November 7, 2010: Home of the Spiral | Nov. 6 | Nov. 8 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
The lateness of today's image is due to a not-so-surprise antiquing
expedition that arose not-so-unexpectedly on Saturday. But
better
late than never.
Today's FOTD is the parent fractal of yesterday's 'Almighty Spiral'
fractal. The actual spiral that filled yesterday's image lies
humbly at the right edge of today's scene.
Many other spirals fill the upper half of the image, which lies on the
bud side of the Mandelbrot valley that is visible as the two brilliant
wedges jutting across the center of the outer shape. The
lower
half of the image, which is the main-bay side, has no spirals at all.
Today's image is not a Julia set, but it comes very close. It
is
double-rotated 0.04 and 0.04 degrees from the actual Julia
orientation. (Double rotation is a mathematical abstraction
most
difficult to comprehend. Nothing at all like it exists in
three-dimensional space.) But the orientation of today's
image
produces many Julia characteristics and also shows the position
of the hairline spirals in relation to the Mandelbrot aspect of the
area.
With today's image being a near-repeat of yesterday's, I could give it
no rating. The name "Home of the Spiral" needs no explanation
however.
The calculation time of almost 10 minutes will need to be endured in
nail-biting impatience. I hear that Paul Lee has been in the
hospital for over a week, and has been unable to update the FOTD web
site. Fortunately, he appears to be on the road to recovery.
But a trip to the FOTD web site that he has maintained for over 13
years and that holds the past FOTD images is always a lot of
fun.
The web site may be accessed at:
http://www.Nahee.com/FOTD/
Heavy scudding clouds, blustery north winds and a temperature of 43F
+6C made Saturday quite brisk here at Fractal Central. The
fractal cats had enough heat inside that they never noticed the outside
chill.
When the antiquing was over and done, my day was reasonably
settled. The next FOTD will be posted in 24 hours.
Until
then, take care, and the answer may lie where least expected.
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
Home_of_the_Spiral { ; time=0:09:52.49-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 passes=1
center-mag=0/0/0.8503401/1/126/0 periodicity=6
params=89.96/0/89.96/0/0.3272613/0.0561252/0/0
float=y maxiter=150000 inside=0 logmap=yes
colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\
EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\
H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\
dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\
rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\
GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\
_YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\
LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\
Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\
TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\
5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\
zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\
wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\
rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\
zrwzrwzrwzrwzrwzrwzrwzrwz }
frm:SliceJulibrot2 {; draws most 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=========================================