Dec. 5, 2014: Threads of Valleys | Dec. 2 | Dec. 8 | 2014 | FOTD Home |
Fractal
visionaries
and enthusiasts:
I am thinking of (but not decided on) putting the FOTD on hiatus until
after the holidays or even until the current social unrest calms down
for good. Well, maybe I'll slip in an occasional image every
few
weeks so those still fascinated with fractals, if any, will not be
thrown into sudden withdrawal.
It's kind of hard to enjoy fractals and fractal math while swimming in
a sea of such unbounded human stupidity and inexcusable
blindness. But, for today at least, we have one more, and I
hope
not the last, venture into the four-dimensional Z^2+C Julibrot.
Today's image is named "Threads of Valleys". This is because
it
has parts of both Seahorse Valley and Scepter Valley in it.
Scepter valley appears as the brilliant short ragged vertical thread on
the left, Seahorse Valley is the longer smoother thread on the
right. A bit of the large minibrot on the main stem of the
M-set
is also visible.
The view is what would be seen if the Mandelbrot set were viewed from
above, filled out in a particular third dimension. The X-axis
of
the image is the real(C) axis of the Julibrot; the Y-axis is the
direction halfway between the imag(Z) and real(Z) axes.
Since I made almost no effort to work on the art aspect, I gave the
image no art rating, leaving it to the interested viewer to apply his
own rating. The math rates an 8 because, even though the math
trick is over a decade old, I still find it fascinating.
The calculation time of 15 seconds simply means that the image is
basically instantaneous. But as always, the web sites can
make
things even simpler.
Lots of clouds, a temperature of 39F +4C and a little light rain made
today one to be forgotten here at Fractal Central. The three
fractal cats had forgotten the day by the time it was an hour
old. The next FOTD will be posted sometime in the future, but
no
promises are implied. Until next time, whenever that might
be,
take care, and can't anyone see what's going on?
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Threads_of_Valleys { ; time=0:00:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=slicejulibrot4 passes=1
center-mag=0.0559808/0/0.83 params=45/90/0/1.965/\
-0.75/0.04/0/0/2/0 float=y maxiter=1500 inside=0
logmap=1 periodicity=6
colors=00004C06D08F0AG1DH2GL3KO4OR5SU6WX7__8bbAeeC\
hhEkkGnnIqqKttMwwiyzkzzmzzozzpzzrzztzzvzzwzzszzozz\
kzzgzpczn_zlWzkSziOzgKzeGzdCzb8z`FwS5t_7p`8l`Ah`Bd\
`zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
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=========================================