January 28, 2012: Hither and Yon | Jan. 27 | Jan. 29 | 2011 | FOTD Home |
Fractal visionaries and enthusiasts:
ANOTHER
NEW FORMULA! THE 'SliceJulibrot6' FORMULA HAS BEEN RENAMED!
I have renamed the 'SliceJulibrot6' formula 'JulibrotMulti'.
I did this because it was pointed out that I previously wrote a formula
named 'SliceJulibrot6'. I never did much with that old
formula, but it might still be floating around, so to avoid confusion I
have renamed the new formula.
Today's image is an almost-Julia set of the eastern edge of the large
minibrot on the main stem of its parent Mandelbrot set, which is
infected with Z^5 energies in its depths. I call it an
'almost' Julia set because it is double rotated 1-1/2,1-1/2 degrees
from the true Julia orientation.
In images this close to the Julia orientation, a small rotation makes a
big difference. The difference in today's image is the
totally chaotic arrangement of filaments, which inspired the name
"Hither and Yon", (come and go). Another difference is the
existence of the two small near-perfect Z^5 minibrots, a rarity this
close to the Julia orientation.
The rating of a 7-1/2 implies that I felt some disappointment in the
artistic aspect of the image, but also that it holds enough math
interest to earn it FOTD status.
The calculation time of a hyperfast 8 seconds will leave no chance for
impatience to raise its jittery head.
The day turned out unexpctedly pleasant here at Fractal Central, with
ample sun and a temperature of 48F +9C. The fractal cats
spent most of the afternoon on their shelf in the southwest window,
enjoying the sun. A brief rain shower passed over late in the
afternoon, but by then the pleasant day was in the bag.
The humans did what introverted humans do best -- thinking deep
thoughts about nothing in particular. The next FOTD will be
posted in 24 hours. Until then, take care, and sometimes it
is possible to think deeply without knowing what you are thinking about.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Hither_and_Yon { ;
time=0:00:08.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=JulibrotMulti function=recip float=y
center-mag=-0.0830872/0/1.173709/1/-90/0 inside=0
params=5/6/88.5/0/88.5/0/-10.4/0/0/0 maxiter=1200
colors=0000000000000000000000100200300400500601712\
823A35C56E6AI8DMAFQCITEKWGNZIPaKSdPUgUXlZZqccvhhzm\
pzzuzzzpzmjzcgzVdzTbzS_vQXrPVmNShMPcKNeJKhHHkGFmOk\
4Pi5Pg6Qe7Qc8Qa9R`9RZARXBSVCSTDTSDTQETOFUMGUKHUJHK\
RBBY6G_7L`8Qb9VcAZeBcfChhDmiEqjEogHndKmbNl_QkYSiVV\
hTYgQ`fOceLecJhbGkaEn`Bq_9sXBqVDoSFmQGlNIjLKhIMfGN\
eDPcBRa8T_6UZ5W_5Y_5__4a`4c`4e`3fa3ha3ja2lb2nb2pb2\
qbIrYYrTVnUTkVRgWPdXN`XLYYJUZGR_EN`CK`AGa8Db69c46d\
23d35e47e49f5Bf6Dg6Fg7Hh8Jh8Kh9Ne9QbAT_AWXAZVBaSBd\
PCgMCjJClHGjKJiMMhOQfRTeTWdV_bYba_e`ah_cg_ajUWlPQo\
KKqFEtA8v52lBNbGgaIZ`KR`MJ_OB_Q3aVAc_HiriedOgiVina\
kshdBeeIgfOhgUih_jiekjklkqmOOad6yIJt`iqblpdnpfpohs\
ojunK9eZZjPrtTssWtr_uqbupfvoiwnfZHgbMheQihUikYjnbk\
qfltj7CdEKfLShS_iZgkeompQzoZwnftmoq4gRGkXRobashp5I\
BdKGgOLiSQlWUn_ZpccsghukfGLgMPhRTiXXia_jgcklglrkPI\
4`bSkNclVflahlijlplN5PWOY }
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=========================================