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Fractal of the Day
by Jim Muth
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Fractal visionaries: How can I describe today's fractal? Well, to begin, I'll let my imagination run wild. (It won't be difficult; that's my usual mental state.)  Picture yourself alone at night on an alien beach, standing under a sky filled with strange constellations. In the darkness you can hear the alien surf washing gently up the sands and shisshing back out. Out on the methane ocean, strange lights are gently blinking on and off. You have no idea what they are -- this world is supposed to be uninhabited. In the distance to your right, a barely discernible glow like that of a city below the horizon reveals where methane ends and sky begins. Perhaps this planet is not deserted. But as you watch and wonder, the glow increases and spreads, until at last, in its undiminished splendor, its radiance piercing the high clouds, accompanied by the opening of "Thus Spake Zarathustra" the great cosmic bud rises into the sky. Day has come and you are still alone, but those dots that were lights blinking in the night still mar the horizon. . . . OK, so I exaggerated a little! Perhaps today's fractal isn't quite that spectacular, but it's still a striking one, and I feel it's good enough to make it as the FOTD for 22-11. When I saw this image, a sunrise, or budrise in this case, was my first and only impression. The image is a scene in the Z^24-(1.1*Z) figure, sliced halfway between the Mandelbrot and Oblate directions. It is another example of an order-2 object where none should appear. I had intended to post a different formula today, but this particular fractal so struck me that I felt it must be shown at once. And so here it is -- my FOTD for 22-11 -- not my best, but not my worst either. The finished image, which takes 6 minutes on an 80486-DX4, is posted to alt.binaries.pictures.fractals and alt.fractals.pictures and of course to Paul's web site at: Tomorrow, if I find no more irresistable images in the M-O rotation, I'll post an image from the M-R rotation. Until then, take care and put your best fractal forward. Jim Muth jamth@mindspring.com |
START FORMULA======================================================
M-O-rotation {; Jim Muth
; real(p1)=power of Z, imag(p1)=angle of rotation
; p2=parallel planes, p3=rotation point and parallel planes
a=real(p1), b=imag(p1)+.0000000000001,
z=sin(b*.01745329251994)*real(pixel)+p2,
c=cos(b*.01745329251994)*real(pixel)+flip(imag(pixel))+p3:
z=z^a-(1.1*z)+c,
|z| <=25
}
END FORMULA========================================================
START PARAMETER FILE===============================================
budrise { ; 6 min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=minusrot.frm
formulaname=M-O-rotation passes=1
center-mag=1.26462/-3.33067e-016/4.372549/1.454/-90
params=24/44.5/0/0/0/0 float=y maxiter=1200 bailout=100
inside=253 logmap=yes symmetry=xaxis periodicity=10
colors=000A00PF0UF0XG0aE0aI0`H0RG67CL7CN8DN<2>7CR6CP<2>8BKEB\
HKBFJACJ9AJ87H64J75K75H85<2>LC5MD5MD5LE5<2>NE5NF5MF5<25>vL6<\
29>lbhkcjlckmdloel<6>taopaor`o<36>rJzrJzrKx<13>rWjqXiqYhpZgo\
_f<13>ekTelSdmRdmQenP<3>frLfsKgrK<28>et9gz2<4>cmIbzMbzPayS`v\
V_vX<8>deZdcZccX<12>hadzwP7V`7U`
}
END PARAMETER FILE=================================================
START PARAMETER-FORMULA FILE FOR FRACTINT VERSION 19.6=============
budrise { ; 6 min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=minusrot.frm
formulaname=M-O-rotation passes=1
center-mag=1.26462/-3.33067e-016/4.372549/1.454/-90
params=24/44.5/0/0/0/0 float=y maxiter=1200 bailout=100
inside=253 logmap=yes symmetry=xaxis periodicity=10
colors=000A00PF0UF0XG0aE0aI0`H0RG67CL7CN8DN<2>7CR6CP<2>8BKEB\
HKBFJACJ9AJ87H64J75K75H85<2>LC5MD5MD5LE5<2>NE5NF5MF5<25>vL6<\
29>lbhkcjlckmdloel<6>taopaor`o<36>rJzrJzrKx<13>rWjqXiqYhpZgo\
_f<13>ekTelSdmRdmQenP<3>frLfsKgrK<28>et9gz2<4>cmIbzMbzPayS`v\
V_vX<8>deZdcZccX<12>hadzwP7V`7U`
}
frm:M-O-rotation {; Jim Muth
; real(p1)=power of Z, imag(p1)=angle of rotation
; p2=parallel planes, p3=rotation point and parallel planes
a=real(p1), b=imag(p1)+.0000000000001,
z=sin(b*.01745329251994)*real(pixel)+p2,
c=cos(b*.01745329251994)*real(pixel)+flip(imag(pixel))+p3:
z=z^a-(1.1*z)+c,
|z| <=25
}
END 19.6 FILE======================================================
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