November 10, 2010: The Mystical Donut | Nov. 9 | Nov. 11 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Like all images in the month of November, today's image lies in an
unfamiliar slice of the Z^2+C Julibrot. I'll not try to
describe
the location or orientation of the parent-fractal slice, other than
reporting that it is centered on Seahorse Valley and is double-rotated
halfway between the Mandelbrot and Julia orientations. This
is
little help, since in the 4-D Julibrot there are countless orientations
halfway between the M and J directions. Today's scene is
located
on the rudimentary main stem of the parent slice.
I named the image "The Mystical Donut". I know it's a rather
silly name. There is little of a mystical nature in a
donut. But I can't help it if I saw a donut in the image.
Most of the image's detail was created by rendering it with the outside
set to 'real'. The 'imag' and 'summ' options work almost as
well.
The rating of a 7 makes the image worth the minute required to run the
parameter file.
Those with over-qualified machines can hopefully find the
eye-ball-ready image posted to the FOTD web site at:
http://www.Nahee.com/FOTD/
A mixture of sun and clouds prevailed here at Fractal Central on
Tuesday, with the clouds predominating. The temperature of
55F
13C was just a bit too chilly for maximum comfort, though it was about
normal for early November. The fractal cats enjoyed the sun
when
it appeared and sought comfort by the heat when it went behind the
clouds.
My day was average. Isn't that boring? The next
FOTD will
be posted in 24 hours. Until then, take care, and do our egos
exist when we are unconscious?
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
The_Mystical_Donut { ; time=0:01:03.50-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-1.41420407/\
0/724383.1/1.5564/-90/0 params=45/0/-45/0/-0.75/0\
/0/0 float=y maxiter=1400 inside=0 outside=real
colors=000JffIeeIddIccIbbIbaIb`Ib_IbZIbYIbXIbWIbVI\
bUKaTLaSNaROaQQaPSaOTaNVcMXeLYgK_iK`kKdmKhoKmqKrsK\
vs2zz2zzzzzzzzzzzzvuzrw2my2hz2ZoCUeMPVWKLfGApCAzB8\
vB6tB4rB3oB3mA4kA4iA5gA6eA6dA7c97b98a98`99_9AZ9AY8\
BX8BW8CV8CU8DT8DS7ER7EQ7FP7FO7FN7GM7GL7GN7HP7HS7IU\
7IW6IZ6J`6Jb6Je6Kg6Ki6Ll6Ln6Lp6Ms6Mu6Mw8Nv9OuAPtBP\
sCQrDRqERpGSoHTnITmJUmKVlLVkMWjOXiPXhQYgRZfSZeT_dU\
`cV`cSZdQYeOXeMWfJVgHUgFThDRiBQi8Pj6Ok4Nk2Ml0Ll2Nh\
3Od4Pa5QY6RU7SR8TN9UJAVGBWCCX8DY5BaDAeL9iT8l`AmaBm\
bDmcEmdGmeHnfJngKnhMniNnjOnkQolRomTonUooWopXpqZpr_\
psaptbpucpuensflrgkqhipigojfnldlmcknajo_ipZhqXgrWf\
n_djbcffabi`Zm_VpYRtXOwWNtVMqVLoVKlVJjUIgUHeUGbUF_\
UEYTDVTCTTBQTAOTCPUDQUERUFSUGTUHUVIVVJWVKXVLYVNZWO\
_WP`WQaWRbWScXTdXUeXVfXWgXVeUVcSVbQV`OV_MVYKUXIUVG\
UUEUSCURAUP8UO6SSDQWKP_QNcXMgbKkiJnoKnpKnpKnpKnpKn\
oKnnKmmKllKkkKjjKiiJhhJgg }
frm:SliceJulibrot2 {; 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================