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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Sometimes I enter parameters into the M-Mix4 formula without thinking, simply letting my fingers go where they may. In today's case my fingers became stuck once again on the '1' key, and tapped out a fractal filled with interesting places to explore. The parent fractal is a hugely bloated crescent-shaped thing filled with chaos, which can be seen in its entirety only after several out-zooms have been made. But despite the overall chaos, a relatively small area of smooth circular bands lies near the origin, with a Mandeloid just to the north. The smooth bands and chaos come together in the East Valley of this Mandeloid, forming the most interesting area of the entire fractal. Today's scene lies in this East Valley, where the smoothness begins breaking down into chaos. I have named the image "Curlers". (Have I used this name before?) The curly things filling the image remind me of those fantastic creatures that appear in certain of Escher's pictures. These curious creatures can curl themselves into balls and quickly roll to wherever they want to go in the impossible worlds conjured up by Escher's imagination. I rated the image at a much-above-average 8. The average in this case is the average worth of the typical hastily constructed FOTD image, not those carefully-crafted images that fractal artists have spent weeks or months in creating. The average FOTD image, by its nature, is a quickie. I rarely spend more than 1 to 2 hours on the entire task of finding and rendering the image, and composing the discussion. Today's image renders in 8 minutes. This is fast enough for those who prefer to render their own images, and slow enough to make the download the more efficient choice. The download may be found at: The fractal weather was actually quite pleasant here at Fractal Central on Wednesday, as a chinook wind from the west raised the temperature to 48F 9C and melted the remaining snow, permitting the dynamic duo a brief romp in the yard, if sitting and looking around can be considered romping that is. Today will be even warmer, but before I can even think of the pleasant day outdoors, I must get some work finished. So until next time, take care, and whatever is a chinook? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Curlers-2 { ; time=0:08:05.82--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.64012469245893500/+1.044967891978891\
00/6.066313e+007/1/-130/-3.89582091792489704e-005
params=1/1.1/-1/-1.11/-0.11/0 float=y maxiter=1100
inside=0 logmap=155 periodicity=10
colors=000H0OI0eJ0dK0cL0bM0aN0`O0_O2ZP3YP4XP5WQ5VQ\
6UQ7TQ7SR8QR9ORAMSAKSBISCGSCFWHEZLEbPDeTDhXCl`CodB\
shBvlAypAwl9vh8ud8t`7sY7rU6qQ6pM5oI4nF4mB3l73k32j0\
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wbXyaWrcWkeWdgWYiWRkUThTVeRXbQZ`O`YNaVLcSKeQJgNHiK\
GjHElFDnCBp9Ar69s4IrVRrtVonZmibkdfhZjfUndPraJv_EzY\
9sUFlQKeMPZIUSE_LAdE6i82nG9bNGRUNF`T4YV7WWAUXCRYFP\
ZIN_KL`NIbQGcSEdVCeY9f_7gb5he3ig9dfF`fLXeRTeXPdbLd\
hHcmDcnHboLbpPaqTaqXar``sc`tg_tk_uo_vsZwwZwzZorXhj\
W`bUUVTMNRFFQKHROJRSLSXNS`PTdRThTTiURiUQiVOiVNiVLj\
WKjWIjWHjXGjXEkYDkYBkYAkZ8kZ7kZ6jXAiVDhTGgRJfPMfOP\
eMSdKVcIZbGabFdaDg`Bj_9mZ7pZ6saBtcFtfJthNujRumWuo_\
uqcvtgvvkvxovsnrnnojnleni`neXnbSm_OmXJmTEmQAmN5mK1\
mH2jH2gH2dH2aH2ZH2WH2TH2QH2NH2KH2HH2EH5GK7HMAIPCJR\
EKTHMWJNYLO_OPbQQdSRfTTdTVcUXaUZ`V`ZVbYWdWWfVXhTYR\
9ZS8_T8`V7aW6bX6`ZBZ_FY`J }
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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times.
