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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today we end the rotation series by viewing two additional Julia sets, which exist very close to the set illustrated in yesterday's FOTD. The first image, 4D-11, shows how rapidly the interior of yesterday's image fills in with brilliant Mandel stuff when imag(C) is lowered slightly from 0.4871 to 0.487. This value places imag(C) within the lower valley of the bud instead of skimming it as was the case in yesterday's Julia set. The second image, 4D-12, shows the undistorted Julia set associated with the center of the period-4 northeast bud. The elegant spirals have degenerated into straight arms, and the Mandel stuff has vanished. In this case, imag(C) has been increased to a value of 0.531, which corresponds to the center of the bud. Since it contains no high-iteration material and can therefore take advantage of periodicity checking, this second image renders in 1/20th the time of the first. The 4D-11 image renders in 2 minutes, the 4D-12 in 6-1/2 seconds. The download of the GIF images takes about the same time and is marginally less work. That download is available on Usenet at: The fractal weather today featured very high winds, with gusts to 56mph (90kph), and a steadily falling temperature from 55F (13C) in the morning to below freezing in the evening. Disliking high winds, the fractal cats spent the day indoors. And I'm about ready to spend what remains of the evening relaxing. When I return tomorrow, I'll have some new M-Mix4 midgets to wonder about. Until then, take care, and stay happy. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
4d-11 { ; time=0:01:59.70 -- SF5 on a P200
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=0.00553216/-0.366921/0.896554
params=90/90/0.36775/0/0.281/0.487 float=y
maxiter=3600 inside=0 logmap=yes
symmetry=none periodicity=10
colors=000BAABWfCAACVfDAAEVfEAAFUfFAAGUfGAAHUfHAAITf\
IAAJTfJAAKSfKAALSfLAAMSfNAANRgOAAORgPAAPQgQAAQQgRAAR\
QgSAASPgTAATPgUAAUOgV9AWOgW9AXOgX8AYNgY8AZNgZ8A_Mg_7\
A`Mg`7AaMga6AbLgb6AcLgc6AdMhd8AdNid9AdOjeAAeQjeCAeRk\
eEFeSlfGKfTmfJPfUnfLUgVngOZgWogRcgYpgShhZqhUjh_rhWlh\
`siZniasi`pibtibricujdtjev<6>kiykiykjz<11>nqznqznrz<\
4>nsznsznsz<31>vzzwzzwzz<2>xzzxzzvyztwzruz<3>jmwhkwf\
iw<2>`cxZbxXbyVbyTby<9>NbzMbzMbz<2>KbzJbzKdz<4>PnzQp\
zRrz<2>UxzVzzWzz<3>Zzz_zz_zz<5>_zz_zz`zz<35>Nzz
}
4d-12 { ; time=0:00:06.67 -- SF5 on a P200
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=0.00553216/-0.366921/0.896554
params=90/90/0.36775/0/0.281/0.531 float=y
maxiter=3600 inside=0 logmap=yes
symmetry=none periodicity=10
colors=000BAABWfCAACVfDAAEVfEAAFUfFAAGUfGAAHUfHAAITf\
IAAJTfJAAKSfKAALSfLAAMSfNAANRgOAAORgPAAPQgQAAQQgRAAR\
QgSAASPgTAATPgUAAUOgV9AWOgW9AXOgX8AYNgY8AZNgZ8A_Mg_7\
A`Mg`7AaMga6AbLgb6AcLgc6AdMhd8AdNid9AdOjeAAeQjeCAeRk\
eEFeSlfGKfTmfJPfUnfLUgVngOZgWogRcgYpgShhZqhUjh_rhWlh\
`siZniasi`pibtibricujdtjev<6>kiykiykjz<11>nqznqznrz<\
4>nsznsznsz<31>vzzwzzwzz<2>xzzxzzvyztwzruz<3>jmwhkwf\
iw<2>`cxZbxXbyVbyTby<9>NbzMbzMbz<2>KbzJbzKdz<4>PnzQp\
zRrz<2>UxzVzzWzz<3>Zzz_zz_zz<5>_zz_zz`zz<35>Nzz
}
frm:multirot-XY-ZW {; draws 6 planes and many rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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times.
