Dec. 9, 2012: Broken Hyperspiral | Dec. 7 | Dec. 11 | 2012 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image of a strange spiral is located in the Scepter Valley area
of the Z^2+C Julibrot. It is sliced in a direction halfway
between the Oblate and the Rectangular, and has been stretched and
skewed to a rather large extent to bring it to a recognizable shape.
The name "Broken Hyperspiral" refers to the infinitely divided nature
of the features in the image. This unlimited division, known
as
'Cantor Dust', is typical of the Julia sets of points outside the
Mandelbrot set, but as today's image shows, it also exists in the odd
planes and angles.
The image consists totally of points, with no two points being
connected. A zoom into one of the sub-spirals will reveal a
never-ending chain of similar broken spirals, and this series continues
all the way to infinity, which is not an end point or a very large
number, but an abstract idea that can never be reached.
The rating of a 5 is pretty pathetic by FOTD standards, but it's all I
could give the image, which has little more than a bit of pop-math
interest going for it. More effort on the coloring might have
raised the rating a point or two.
The calculation time of 1-3/4 minutes is about average, but perhaps a
bit slow for an image with so little reward. The situation is
resolved on the web sites.
Clouds ruled the sky today here at Fractal Central, while the
temperature of 45F +7C kept things feeling seasonal. The
forecasted rain held off until sunset however. Both the cats
and
humans had a typical uninteresting day.
The next FOTD will be posted when it is ready. Until
whenever,
take care, and if humans ever populate the galaxy, how will they agree
on a universal galactic time? (IMO, we will never populate
anything but planet earth, so there is no problem.)
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Broken_Hyperspiral { ; time=0:01:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1
center-mag=+0.03264445237728411/+0.172536526663781\
00/8438.382/0.1402/79.9353442340639617/73.17794208\
35490413 params=45/90/0/90/-1.25/0/0/0/2/0 float=y
maxiter=2200 inside=255 logmap=-126 periodicity=6
colors=000knUknUloUloTmpTmpSmqSmqRmrRmrRmsQmsQmtPm\
tPmuOmuOmuNmvMmvLkvKiwKhwJfwIdxHcxGaxG_yFZyEXyDVzC\
ayIcyMeyQgyUiyYky`mydoyhqylpykoyjmygjxdhxafxZcwWaw\
T_vQXuN`sT_qSZoRYmQWkQViPUgOTdNSbMQ`MPYLOWKNUJMRIK\
PIJMHIKGHIFGFEEDEGBDI8CK6BM3AO8HQ7MS6RU5WW4`Y3eZ2j\
Z4kZ6kZ8kZAkZCk_EkaGlbIncKodMqfOseQsdSrcUqbWq`Xp_Y\
oZYoYYnWZmVZmUZlTZkSZkQ_jP_iO_iN_hL`gK`gJ`fI`eH`eF\
adEacDacCabAba9ba8b`7b_5cZAbaBcaDdaEdaGeaHfaJgaKga\
MhaNiaOiaQjaRkaTlaUl`Wm`Xn`Zo`_o``p`bq`cq`er`fs`ht\
`it`ku`lv`nw_nw_mw`mw`lwalwakwbjwbjwczzczzdzzdzzez\
zezzfzzfzzgzzgzzhzzhzzizzizzjzzjzzkzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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=========================================