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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal was found entirely by accident. When I entered today's parameters into the faithful M-Mix4 formula, I expected nothing. What I found was a fractal worthy of being declared FOTD. Those unlikely parameters define the expression -1.3Z^(0.9)-1.3Z^(-0.9)+(1/C), and any fractalist worth their iterations knows that Z^(0.9)+(1/C) gives nothing resembling an interesting image, and the string of blobs created by Z^(-0.9)+(1/C) is little better. But when the two are combined, multiplied by -1.3, and the critical point calculated, a near miracle happens -- a real fractal appears. The parent fractal is a curious 3-lobed distortion of the M-set. Today's scene lies on the north shore of the north lobe. I named the image "Midget with 16 Petals" for the same reason that Brahms named his long-delayed first symphony "Symphony in C minor, No. 1". The name is a pure description. And no, I'm not trying to compare myself to Brahms. After much deep thought, I rated today's effort an average 5, though I feel that the parent fractal has far better images in it. I may check the eastern fringes of the parent fractal for midgets tomorrow. As for viewing the image, the most direct way is to start the parameter file and tend to something else while it's rendering. A second way is to wait 16 hours and go to: Another way to see the image is to visit Paul Lee's web site at: The fractal weather today featured icy roads and cold winds. Of course, the temperature of 28F (-2C) was far too cold for the cats, who passed the day sprawled before the warmest radiator. The always-promised but rarely-delivered philosophy is once again missing. My intentions are good; my accomplishment is not. But I'll try once again tomorrow, and if I fail to deliver enlightening philosophy, I will at least deliver an interesting fractal. Until then, take care, and fractals are here to stay. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
MidgetWith16Petals { ; time=0:11:08.22 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.06646788176226491/+0.17212735246396270\
/3.801586e+009/1/67.5 params=1/0.9/1/-0.9/-2.3/0
float=y maxiter=1600 inside=0 logmap=200 periodicity=9
colors=00080R80Q80O90JB0GD0BE08G02G00I00J00L10N20N40\
XRIOTDIT9BV44V10X00X0xR_sTYnVYiXXdXX_YXV_VQ_VLaVGbTB\
dT6dT1fR0gR0cR1bO9YNITJQOIXJEdEDl99t48z04z02z04z46z9\
6zE8wI9tN9qRBpXDn_D_QINGN86R00V00T00T00T00_9DfJTkViq\
fzxpzznxzlzzlxzkxzkwziwziuzluz<2>qnzskztgzxbzz_zzXzz\
RzzOzzLzzIz<2>zDzzBzz9xx8ww6sw4qt2ns1l<2>n0dl0bl0an0\
_p0_q0_s0Yt0Yt0Yq0_<2>iE_fJ_dOaaTaYYaXbaTgaRkaRibRgd\
RgfQffQfgQdiQbkQbkQalOanO_pOYpOYqTXiOXszzYzz_zz_zzaz\
zaxzbwzbtzbtxdsxdqwfptfnsglqgkqgipiiniglkflkdkkbilag\
l_fnYfnYdpXbpVapTaqR_qQYsOXsz00<4>z00z01z02z04z06z06\
z08z19x2Bw2Dw4Dt4Et6Gs6Iq8Jq8Jp9Ln9NnBOlBOkDQkERiGTg\
IVgJXfLYdN_dOabQbbRdaTf_Vg_XiYYkX_lXanVbpXdqYfs_gtai\
wbixdkzfkzglzilzknzlnznpzppzqqzsqztszwszxtzztzzwzzwz\
zxzzxzzzz<22>zzz
}
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.
