z5_z5_z6\
_z7`z7`z8`z8`z9azAazAazBazBbzCbzDbzDbzEczEczFczGcz\
GdzHdzIdzIdzJezJezKezLezLfzMfzMfzNfzOgzOgzPgzPgzQh\
zRhzRhzShzShzShzShzShzShzShzShzShzShzShzShzShzShzS\
hzShzShzShzShzShzShzShzShzShzShzShzShzThzShzShzShz\
ShzShzRhzRhzRhzRhzRhzQhzQhzQhzQhzQhzPhzPhzPhzPhzPh\
zOhzOhzOhzOhzOhzPhzPhzPhz }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*floor(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| < a }
END PARAMETER FILE=========================================
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times.
