Fractal of the Day
by Jim Muth
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FOTD -- March 10, 2009 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image might be real or it might be an artifact, but whatever it is, it's interesting. I named it "Mandelbrot or Not?" because it might be a real scene in the Hyper-Mandelbrot set, or it might be an artifact of the rather strange HyperMandelbrot2 formula that creates it.
The scene is located on a filament extending from the northeast shore of the main bay of the large minibrot on the main spike of the parent fractal, which is basically a fancy M-set.
The object in the image is a minibrot, or at least it is supposed to be one. And at any distance from the minibrot there is nothing unusual in sight, but as the minibrot is approached, something goes awry. The original shore line of the minibrot has become diffuse and spread into the interior, where it forms something entirely new. I guess the thing in the image is better called a hyperminibrot.
The rating of a 7 seems about right, considering that this type of effect has appeared several times already in FOTD images. The calculation time of 21 seconds is fast enough to make the effort worthwhile. And as always, the finished image is posted on the FOTD web site at:
Partly cloudy skies, brisk winds, and a temperature of 54F 12C made Monday a rather pleasant March day here at Fractal Central -- at least the fractal cats thought so. My day was fair enough -- once the work was out of the way, that is.
I'll post the next FOTD in 24 hours. Until then, take care, and the best is always yet to come.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
Mandelbrot_or_Not? { ; time=0:00:21.44-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=HyperMandelbrot2 inside=0 periodicity=0
center-mag=-1.74593089071/+0.0201490666/328965.8/1\
/-84.44/0 maxiter=15000 outside=real logmap=55
params=0/0/0/0/-4.18/0/1e-015/0 float=y
colors=000k0Ah0Ae0Ab0A_0AX0AV0AR0BO3CN3IQ3NS3TW3SZ\
AXYHXYJWXLWYJXZHXXGYVFZU8ZR2ZWAa_HdcPggWilclpjotrr\
xytmtlbpdSlXHhP6dHBiJGnLKrNZuelwwbZdTANQFPOJQMNSKR\
THWUF_WDcXBgYVdcnbikhjhnketlTmhGfdI`ZKWUMQPOLKQFFR\
AAgBVxCnvLdtTWr`NqhEceOQcYDagKchQdiWejafkhhlnimtjn\
zknrmpknrdptYqvTrpOskKseFt`BtWptporkoqfnpannYmmTml\
OmkKkjGjjCii8hi4gi0ag2Xe4Rc6Mb7H`9BZB6XD1WEATCIRBQ\
OAYM9eJ8mH7oN6pS6qX6ra6tf6uk6vp6wu6zwEzzMzzTzz`zzh\
zzozzlzzizzfzzgz0gz0cz0oz0zz0zz0zzcMzcVzmXxzWcWVhb\
UmhUrkcvvmzzzUXOJ9LQBIXDFcFCjHAmMCpRDsVE7Qd9WYB`SC\
fMEkGFpAl0zSMlzg_m`TmVNmPHmJBmG9mE7zC6z94z73z51z30\
GeiMOPupqgmoUjmNSzMVxLXvK_tJarIdpHznktD`pPQl`KewIf\
sHgonP1GzJGzOGzTzNYzVbzagzbizcjzzjzzkzzkzzkzzlzzlz\
zgzzjzzkzzlzzEzzJzzNzzSzzWzz_OzdKzhbzpRznkzyUzaNzg\
nz`izbezc`zeXzfTzhOziKzkAzBBzGCzLDzQDzUEzZizLjzSkz\
Zlzemzlnzslztkztjzuizuhzv }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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