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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: It's another very busy day here at Fractal Central, which means another brief FOTD discussion. I view such days with mixed emotions, of course. On the one hand, busy days mean more money to buy a faster fractal-finding machine, but on the other hand, busy days mean little time to actually search for the fractals. Also due to the rush, the continuation of the misadventures on the hypersphere will have to wait at least two more days. Today's fractal, which takes 13 minutes to render, took about 1/2 hour to find. This is about the average time that passes between going into fractal mode and actually finding the midget of the day. To this time must be added the render time of the image. Luckily, I can write the discussion on a separate machine. The formula that created today's image takes 10 parts of 1/Z and subtracts one part of Z before adding 1/C. The resulting parent fractal appears as a half-obscured Mandeloid standing on its nose. The midget in today's image is located in a spiral on the left shore of the East Valley of the Mandeloid, which in today's case is actually a North Valley. The elements of the spiral are unusually rope-like, inspiring the name "Threads of Infinity". The name also could have been inspired by the name of an old TV program about fractals, which is titled "Colors of Infinity". The image rates a 6, and renders in 13 minutes. The GIF image downloads in only one minute. The image may be found at the URL's: The fractal weather today was very summer-like, with warm sun and a temperature of 83F 28C. The fractal cats, who have been quarreling lately, enjoyed an afternoon in the yard, and actually managed to get through the entire afternoon without getting into a fight. And I'm about to 'enjoy' a busy day, so until next FOTD, take care, and the less you try to make sense of things, the more sense they'll make. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
ThreadsOf_Infinity { ; time=0:13:19.83--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.00007793807533362/+0.112392194825511\
90/5.776346e+008/1/22.5000000881690916/-2.05411887\
214956845e-007 params=10/-1/-1/1/0/0 float=y
maxiter=1200 inside=0 logmap=178
colors=0000JdTWYegThfMldHpcAsc5ig6`j6VgCOdHIbMC`Q5\
ZV0W`0Te0Si0Vf1Xd2_a9``FbZLbYQcXXdVadUhfTmgSsgSh_U\
YTXONZDG`CGXCGUCGQCGNCGJCGHCGDCGACG6CG3CG0CG0BL0BR\
0BW0B`0Bf0Bk0Bp0Bv0By0By0By0Dy0Gx0Is1Ll6OfCQ`HTVMW\
OSYJX`Caa7eeChhGikKjmOlpSmtWpw_qxcrxgtxkuxjttjtojt\
ijtdjt_jtVjtPhrKhrFhr9hr4hr0hr0hr0fp2dn6clB`jD_hHZ\
fLXePVbTTaWSZ_PYcOVgNUiLTkNQlNNlOMmOJmPIoPFoREpRCp\
SAqS8qT6sT3uV2xV0xX0x_3xW9xPDwOIsNMpKSpJVpH`oGdoFi\
oEmhCeaCYXBQQBIK9AF92880280B70I73Q7AY7Id7Pl7Xt7bx7\
jx7qxClxGfxKbxOYxTUxXPx`LxdFxhCxcFwZIsTLmONiJQdET`\
BVWEYSG`PJbMLeKOhMRjPTmSWpW_rX`rYbu_cu`duafucgudhj\
ejagkShlIimNkoJlpHmqEosApt8qv5sw1tw0wv0xv0xt0xt0xq\
0up1qm3ml6ij9ehCafEYdHVbJQ`MO_PQ_ST_UW_XY_Z__aa_dd\
_fg_ih_lk_nm_qp_tq_ulZuhZud_u``uXbuScuSduSfuSguShu\
TjuVkuWluXmuYou_pu`quasuctudvudvudvudvudvudvudvudv\
udvudvudvuevugvuhvuivukvu
}
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.
