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Fractal of the Day
by Jim Muth
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Fractal visionaries: Happy Solstice! This, after all, is what the season is really about. In the Northern Hemisphere it's the shortest day of the year; in the Southern Hemisphere it's the longest day of the year; at the equator it's just another 12-hour day; while at the North Pole it's the middle of the six-month-long night, and at the South Pole it's high noon of the six-month-long day. Here at coordinates 39 north-77 west, the sun sets at 4:45pm, which is not too bad when one considers places like Norway and Sweden, which receive almost no sunlight at all at this time of year. But the shortage of sunlight certainly does not imply a shortage of fractals. Today's fractal is ample proof of this. I've named it "The Lost Midget" because, like yesterday's FOTD, (which BTW was wrongly dated 19-12), it illustrates one of those obscure midgets that instead of actually existing, has merely a tendency to exist. I chose this particular midget because it best illustrates the effect of a ghostly something that is not really there. The formula is a generalized one of the form, (Z^n+C)+(C^n+Z). It is one of an experimental series that I worked up a few months back and then laid aside. I've actually got versions of this formula that draw all six perpendicular planes. (I do this with most all my formulas.) Some of the odd planes of this series are most unusual, so expect to be seeing more of them in the near future. The image has been posted at 640x480 resolution to a.b.p.f. and a.f.p., and to Paul's web site at: Tomorrow will bring a longer (or shorter) day and a new fractal. At this time, I can't say what I'll decide on, but what ever it is, it will be interesting. So until then, take care and never choose a fractal when you play charade. Jim Muth jamth@mindspring.com |
START FORMULA===================================================
MandelbrotZC {; Jim Muth
z=p1, c=pixel:
z=real(p2)*(z^imag(p2)+c)+real(p3)*(c^imag(p3)+z),
|z| <= 100
}
END FORMULA=====================================================
START PARAMETER FILE============================================
lostmidg { ; 7 min, 486-100, 640x480
reset=1960 type=formula formulafile=test.frm
formulaname=MandelbrotZC passes=1
center-mag=-0.601331/1.52656e-016/31.61269
params=1.26/0/0.5/-2/0.5/1 float=y maxiter=100 bailout=25
inside=bof60 logmap=yes symmetry=xaxis periodicity=10
colors=000i`2Uc3TAmLIQYA_THROQJzKBuCAzU0wHSzm0VQWzUyKZetLBkK\
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}
END PARAMETER FILE==============================================
START 19.6 FILE=================================================
lostmidg { ; 7 min, 486-100, 640x480
reset=1960 type=formula formulafile=test.frm
formulaname=MandelbrotZC passes=1
center-mag=-0.601331/1.52656e-016/31.61269
params=1.26/0/0.5/-2/0.5/1 float=y maxiter=100 bailout=25
inside=bof60 logmap=yes symmetry=xaxis periodicity=10
colors=000i`2Uc3TAmLIQYA_THROQJzKBuCAzU0wHSzm0VQWzUyKZetLBkK\
B_F8QB5KA50hz<6>0hzcA8SN6Hb4MQ6RD8WAA_ACkAXwAp3D0aH4<2>RBwSU\
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AEb6FFvETV`J8<2>J`4NhA<2>Gf4UAzMOXsRy<2>ObHAA`CEKyNtaXU8KBBW\
7Je6Gf4WMy<2>IaHkWa0F37T3dK1<2>Ka3cGyRUWiAwpAxfAiXGWNUH
}
frm:MandelbrotZC {; Jim Muth
z=p1, c=pixel:
z=real(p2)*(z^imag(p2)+c)+real(p3)*(c^imag(p3)+z),
|z| <= 100
}
END 19.6 FILE===================================================
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times.
