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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image pictures a midget that exists 2 turns down the infinite logarithmic spiral of the Z^1.618034 Mandeloid. Or maybe I should say 5.1415926... turns down the spiral, because pi is considered ground level. Studying the midget in the image, I saw things such as an undersea creature swimming through the water, or a sprite floating blithely through the air. I finally chose the happy sprite and named the picture "Spritely Iterated". When it came time to rate the image, I tried to see a 6 or 7 rating. But try as I might, I could find nothing above average in the scene, and had to settle on a fully average rating of 5. Being an armchair philosopher who wonders what is real, (the objective universe is far too simple an answer), I found myself pondering the nature of fractals as I studied today's image. When the image of a fractal is on the screen, that image is objective, but what of the reality behind the image? The Mandelbrot set, for example, is not objective, because it has no physical existence, nor is it totally subjective, since pictures of it can be shared the same as any objective thing. I suppose fractals are best considered mathematical abstractions. But they are not true abstractions in the sense that an attribute such as honor is. True abstractions such as honor cannot be pictured. Fractals might be an entirely new form of reality, or non-reality. I must do far more pondering on this fascinating topic. But regardless of what fractals turn out to be, there is an endless supply of them, and I'll continue searching for them for quite some time to come. Speaking of time, only 4 minutes of it are required to render today's image from the attached parameter file. And less than half that time is required to download the completed GIF image from: The weather Thursday here at F.C. was once again summer-like, with hazy sun, a temperature of 86F 30C, and high humidity. The fractal cats did what they always do on warm summer afternoons -- they slept in their porch chairs until evening, when hunger brought them indoors to cry for food. And if I fail to finish the work now before me, I'll be crying for food before long. So I guess this is the end of the FOTD for another day. Until tomorrow, take care, and are fractals objective, subjective, abstractions, something in between, all of the above, or none of the above? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Spritely_Iterated { ; time=0:04:06.56--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-0.69168091699571880/-0.070955268683603\
58/72.81884/1/-175/-1.26836041669520228e-013
params=1.618034/0/-2/0 float=y maxiter=2500
inside=0 logmap=19 symmetry=none periodicity=0
colors=000C_OFiTIgPLfKOeGRcCU`8XZ4WT5WK6RB7K38PDEU\
NJZXWcfchpmmzzhpeng`lc8k`AiYChUEfRGeOIdKKbHMaEO_AQ\
Z7SY4Tb5Rf5Pk6No6Ls6Jp8Km9KkAKhBKeCLcDL`ELYFLWGLTH\
MQIMOJMLKMJLMNMPRNSVOVZPYbP``M__KZVccVfeVjgVniVqkV\
umVxnWmqWbtWSwWIzXHuYHpZGlZGg_Gb`FZaFUaFQXVHTi9Px1\
Ru5Ts9UpDWnHXkLZiP_fSadWca_d_cfXggVkiSojQrePo`PmWP\
kSPiNPgIOdEOb9O`4OZ0OX4SZ8W`B_bFcdIgfHhaGhXFhTEiOE\
iKDiFCjBBj6Bj2Dh5Eg8FfBGeEHdHIcKJbNKaQL`TM_WNZZOYa\
PXdL`_HdWEhRAlN7pI3tE0wA3nH5eN7YT9PZBHdD8jF0pP6qYC\
qgIqpOqyTquR_qPImN1jO2gP3eQ4bR5`S6YT7WT8RV4MX1M_7M\
aDMdIMfOMiTMkZMncMpiMrnPqiRqeUqaWqXZqT`rP_sQZtQYuQ\
XvQWwQVxQUyQTzQSzQRzQQzQPzQPzQMzfKzvHzcFzLDz3JzAPz\
HVzN`zUfz`lzfhzgezgbzgZzgWzgTzhPzhMzhJzhGzhIzgKzgL\
zgNzgOzfQzfRzfTzgVziWzkYzmZzo`zqazsaztazuXzvTzwRzx\
QzyOzzNzzLzzKzzJzzIzzHzzHzzGzzFzzFzzEzzDzzDzzGzzIz\
zKzzMzzOzzQzzSzzUzzUzzUzz }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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 20.0 PAR-FORMULA FILE==================================
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