November 20, 2010: Manipulated View | Nov. 19 | Nov. 21 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
In yesterday's image a segment of the classic Mandelbrot shape appears
in the background as the brilliant blue stuff. But the shape is
so distorted that it is almost impossible to recognize the part of the
M-set shape that is showing. In today's image we have taken
yesterday's scene, rotated, twisted, and skewed it until we have
restored the Mandelbrot shape to recognizable familiarity.
Much to our surprise, we find we have cut a slice through the M-set
shape that covers the main period-2 bud, the northwest part of the Main
Bay and the northern period-3 bud. To find the slice, I totally
winged it by eye. It might be possible by complicated
trigonometry to determine the correct anti-distortion
mathematically. It works quite well with simple single rotations,
where all that is required is to enter the cosine or the reciprocal of
the cosine of the angle as the X-magnification factor. But in
yesterday's image, where four angles are involved, the mathematical
method is too complex, at least for my Arithmetic-101 level of
knowledge.
At this point, I am left wondering which version of the same slice is
more correct, yesterday's or today's. The actual Mandelbrot part
of the Julibrot is a 4-D thing, kind of a nest of hypercylinders shaped
like the M-set in the C-plane, but extended to infinity in the
Z-plane. (Don't try to visualize the entire shape, it's
impossible.) This Mandelbrot hypercylinder nest becomes distorted
when it is sliced at an angle, as we did in yesterday's image.
Today's image, which corrects this natural distortion, is actually the
more distorted, and therefore the least correct image. But at the
same time, it is almost impossible to tell our position when viewing
yesterday's image, so I suppose this makes today's image the more
correct one.
All math and almost no artistic value equals no rating. The name
"Manipulated View" tells it like it is. The calculation time of
under 2 seconds is incredibly brief, and should be not be a
factor. The finished image may also be seen on the FOTD web site
at:
http://www.Nahee.com/FOTD/
Conditions here at Fractal Central on Friday were acceptable, with
partly cloudy skies, a temperature of 48F +9C and cats that were fairly
contented. The commercial work was about average, while the FOTD,
is more a curiosity than a work of art. The next FOTD will be
posted in 24 hours. Until then, take care, and try to uncover the
alien plot before we end up on a slave ship to Arcturus.
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
Manipulated_View { ; time=0:00:01.88-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=0.177576/\
-0.440939/0.5850274/0.3595/142.341509490465285/\
-74.8871977088931544 params=152/105/-64/49/-1/0/\
1.118/0 float=y maxiter=1800 inside=0 logmap=yes
symmetry=none periodicity=6
colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\
NJbQKfWKi`KleKngKljKjjKhfKgcKe`Kc_KbZKcYKdXKeXKfXK\
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rzOrzLrzJrzHrzFrzDrzBrzCrzCrzCrzDrzDrzDrzErzErzErz\
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zzNzzMzzLzzKzz6zz7zz8zz8zz9zz9zzAzzAzzBzzBzzCzzCzz\
DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\
z7zz8zz9zzAzzBzzPzzOzzNzz }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================