|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: There is a very unusual rectangle in the Z^(2.003)+C Julibrot. It is located in the Julia set with a C-value of -1.7435 at Z-coordinates of 0.00019,0.07388 and a magnitude of around 75. I have several times mentioned this nearly-perfect rectangle in my FOTD discussions, and since the two most recent FOTD's took me to the general area, I decided to take a peek at the rectangle while I was there. The rectangle is quite critical. If imag(C) is changed even 0.0001 from zero, the near-perfection is lost. In today's image, the value is changed only 0.00004 and already strange things are happening. I aided the strange happenings by rotating the view less than one degree from the exact Julia orientation. As a result of my tweaking, the once near-perfect rectangle has been changed into what can be best described as a semaphore flag. (What ever happened to the days when they actually communicated with those things?) The lower right half of the rectangle is filled with reddish high-iteration outside stuff, while the upper left half is composed of trapped inside points given life by the 'fmod' inside fill. Several other inside fills would have worked nearly as well. The "SliceJulibrot4" formula that generates today's image is a generalization of the "SliceJulibrot2" formula to any power of Z. It is a new formula, which I have not previously posted. I named the image "Semaphore" and rated it at a 6. When the render time of 7 minutes is considered, the overall value equals an 82. Rendering may be avoided entirely by downloading the finished GIF image from the FOTD web site at: Thursday was not too cold and not too cloudy. It was also not windy, and as a result, the fractal cats had almost two hours of quality time in the yard. When they came in, they settled down without demanding their usual treat of tuna. Rain fell during the night, but it has already moved off. If the clouds move out, the cats will have a fair chance at another good day. The work that I must finish is about average. It's 10:30am and time to get started, so until next FOTD, take care, and be lively. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Semaphore { ; time=0:07:16.94--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=1
center-mag=0/0/77.51938 params=89.63/90.33/89.72/9\
0.32/-1.7435/4e-005/0.00019/0.07388/2.003/0 float=y
maxiter=6000 bailout=9 inside=fmod
proximity=0.02 logmap=50 periodicity=10
colors=000MKMNKLOKKPKJQKJRKMSKOTKRULTVMVWNYXN_YObZ\
Pd_Qf_Ri_Sk_SmWVoTYpQ`rNcsJfuGivDlxAnyDozFpzHqzKrz\
MrzOszQtzTuzVvzXvz_wzaxzcyzeyzgxyhwxiwxkvwlvwmuvnu\
vptuqturstssttkjuc`vWRwOHxG7oFEfFLYFSPFZGFdII_KczL\
PPWTJYRK`PLbNNdKOfIPhGRjESlCT5MO9OPDQPHRPLTPOUPSWP\
WYP_ZQc`QfaQjcQneQrfQvhQyiQvgOtfNrdLocKmaJk`HhZGfY\
EdWDbVCdTBfRBgPBiNBkLBlJBnIBoGBqEBsCBtABv8Bw7BoEHg\
KN_RSSXYKbbLd`Mf_NhYOjXOlWPnUQoTRqRRsQSuPTwNUyMUzL\
SwMRtMPqMOnMNkMLhMKeMIbMH_MGYMhrBdlE`gHmbKmXNmSQmN\
TmHWmCZm7am8bm9cmAdmBdmCemDfmEgmFgmGhmHimIjmJjmO`m\
SRmWImVMmUPmUTmTWnSZpSbqRerQhtQluPovPruLhtIZuFQvCG\
w97x8Cy8Hz7Lz7Qz6Vz6ZzDVzKRzPNzVJz`Gz`CzdjzZazTUzS\
YzS`zSczSfzSizTezUbzV_zVXzWUzXRzXNz`8zYKzZHzZEz_Bz\
`8zUFzWDzXBzZ9z_7zKYzLvzNqzOmzPizQezSazTYzUTzVPzXL\
zYHzZDz_9zCOzLHzTBzASzDPzFNzILzKJzNHzPFzSDzUBzX9zZ\
7zvnzrgzo`zlVziOzfIzcBzJj }
frm:SliceJulibrot4 {; 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=z^(p5)+c
|z| <= 9 }
END 20.0 PAR-FORMULA FILE==================================
|
times.
