FOTD -- January 26, 2008 (Rating 8)
Fractal visionaries and enthusiasts:
NEW FORMULA ALERT!
Today's image uses a new formula, which is simply yesterday's
formula with initial 'b' generalized rather than set to 0,0.
This might give a little more variety to the images it draws.
I named the new formula HyperMandelbrot2.
Today's image is named "Pentagon Heptagon" because of the very
prominent pentagon. And there is also a heptagon, much smaller
and closer to the center. And yes, the series of polygons with
an odd number of sides does continue indefinitely. An outzoom
will reveal a triangle, while a couple inzooms will reveal a
nonagon, a hendecagon, and a tridecagon. (I think these are the
right names for polygons of 9, 11 and 13 sides.) How far the
series goes beyond this point is anybody's guess, but I suspect
that, like so much else in the world of fractals, it continues
without limit.
I have made no effort to figure out the number series of the
arms stretching between the polygons, though it probably has a
logical order. But at the same time, I see that the arms within
the pentagon are unevenly distributed. Two of the pentagon
vertexes have arms connecting with them from within, while the
other three are cut off from the center.
Today's coordinates define a blank area in the classic Mandel-
brot set. If real(p3) and real(p4) are set to zero, the result
is a flat black screen. The area actually lies somewhat inside
the main bay of the M-set.
Even though I have no idea how today's image ranks among Sea-
horse Valley images of the HyperMandelbrot set, I have rated it
at an 8. Its mathematical interest is enough to be worth at
least that rating.
The calculation time of 4-1/4 minutes is fast enough to keep
impatience at bay. And if it is not, the finished image will
soon be available on the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Friday was bright and sunny here at Fractal Central, but it was
also cold and blustery, making it a rather unpleasant day to be
outside. The high temperature of 27F -3C fely cold even in the
strongest sun. With numerous sources of heat inside F.C., the
fractal cats had their problem deciding where to spend the day.
I had no such problem however. I spent the day working, then
searching for a FOTD. As today's image shows, I was successful.
And the next FOTD image will be posted in 24 hours. Until then,
take care, and where's it at?
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
Pentagon-Heptagon { ; time=0:04:14.05-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=t
center-mag=-0.749480813398176/+0.031703452082799/\
3.321327e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0
float=y maxiter=3600 inside=0 periodicity=0
colors=000mL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk\
`_lYZmWYnUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVT\
iYTh`TfcTjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4d\
N2cQ0cSgcaXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnno\
pzrszuuzzzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUN\
pSLpQIpOGrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agA\
ZeBWcCTaDQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRz\
zOifKndGrcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnF\
CmFEmGGlGIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwq\
NwrJwwGwxCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5\
oz3pz3qz4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaO\
FYKDUFGUHJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalO\
dnLgoJjlMeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDd\
kEglFjmBimFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7s\
c4va5r`5o_6kY6hX6dW7aV7YT7VS8RR8OV4RQ8LLBGGFA8H2CI\
5GI8KIBNJERJHVJKZJNaKQeKT }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
