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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today, I entered parameters into the MandelbrotMix4 formula which produce a grossly oversized parent fractal consisting mostly of filaments that terminate in loops shaped like lima beans. So bloated is this fractal that several complete outzooms are needed before the whole thing fits on the screen. Today's scene lies on one of these filaments, at the point where the filament is about to join its terminating lima bean. And indeed, as is almost always the case, the midget at the center, with its surrounding pattern of filaments and lima beans, reflects the nature of the area of the parent fractal in which it is found. I named the image "The Wine Dark Basin" not to imitate classic literature, but because of the wine-like color of the area surrounding the midget. I emphasized this dark red by edging it with bright green. As a result of the colors, I found myself able to rate the image at an above-average 7 -- quite a come-up from yesterday's hurried 3 rating. A close examination of the image will reveal a slight raggedness along the sharply-defined edges. This is the beginning of loss of resolution, which appears in today's fractal at the relatively low magnitude of 10^9. Breakdown appears at such a low magnitude because the huge size of the parent fractal has shifted the decimal point rather than increased the range of resolution. The parameter file renders in 7-1/2 minutes on my tired old Pentium 200 mhz machine. Compared to the 'good old days' of fractalling, this is fast, but an even faster way of viewing the image is to download it from Paul's web site at: Today (Tuesday) here at Fractal Central, the weather was fall-like, with brisk winds, falling temperatures, tortured clouds, and flurries of drifting leaves. Since we're getting well along into Autumn, such conditions are normal for this part of the world. But the fractal cats don't care about normalcy -- they want comfort. Unfortunately, after trying every door, they found no outdoor comfort today, so they sulked indoors all afternoon. They cheered up temporarily when I shared my junk food with them, but soon resumed their sulky attitudes. If I don't finish the day's tasks, I'll have sulky customers on the phone, and sulky customers are even worse than sulky cats. So I'd best get started. Until next time, take care, and meditate on a fractal mantra. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
TheWineDarkBasin { ; time=0:07:29.89--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=b
center-mag=+4.56646300247574600/+76.52412363434266\
000/1.188253e+009/1/-175/-9.23344662596276011e-005
params=-60/-1.3/-120/-3.1/0/800 float=y
maxiter=1250 inside=255 logmap=246 periodicity=20
colors=000ERJEIJFSKGMLHTMIQNJVOKUPLXQMYPN_OOaMPcKQ\
eIRgHSiNTmTUoZWqcYsi_uoawucwzYquTkpOekJ_fEUa9SYHTR\
PYLWcFci9_n3Wq6Hz92zBA39939C39F2AH2AJ2AL2AN2AP2AS2\
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5fkO_cebdgedhhdjkeknemqenteopbnm`mjZmgXldVkaTkYQjV\
OjSMiPKhMIhJGgGEgJIfMMeOQdRUcTXcW`bYda`h`bk`eo_gsZ\
jwYlzYpjVtVSwGPrNNmUMh`KcgJZmIefFk_CqU9mTDiSGfRKbQ\
N_PQWOUTNXPM`MLcIKfFJjBIm8Hq4Gt1Gw3Ft4Fq6Fn7Fl9FiA\
EfCEcDEaEEZGEWHDTJDRKDOMDLNDIODGQEJSFLUGNWHPXHSZIU\
`JWbKYcK`eLbgMdiNfjNhkLflKemJdnHcnGboFapD`qC_rBZrA\
YkL`dVcYdeRnhQxjSv`UtSWrIYp9_o0am5clAejEgiJihNkfSm\
eWoc`qbdsaiu_mwZrxYvzZzzZzzZzzZzz_zz_zz_zz_zz_zz_z\
z_zz_zz_zzXzzUzzSzzPzzNzzKzzIzzQzzYzz`zzbzzezzgzzj\
zzlzznzzkzzizzgzzdzzbz000
}
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.
