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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Knights of old were brave and strong (puissant). They passed their days roaming the countryside doing good deeds, protecting the weak, defending the kingdom, and hoping for a mystical vision of the holy grail. I have no idea how many knights actually experienced such a vision, but when I saw today's image, it reminded me of a vision of the Mandelbrot set hovering in the sky. With only a moment's consideration, I named the image "Mystical Vision". The formula behind the image, whose parameters I entered at random, produces a reasonably undistorted Mandelbrot set lying in the normal orientation and surrounded by a cloud of disconnected areas of chaos. Today's midget lies in one of these areas located just to the north of the main stem, about 2/3 of the way out to the tip. After a brief moment of thought, I rated the image, with the hook-like features surrounding the midget, at a 6. On second thought, perhaps I should change that to a 6-1/2. The short render time of around 2 minutes takes much of the effort out of running the attached parameter file. No, we'll keep it a 6, because depending on the efficiency of the connection, downloading the GIF image can be even less of a task. The GIF image can be found at: The weather today here at Fractal Central turned just the slightest chilly, with a warm sun, but a temperature that rose only to 57F 14C. The two cats of the fractal variety enjoyed the limited perfection to the utmost of their ability, sleeping several hours in their favorite porch chairs. I've got a bit of work to get done before noon, so I'd best get started on it. But in 24 hours I'll be back with the next in the long string of fractals. Until next time, take care, and I'll see you then. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mystical_Vision { ; time=0:02:15.94--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.41128955306025280/+0.000665120494983\
14/6.366646e+007/1/-137.5/1.2417994603303173e-006
params=-0.4/-2.6/-0.8/2.4/-0.3/525 float=y
maxiter=300 inside=0 logmap=40
colors=0004isBjrIkqPlqVmpanohooopnupnolkiihdeeZbbU\
__KYZBUY2SYCOULKRUJNbHKjCMr8Nz3Or3Ll3Id3GY3DT3AN38\
I35D33KGMRTdYew`ctcaqe_nhYljWimUfoTdkUahUZdVXaVUYW\
RVWPRXMOXKcbLsKSp1ZUHN7XCIYDTZDc_El`EfaEaQXFEoRBAL\
G8GL6AQ55V30Z25U59Q7DMAHICLEFPAHQFOQJVROaRShRWoXPf\
aIYfBQUFK_HNdIQiKSnLVsNYxO_xRbxTexVhxXkx_nxaqxKtxK\
wzKrzKnzKrzKuzKuzKuzMuzOvzQwzSxzUyzWzzYzz_zzazzczz\
czzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzcz\
zczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzc\
zzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczz\
czzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzcz\
zczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzc\
zzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczz\
czzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzcz\
zczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzc\
zzczzczzczzczzczzczzczzcz
}
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.
