October 26, 2010: Blazing Slices | Oct. 25 | Oct. 27 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image is a view of the western part of the Mandelbrot set
rotated so that west is facing up. It is sliced at an angle
rotated 66 degrees toward the Oblate orientation. The image
is actually a scene in the four-dimensional Z^2+C complex known as the
Julibrot, which holds all the perturbed Mandelbrot sets as well as all
the Julia sets.
Over the years I have stumbled upon countless other Julibrot scenes
sliced in odd directions, which look nothing at all like either Julia
or Mandelbrot images. Perhaps I'll use some of these odd
images as FOTD's before too long. They certainly are
interesting enough even though they might not always excel in artistic
worth.
The spurious buds in today's image are neither Julia nor Mandelbrot
things. They exist only at the orientation of today's
image. Changing the P1 or P2 parameters will show how
critical the orientation is.
The name "Blazing Slices" has no connection to an old western comedy
movie. It refers to the fiery colors I intentionally gave the
image.
The calculation time of 10 seconds makes even a 5-rated image such as
today's a bargain.
I made a big mistake Monday afternoon when I caught FL watching one of
those mushy latin soap operas and asked her what the show was
about. When she described the plot, it went something like
this: `that woman loves that man but he doesn't love her and the woman
he does love doesn't know that he is her brother. This other
woman wants a divorce from her no-good husband, but he has just won a
huge lottery and now she doesn't know what to do about the man she
really loves. This other man loves the first woman but he has
a crippled wife who depends on him.' On and on the convoluted
plot description went until, after a few minutes of trying to fathom
the intricacies, I dozed off. When I jerked to my senses, I
asked FL where does the action fit in. The resulting laughter
made my day.
A fairly pleasant day passed almost un-noticed here at Fractal Central
on Monday. The fractal cats did notice the intermittent
periods of sun and the unseasonably warm temperature of 72F 22C, but
the humans were involved in other things.
The next FOTD will be posted in 24 hours. Until then, take
care, and the golden rule is supposed to work both ways.
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
Blazing_Slices { ;
time=0:00:10.10-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=0/1.10231/\
1.5/2.0709 params=0/66/0/90/-0.75/0/0/0/2/0 float=y
maxiter=450 inside=0 logmap=yes passes=1
colors=00091ZB2_E3`H4aK5bM6cP7cS8cV9cYAc`BccC_fDWj\
ESmFOpFMqEKs9Iv2Jz0KzALzDMvGNsJOpMPpPQpSRpVSpYTp`S\
ocSofSoiRpiRpjQpkQqlQqlPqmPrnOroOroNspNsqNsrMtrMts\
LttLuuLuuKuvKvwJvxJwzKvxJvwJuvJutJtsJtrJspJsoJrnJr\
zJqzJqzJpzJpzJozJozJnzJnzJmzJmzJlzJlzJkzJkzJjzJpzK\
mzJjzJhzIzzzbzzzzzYzzWzzzzzQzzOzzzzzKzzJzzJzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot4 {; 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^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================