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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yesterday's image demonstrated that the Northeast period-4 bud of the Mandelbrot set exists as an interrupted cylinder in the three-dimensional real(C)-imag(C)-real(Z) slice of the four-dimensional Julibrot. In today's image, which is centered on the same point as yesterday's, we'll rotate the view and observe what happens to the ghost of the bud. The orientation of today's image has been rotated 52 degrees around the Y-axis (imag[C]) toward the Rectangular direction. The slice of the image now cuts the cylinder at an oblique angle, causing the brilliant remnant of the bud to appear as an ellipse. I have done no stretching or skewing; the features of the image appear in their natural undistorted shapes. Though the Mandelbrot bud enlongates in an orderly manner, the banded Julia stuff stretches at random, with no apparent order at all. The same 4-armed spiral convergence still exists within the outline of the Mandelbrot bud, but the arms have undergone a complete change of appearance. In tomorrow's FOTD I'll rotate the image much further, leading to some totally unexpected results. Today's image is once again a very fast one from the parameter file. If the 30 seconds is still too slow, the GIF file of the image may be found at: The fractal weather today was sunny but quite cold, with a temperature of 34F (1C) that kept the cats glued to their sources of heat. And speaking of being glued, I'm going to spend the rest of the evening glued to the TV, watching a junky old movie or two. Until tomorrow, take care, and see you in 24 hours. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
4D-03 { ; time=0:00:37.54 -- SF5 on a P200
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=-1.11022e-016/8.32667e-017/10.4\
1667 params=0/52/0.36775/0/0.281/0.531 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
}
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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