March 16, 2015: Fractals-101 | Feb. 20 | 2015 | FOTD Home |
Fractal
visionaries
and enthusiasts:
I have been pretty silent lately but I am certainly still
here.
Though today's image is nothing new, it shows that between my more
artistic efforts I still find time to check into the world of
fractals. And don't give up hope. Some of my latest
efforts
should soon be worth posting on the web sites.
If the Mandelbrot set is the mother of all Z^2+C fractals, then the
Julibrot is the grandmother, for it is the four-dimensional
superfractal that contains the Mandelbrot set as a single
two-dimensional slice.
Today's image shows an undistorted view of a different slice of this
Julibrot, sliced in a totally new orientation, with the vertical
direction the imaginary C axis and the horizontal direction the real Z
axis. I call this orientation the Oblate direction, though
this
is totally unofficial. The image slices through the M-set at
the
point -0.8 on the real C axis, just beyond Seahorse Valley.
I have named the image "Fractals-101" because the 4-D aspect is basic
to so many fractals. I could rate it no higher than a double
6
however because we have been here so often before. The
calculation time is almost instant however, and this is the image's
best point.
The temperature of 52F 11C made up for the limited sun here at Fractal
Central today. Now that the winter to be remembered is
winding
down, and the snow and ice is quickly disappearing, the three fractal
cats are giving more attention to the activity in the outside cat
world. Lida has her eye on a big tough-looking orange tomcat
that
frequents the area, while Jasmine prefers a tuxedo colored
tomcat. Nicholas simply watches the ladies silly behavior
with
aloof detachment, while the fractal people watch all three with
puzzlement.
The next FOTD will be posted, that much is certain, but only the
invisible shadow knows when, and he's not talking. So until
whenever, take care, and everyone should have at least one crazy
conspiracy theory he can believe in without feeling silly.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Fractals-101
{ ; time=very brief
SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrotSqr center-mag=0/0/0.86
params=0/0/90/0/-0.8/0/0/0/0/0 float=y passes=1
maxiter=750 inside=0 symmetry=xyaxis periodicity=6
colors=0004Ct5Et6Gt7It8Kr9MrAOrBQqCSqGUpIWpLXoNYnR\
ZmT_kX`i_`ga`e`adZbdXacQacKabEab8cb7dg6hk5jo4ksDic\
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ezbdzcczcczdbzdazeaze`ze`zf_zfZzgZzgYzgYzhXzhWziWz\
iVziUzjUzjTzkTzkSzlRzlRzl }
frm:SliceJulibrotSqr {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z*z+c
|z|< esc }
END PARAMETER FILE=========================================