|
Fractal of the Day
by Jim Muth
|
|
|
Fractal visionaries and enthusiasts: There's little to say about today's images, which have now been rotated all the way to the Julia orientation. The bridge has now broadened to infinity, so that the entire interior of the scene, and of the entire fractal as well, is in effect filled with a single point. The bridge is no longer visible because we have been skimming it just above the surface. The interior of the fractal is therefore filled with the point just barely above the bottom shoreline of the original period-4 bud. The second image illustrates the entire Julia set. If the real(p3) (or imaginary 'C') parameter were reduced just slightly, the image would fill in with the Mandel stuff of the lower valley of the bud. If it were raised, the spectacular spiral arms would straighten and lose their chaotic extensions. Raising the maxiter would also cause the image to fill in as even higher iteration Mandel stuff becomes visible. With a render time of 5 minutes and 3 minutes, today's images can be viewed more easily by downloading them from the internet. The images are available on Usenet (if you have it) at: With a temperature of 36F (2C) and heavy clouds, today proved unfit for the delicate fractal cats to venture outdoors. They passed the day instead either stretched by the radiator or sitting on their window shelf, watching the birds fly by. We have but two more in the rotation series of images. These final two images will appear tomorrow along with a final few words about rotation in spaces of four dimensions. After that it's back to the wonderland of midgets. I've got a few pretty good ones backed up. Until tomorrow, take care, and know that a fractal at bedtime makes sleep come easier. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
4d-10 { ; time=0:05:12.09 -- SF5 on a P200
; Version 2000 Patchlevel 14
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=-1.11022e-016/8.32667e-017/10.41\
667 params=90/90/0.36775/0/0.281/0.4871 float=y
maxiter=3600 inside=0 logmap=yes
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-10a { ; time=0:02:53.35 -- SF5 on a P200
; Version 2000 Patchlevel 14
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=90/90/0.36775/0/0.281/0.4871 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==================================
|
times.
