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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal continues the theme of the past 3 fractals. We combine portions of Z^(-1.7) and Z^(-1.7), and add (1/C) to get a many-bayed parent Mandeloid with a separate ring of chaos lying some distance to the north. Today's scene lies in this outlying ring of chaos rather than in the main body of the fractal itself. But today's image is an 'evaporated' one, in which all 'outside' parts have shrunk until they vanished, so speaking of bays and outlying areas of chaos makes little sense. The escape radius has been raised so high that the parent fractal has been reduced to a sea of trapped points. Luckily, these points do interesting things in their confinement, which can be revealed by rendering the scene with the inside set to 'bof61'. The trapped points that make up today's image remind me of a seasonal wreath. I named the image "Iterative Wreaths", needing no reason at all for using the plural. The rating of 7 is high enough to justify the brief 2 minutes required to render the image from the included parameter file. The image may also be seen by downloading it from: Friday was another routine day here at Fractal Central, both with the weather and the activity of the fractal cats. The pleasant winter sun and temperature of 54F 12C was just enough to give the cats a couple hours in the yard. When evening came the duo was ready to settle for the night. Today is starting foggy. We'll see what develops. It's now time to wrap up the little work yet to be done and enjoy a day with not much else to do but relax. Between bouts of relaxation, I'll find the fractal that will appear as tomorrow's FOTD. Until next time, take care, and take time out to ponder a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Iterative_Wreaths { ; time=0:02:05.34--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.12781826180191500/+3.156480392217424\
00/288207.2/1/152.5/-1.82667648160328433e-008
params=1.7/-7.1/7.1/-1.7/0/1e+100 float=y
maxiter=1200 inside=bof61 outside=tdis periodicity=10
colors=000ARHDUIFWIIYJK`JMbKPdKRgLUiLWkMZnM`pNbrN`\
bHZOCX97WFDWKIWQOWVTW_ZVecVjiVpnVuwhzz00ASP9RU9PX9\
Oc9Ng91KG4TF7`hAiDCqDFzEIkELhENeFQbFT_FVXGYUG`RGbO\
HeLHhIHjFImCIp9Ir7Ir8Ks9MtAOuBQvCSvDUwEWxFYyG_zHaz\
HbYJM6L55K25J07M39P5AS72Hp2Hqdqhfrfgsdhtciuaju`lvZ\
mwXnxWoyUpyTmvRjsPgpNdnMakK_hIXfGUcFR`DOZBMW9JT8GR\
6DO4AL28J17M47O66R96TB6WE5YG5`J5bL4eN4gQ3jS3lV3oX2\
q_2ta2vc7uaCt`Gs_LrYPqXUpWZoUbnTgmSklQpkPtkOsjQrjR\
rjSqjTpjUpjVojWnjYnjZmj_lj`ljakjbkjchhaff_cdYacX_a\
VX_TVYSTXQpGXlFZiDafCcbBf_9hX8kT6mQ5pN4rPCYSGUUKRW\
NOYRL_UIbYEdaBfd8hh5jk2dj9ZiFTiLNhRHhXVkehmnYfhN`b\
CVX1PR6VSB_TFdTKjUPoVTtVVrTWqSXpQYoPZnO_mM`lLbjKci\
IdhHegGffEgeDhdCecGcbK`aNZ`RW_UUZYSYaPXdNWhKVkIUoG\
UrIVnKVjMVgOVcQV`SVXUVUWVQXVNUTOSSOPRPNQPKOQINQFMR\
DLRAJS8IS5HT3GT1FT6cCCaII_OOYTUWZZVcdTijRnpPtuOyrR\
upTrmVnQliKeaFZVASN5MG8PH }
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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