|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: For over 3 years I've been opening the FOTD discussion with the introduction: 'Fractal visionaries and enthusiasts'. The description of a fractal enthusiast is obvious, but what is a fractal visionary? The truth is that I am not sure. I simply invented the phrase one day early in the life of the FOTD, and it kind of stuck around. The dictionary defines a visionary as a dreamer whose ideas are impractical, and also as a seer -- one who sees visions. It would therefore appear that a fractal visionary is a person who wastes too much time searching for fractals -- In other words, someone like myself. But is it truly a waste of time working with fractals? I think not. After all, one must do something with their spare time, and despite the words of some unenlightened critics, fractals have become a form of art. So a fractal visionary might well be an artist -- an artist whose medium is numbers. And there's nothing impractical about that. I named today's picture "Mega-Minus Fractal". I gave it that name because it shows what can be done by adding together negative exponents of Z. The formula that drew today's image is 1.25(Z^(-0.5)+Z^(-10))+(1/C). The parent fractal is near the point of inversion -- too large to fit on the screen even at the smallest magnitude available. Ignoring the almost infinite extent of the entire fractal, I directed my attention to a double-bay midget near the center. I zoomed into a double valley separating the two large bays to find today's midget. Unfortunately, when I found it, I spent too little time coloring it. Thus the rating of an average 5. The image of today's fractal is better viewed than described. It may be viewed by running the parameter file and waiting almost 7 minutes, or by downloading the fully-rendered image from Usenet at: The fractal weather today would have been ideal had it not been for an hour-long dry lightning storm this afternoon, which was a true spectacle, and sent the fractal cats scurrying for their most secluded hiding places. The temperature of 78F (25.5C) was ideal, though unappreciated amid the turmoil. The fractal philosophy went nowhere. It might go somewhere tomorrow; it might continue stagnated. Check then to find out. And until then, take care, and become a fractal visionary by becoming one with your fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mega-Minus_Fractal { ; time=0:06:43.64 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+6.45906747057268800/+1.10441249439956900\
/6873.396/1/7.499 params=1/-0.5/1/-10/0.25/0 float=y
maxiter=1400 inside=0 logmap=98 periodicity=10
colors=000sfPofNmfLkeJijH<3>af9_e6Yd7Wc8Ub8<3>PZAOXB\
OWB<5>KPFJNFJMG<3>GHIFCJFFJ<3>CALB8MB7MA6N83M<27>dca\
edbfeb<3>jjd<25>o_LoZLoZK<2>pYIqXHsXGuWG<2>yVDzVDzUC\
zUBzTA<3>zUBzUCzUC<2>wUD<3>gVEcVE_cEXmE<3>SVF<10>CWI\
BWI9WI<3>4WJ0XJ<16>NHJPGJQFJ<2>UCJVBKXAM<3>a6Ub5Wd4Y\
e3_f2a<6>dAhdBicCjcDkcFl<3>bJsbKuaLwaMy<16>YdzYezXfz\
XgzXhzYjz<18>UgzTgzTgz<3>Sfz6gz<2>Bfz
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
|
times.
