|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Great news! When I checked my e-mailbox earlier this morning, I found not one but two letters informing me that I have just won twelve-million-dollars in a lottery. All I have to do is send my bank account number so that the lottery commission can deposit my winnings in my account. But I must keep my good luck a secret. If the I.R.S. hears of it, they will take over half for taxes. No problem! I am not stupid enough to let the I.R.S. know I am rich. Oh happy day! It's nothing but fractals for me from now on.  Today's image reminds me of a light at the end of a tunnel. My first instinct was to name it "N.D.E.", but on second thought I named it "Cave of Dreams", which can be interpreted to mean anything one wishes. The rating of a 'very good' 7 may be a bit overblown, but the image is at least somewhat above the usual mass of FOTD images, so with not too much stretching, the rating is justified. The image was found in a parent fractal which combines Z^(5) with some negative Z^(-2) before adding (1/C). This parent can hardly be called a fractal. It is more like an oversized scattering of fractal debris -- the remnants of a fractal explosion. But it does hold one very obvious though undersized M-set. This small M-set is surrounded by smaller bits and pieces, and is rotated so that its negative stem trails off to the southeast. The stem is unusual in that it does not come to a definite end, but slowly loses definition, trailing off into nothingness and breaking up into ever more fragmented clouds of fractal stuff. The scene of today's image is located in this cloud of dissipating stem-stuff. The image itself was created by rendering the scene with the outside option set to 'tdis', which colors the points according to how far they travel before passing beyond the escape radius. The effect of light reflecting off the damp walls of a cave was intentionally produced by manipulating the colors. Today's image therefore may be considered more a work of 'fractal-art' than my usual images. The short render time of only 2 minutes makes watching the cave interior emerge on the screen a pleasure. It is almost as much fun visiting one of the FOTD web sites at: Friday was a very average day here at Fractal Central, with a temperature of 61F 16C and enough sun to keep the cats happy. Since the work went smoothly, the fractalist was happy also. Today is starting sunny but notably colder. It remains to be seen whether the cats will approve of midday temperatures in the 40's (on the Fahrenheit scale). Since the evening is due to be clear, I'll probably take an hour or so to watch a lunar eclipse that will start around 8pm this evening. And when the eclipse has ended, I will likely travel to Fractal Land. Until next time, take care, and where is Fractal Land located? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Cave_of_Dreams { ; time=0:02:08.85--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.84707662108601570/-0.077027415795625\
03/4.34485e+011/1/5.4998732086033213/0.00317742443\
842483624 params=1.25/5/-0.3/-2/0/0 float=y
maxiter=600 inside=0 outside=tdis periodicity=10
colors=000Jq_InYHkWGhUFeSEbQD_OCXMAUK9RI8OG7LE6IC5\
FA4C8396264132aLxYJrVHmSFhPEcMCZJAUF8PC7K95F63A315\
0G90E80D70C60A6095084063053042021210juvgqtajsYcqTX\
pPNoPKkQHhPFeQCaQ9ZQ7WUDVYJUaPTdVSh`RlfQolQofOoaMo\
WKoRIoMGoGEoBCo6BnTfmXfm_flbflefkifklfjofjrfiqahpX\
hpSgoNgoIfnDfn8RgyhjzzmzxknwjbviRuhGvfLvdPwcTwaXw_\
`xZdxYhxZlt_fq``maVjbQgcKcdE`e8Yf3QgIPhWUijZjxckrh\
lmmmhnncoohppmqqrrrwssjttYuu_vvbwwexxgyyjzzlzzozzq\
zztzzvzznzzfzzZzzXzzVzzTzzRzzPzzNzzLzzJzzHzzFzzDzz\
Bzz9zz7zz6zz6zz6zz5zz4zz5zz5zz4zz4zz4zz4zz3zz3zz3z\
z2zz2zz2zz2zz1zz1zz1zz0zz0zz0zzzzzjzzVzzFzzozzbzzQ\
zzDzzdzz`zzYzzVzzSzzPzzMzzIzzFzzCzz9zz6zz3zzxzztzz\
qzznzzkzzgzzdzzazzZzzWzzSzzPzzMzzJzzGzzCzz9zz6zz3z\
zLzzJzzIzzGzzFzzDzzCzzAzz9zz7zz6zz4zz3zz1zzTzzQzzO\
zzLzzJzzGzzEzzCzz9zz7zz4zz2zzTzzOzzJzzEzz9zz4zzozz\
gzz`zzTzzMzzEzz7zzfzzczza }
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==================================
|
times.
