I don't understand this completely, but it sure makes a nice image! (The
image it links to, http://jdc.math.uwo.ca/roots/polynomial_roots.png , is
90 MB as a png file but over 1 GB as a .tif file, be warned... it's 16263 x
23000 pixels in size!)
Is there any way that this calculation, and zooms of it, could be rendered
in Fractint?
FOTD -- January 31, 2012 (Rating 8)
Fractal visionaries and enthusiasts:
The oversized parent Mandelbrot set of today's scene has been
corrupted by Z^23 energies. On the surface, the corruption
barely shows, but only one zoom into the depths will show that,
in its depths, the parent is anything but a typical Mandelbrot
set.
Today's image lies in a minibrot on the prominent filament
extending northwest from the large period-2 but of the parent
near-Mandelbrot set. This minibrot is morphed about halfway
between a Z^2 and a Z^23 one, with lots of interesting nooks and
crannies to investigate. Today's scene is located in the area
of what once was the northwest shore line of the main bay.
I frequently mention directions when writing about minibrots in
the FOTD discussions. When I do this, I consider the minibrot
to be lying in the 'normal' orientation of the classic
Mandelbrot set, with the main spike pointing west and Elephant
Valley on the east side of the heart-shaped main bay. North is
then up, and south is down. We really could use a good atlas of
the Mandelbrot set, describing and naming all the valleys and
buds, etc. Several probably are on the internet, though I have
never made a search.
I named the image "A Very Common Object" because objects like
the one in today's image are almost universal in corrupted
parent fractals such as today's. This of course assumes that
the things appearing in fractal images are actually objects at
all.
The rating of an 8 seems appropriate for a rather nice
illustration of such a common object.
The calculation time of 15 seconds is a bargain that can hardly
be resisted.
Find happiness without calculation on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
where the finished image is posted for instant gratification.
Find even instanter gratification on the hi-def web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Nostalgia reigns supreme on the original web site at:
<http://www.Nahee.com/FOTD/>
An early taste of spring came to Fractal Central today, as the
sun shone in and out of the clouds and the temperature reached a
relatively balmy 54F 12C. The fractal cats took advantage of the
sun when it was shining by finding the sunniest spots and
stretching out like only cats can do. FL and I simply had
another routine day, which means a day that would be boring to
describe but was not too bad to live through.
The next FOTD will be posted in 24 hours, come rain or shine.
(Shine is expected.) Until then, take care, and aliens from
outer space, spirits of the dead, lake monsters, sasquatches
wandering the woods, etc. etc. might or might not be real, but
one thing modern science has shown is that the world extends
far, far beyond the things we can observe with our senses or
instruments. And it's getting so confusing that even the word
'real' is losing its meaning. (As philosophers have always
debated and I have always suspected.)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_VeryCommonObject { ; time=0:00:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=JulibrotMulti function=recip
center-mag=-37.56466262894342/+10.3069228272142/\
3.19272e+011/1/-22.5/0 params=23/30/0/0/0/0/0/0/0/0
float=y maxiter=1800 inside=0 logmap=24
periodicity=6 mathtolerance=0.05/1
colors=000rCYoBWmAUj9Sg8Qd7Ob6M`5KZ4IX3GU2FS2DQ1BO\
1AM08K07J3BI5EH8HGALFCOEFREHUDJYCM`BOcAQg9Tj8Vm8Xp\
C_lGaiKcfOecSg`WiY_lVcnSgpzkzzozzzzzzzzzzzzzzizzfz\
zdbza_z_WzXTzVQzSMzQJzNGzLDzMHzNLzOPzPTzQWzR_zSczT\
gJUjKVnLWrLXvMYyMTvQPsULpYHm`Djd9gh5dl1aoGzTNzUUzU\
`zUgzUnzUlvWkvYju_iuahucfteetgdticskbsmasoXqnSzmOz\
lJzkFzjAzi6zh8ze9zcAz`CzZDzWEzUGzRHzPIzMKzKLzHMzFV\
zLczRkiWlgUmfTneSocRpbPpaOq_NrZMsYKtWJuVIuUHjOP_zX\
PzdEzlFzmFzmGzmGznHznHznKznMznOznQznSznUdnWjnYpn_u\
nYrkXpiVmgUkeTjdShcRfaPd_OaYM_VLXTJVR2oX4nV6mT7lR9\
kPBjNCjLEiJGhHHgFJfDJe9KfCKfELgHLgJMhLMhOMhQNiSNiV\
OjXOjZPkaPkc5ykFrhPkeYdbgY_pRYdTXTzWHzVLzvNzsPzqRz\
oTzmUzkWzhYzf_zdagbcm_bj`aha`eb_zbZzcYzdYzdXzeWzfV\
zgUzgTzhSziWzeUzgSziQzjOzlMznKioIpqHwrJtpLqnNnlPlj\
RiiTfgVdeXacZZahmNddU`X`XOfTzmPzsJzgEzX8zM0z82zA3z\
B4zC5zD6zE7zG8zH9zIAzJBzK }
frm:JulibrotMulti {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p2*0.0055555555555556),
b=pi*imag(p2*0.0055555555555556),
g=pi*real(p3*0.0055555555555556),
d=pi*imag(p3*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), aa=-(real(p1)-2),
bb=imag(p1)-0.0000000000000000001,
c=p+flip(q)+p4, z=r+flip(s)+p5:
z=z*z*fn1(z^(aa)+bb)+c
|z|< 100000000 }
END PARAMETER FILE=========================================
