|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: For today's average-quality fractal it's back to the formula -1Z^(-11)-11Z^(-1.1)+(1/C), with a bailout radius of 200. As I stated in yesterday's FOTD, this formula draws a most unusual fractal, which is too large to fit on the default screen, but is worth closer examination from one end to the other. A prominent feature of this parent fractal is a large fan-shaped object. Today's scene with its unusual midget lies buried deep at the edge of this fractal fan, where chaos begins. I named the picture "The Pinkness of Infinity" mostly because I liked the poetic sound of the phrase. The 16 minutes required to render the scene from the parameter file is not so poetic however. But as always, relief is as close as the internet and the Usenet group: The fractal weather today was rather pleasant, with mostly sunny skies and a temperature of 86F (30C). The fractal cats approved of the conditions, and showed their approval by spending most of the afternoon in the yard. In the evening, when the mosquitoes got too thick, they came indoors. I did a bit of philosophical pondering this afternoon on the question of whether fractals are art, a topic that has been keeping the UltraFractal list so busy these past few days. Of course it's a futile topic, since no definite answer is possible, but it never fails to bring a flood of comments. Why, I wondered, does this one topic bring such activity every time it arises? Sometimes I feel that the UF list exists only as a forum for fractal artists to re-assure each other that they are indeed creating real art. I had assumed that fractals are art if that's what the creator intends, and that they are mathematical curiosities if this aspect is emphasized. In my case, I consider my FOTD's to lie in a grey area somewhere between art and math. IMO, It is the attitude of the creator at the time of creation that determines whether an image is simply an illustration of a pre-existing object or a newly-created work of art. If we want our fractal images to be art, then they are art. We don't need the rest of the world reassuring us that we have indeed created a work of art. If we want our fractals to be illustrations of the amazing things numbers can do, then they are such illustrations. If we want our pictures to be a bit of both, as I do, then they are a blend of art and mathematics. On the other hand, I can understand why traditional artists denigrate fractals as art. By profession I am a graphic artist. At one time, the tools I worked with were things such as a light-table, rubber cement, x-acto knife, straight edge, t-square, ruling pen, air-brush, zip-a-tone, and so on. I spent years becoming skilled in the use of these things. Then computers came. Of course, a computer now does all this tedious work far better than I ever could by hand. I don't resent computers, for they make my work far easier, but I miss the old days of 25 years ago, when it was not so easy to produce a clean and accurate camera-ready mechanical. Having spoken my bit, I find it's time to shut down the Fractal Central and call it a night. Until tomorrow, take care, believe that fractals are art, and they'll be art. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
PinknessOfInfinity { ; time=0:16:15.15 -- SF5 on a P200
; Version 2000 Patchlevel 13
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+4.737422431714508/+0.4307302795571638/2.\
330699e+007/1/75 params=-1/-11/-11/-1.1/0/100 float=y
maxiter=1600 inside=0 logmap=299 periodicity=10
colors=000B5M<6>84K74J74J<3>54I<13>Z9f`AhbAi<3>jBplE\
rmHmhKhdNc`QZYRU<2>YUFYVG<3>YZQY_SY`UYaXYbZWdb<5>bVW\
dTVeSUfQTgPShNRjKP<16>afXagY`iY<3>Zn_OnWbo_km_<3>e`l\
dXpeUsfRvgPx<5>mKynJyoIzpHzqHz<3>xDzzDzwCx<3>kCshCqd\
Cp<8>PBdNBcLBa<2>GBYEBXB8V<12>QadRceSef<3>Wnh<3>9fI4\
hB<6>4QF4NG4LH<2>4DI4AJ26A<2>8CZ6DhAEfDFe<3>VI`ZJZcK\
YhLXnLYjLWfLUaLSXLQ<4>LLGJLEGLC<3>7L4PHk<2>_Znccr<12\
>RmPQnMPoK<3>LrBGs8<3>VvBYwCaxC<2>kzEbzEUzMLzU2zV<2>\
UznHzQ<8>CzM
}
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.
