December 26, 2011: Seasonal Fantasy | Dec. 24 | Dec. 27 | 2011 | FOTD Home |
Fractal visionaries and enthusiasts:
The
Christmas
activity here at FC yesterday left me with too little time to create a
proper FOTD. But today, we're back up and running with a
remarkable scene in the 4-dimensional Z^2+C Julibrot.
The scene is located in the Scepter Valley area at an angle oriented
halfway between the Mandelbrot and Oblate planes. (The
Mandelbrot
orientation is determined by the real(c) and imag(c) axes; the Oblate,
by the imag(c) and real(z) axes.)
At first glance, the image bears little resemblance to either a
Mandelbrot scene or a Julia scene. This is because it is a
hybrid
scene, half Julia and half Mandelbrot.
Much of the unexpected appearance was created by the outside fill of
'bof61', which is responsible for most of the smoothly colored areas.
The original name I gave to the image was 'Christmas
Fantasy'. I
changed it to "Seasonal Fantasy" to avoid offending the secular
community.
The calculation time of 2 minutes is a fair price for the image.
The weather today was uneventful and rather pleasant for late December,
with partly cloudy skies and a temperature of 45F +7C. As for
the
fractal cats, after a day of getting into trouble with the tree and the
wrappings, they had no energy to worry about the outside
weather.
They took it easy most all day. Their big excitement came
when an
orange tomcat we have named Marmalade passed by, marking the territory
as he went.
The humans spent the day recovering from the day before. The
next
FOTD will be posted in 24 hours. Until then, take care, and
in
the seventh grade, when I asked Sister Mary Thomas why heaven is
invisible, she replied that if we could see heaven, there would be no
need for faith. When I tried to say more, she told me to sit
down
and shut up. Her reply made no sense to me then.
Today,
after a half century, it makes even less sense.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Seasonal_Fantasy { ; time=0:02:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=-0.742221/0/\
16.848/1/-90/0 params=0/0/45/0/-0.75/0/-0.503/0/2/0
passes=t float=y maxiter=1000 inside=bof61
logmap=37 periodicity=0
colors=00030S0E_0E_0E_32R0E_1E_2E_33Q4G_5G_6GY34P8\
KY9KY8KY35N6OY6PY5QY35M7Xi5We5Wb15L4SY3QW2PR25L1LO\
1JL1HK05K0GK0FK0EK05K0DK0CK0BK05K09K08K08K04K06K06\
K05K03J04I03H02G02F02E02D02C02B02A02B02C02702E0250\
2402301201101001001201401602803A04C05E15G05I05K16N\
48Q27T59W6AY8E_BHbDJbGMeIPgLTiNWkR_nWcqXerajwdnzel\
zktzqyzvzzizzszzszzqzzqzzpwzpwznwznwznwznwzjtqjtqj\
tqhtphtogqngqmeqkeqkeqkeqkbohbohbog`of`oe_le_ldZlc\
ZlbZlbZlaWi_Wi_Wi_UiYUiXUgXUgWSgUSgUSgUSgTPeRPeQPe\
QOePOePMbOMbOLbLLbLLbLLeKLbLLbLK_LJ_KIYKIYLHYKGWKG\
WKETIETJERJCRJCRJCPIAPJAOIAOJ8LI8LI8LI6KH6KI6II5II\
5IK5IK5IL5HL5HL4HO4HO5HP4GP4GP4GR3GR4GT4GT3ET3FW3F\
W3EY3EY3DY2E_2D_3Db2Db2Cb2De2Ce2Cg2Bg1Cg2Ci2Bi2Bl2\
Al2Al29o29o08q18o19o29o2Al2Al3Bl4Dl4Di5Ei6Fi7Gi8Hg\
9IgKIgKJeKKeKMeUOeUMbUPbUPbcRacQ_cSYcTWcVUcVSmWQmZ\
OmcMmhKzmIzrGzvEzzCzzAzz8 }
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=========================================