Dec. 29, 2012: Faerie Fantasyland | Dec. 28 | Dec. 30 | 2012 | FOTD Home |
Fractal visionaries and enthusiasts:
On
its surface, the
Z^(-2)+C Mandeloid is not much to look at -- little more than a
triangle consisting of flat overlapping disks. The disks can
be
made larger or smaller by changing the escape radius, but this has
little effect on the worth of the fractal.
All is not lost however. When the entire Julibrot is sliced
in
different directions, it shows some aspects that are more
interesting. In today's image I have double rotated the slice
66
and 66 degrees toward the Julia orientation, and rendered it with the
outside parts set to 'real'. In the image, we see that the
flat
disks have become organized into more attractive semi-chaotic
spirals. (The parent fractal actually has buds, but this is a
story for another day.)
I named the image "Faerie Fantasyland". The odd spelling is
kind
of a trendy pseudo-magical way of spelling the word 'fairy', which is
used by those who are into new-age stuff.
The rating of a 7 includes a full point for the smooth GIF coloring,
which I really did put an hour or so of effort into. Without
the
coloring, the underlying scene would rate only a 6.
The image is very fast. It finishes in under one minute on
all
but the oldest and slowest units.
Snow fell all day here at Fractal Central today, while the light winds
and relatively mild temperature of 30F -1C actually made the snow
enjoyable. At post time about 5 inches or 12cm had piled up,
but
it was still falling. I'll give a final report in the next
FOTD. The fractal cat alternated between stretching out on
the
radiator and hunching on the shelf in the southwest window, watching
the snowflakes drift down. The humans took it as easy as
possible, but I am concerned with the sidewalk that will eventually
need to be cleared.
The next FOTD will be posted when it is ready, most likely in 24
hours. Until whenever, take care, and I see that two people
have
been pushed in front of subway trains within a month. These
trains are dangerous. We must do something about the needless
deaths caused by misused subway trains. We must pass tighter
train-control laws to keep subway trains from the hands of those who
would misuse them.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Faerie_Fantasyland { ; time=0:00:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=+1.49344425/\
+0.22623503/210/1/-90/0 params=66/0/66/0/0/0/0/0/\
-2/0 float=y maxiter=1500 inside=0
outside=real periodicity=6
colors=000CbFCcGDcGEcGEcHFcHGcHGcIHcIIcIIcJJcJKdJK\
eKLfKMgKMhLNiLOjLOkNPlNQmOQmPRmQSnQSnSToUUoWUoYVo_\
WoaWocVoeUogToiSokRomQnoQnqRnsRnuRmvQlwRkwRjvRitRg\
sSfqSdoSbnSalT_jTZiTXgTVeTUdUSbUR`UP_UNYVMWVKVVJTV\
IRVJQWJRXJSYKTZLUZMV_NV`OWaPXaQYbSZcT_dU_dV`eWafXb\
gYchZch_di`ejbfkcgkdhlehmfingjnhkoilpjlqkmrmnrnoso\
ptpquqqurrvsswttxuuxvuvututttstsrtrqtqpsposonsnmsm\
lslksjjriirhhrggrffreerddqccqbbqaaq``q__qYZpXYpWXp\
VWpUVpTUpSToRSoQRoPQoOPoNQrNOoNNmNMkNLiNKgNJeNHbNG\
`NFZNEXNDVNCTNAQN9ON8MN7KN6IN5GN4EM6HL8KKAMJCPJESI\
GUHIXGKZGLaFNdEPfDRiCTkCVnBXqAZs9`v9ax9cu9ds9ep9fn\
9gk9hi9if9jd9ka9l_9mY9nV9oT9pQ9qO9rL9sJ9tG9uE8u99v\
CAvFBvIBvKCvNDvQDvSEvVFvYFvYHtYIrYJpYKnYMlYNjYOiZP\
g_Re`ScaTabU_cVZdXXeYVeZTf_RfaPfbNgcMgdKhfIhgGhhEi\
hCig9lgBifDfcFc_H`WJYTLVPNSMPPIRMETJBVG7XD4YB5ZC6Z\
C6_D7_D8`D8`E9aEAaEAaFBbF }
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=========================================