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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: There once was a time when I wandered freely through Fractal Land, roaming wherever my day's journey took me to study the surroundings. I was not on a search for any particular quarry. I photographed whatever was surrounding me in the place where I stopped for the day. Then something happened. I became fascinated with the so-called 'midgets' that I occasionally stumbled upon. I began seeking midgets, ignoring the sometimes spectacular scenery that I passed by in my search. Midgets in fractals are higher-dimensional analogs of the maximum or minimum stationary points so often found when the graphs of functions are plotted. And just as all stationary points have a similar parabolic shape, so do all midgets have a similar shape. With only a few hard-to-find exceptions, this shape is that of the classic Mandelbrot set. The familiar shape is sometimes distorted beyond recognition, but even when unrecognizable the shape is there, and could be undistorted back into the M-set. It is hard to say why I became so fascinated with midgets, but this kind of thing seems to happen with fractals. Many become fascinated with spirals. When I come upon spirals, which I do many times in my search for midgets, I usually pass them by. They all look the same to me. It is curious that the same boredom has never arisen as I discover ever more of the super infinity of similarly shaped midgets that are out there, waiting to be found. Maybe I should devote a month or two to fractals without midgets. The discontinuity patterns in low-order fractional-power fractals can be quite interesting, and certainly deserve more exploration. The odd slices of the Z^2+C Julibrot can also be interesting. It is really surprising what Seahorse Valley looks like when viewed from some of the unfamiliar angles and double angles of four-dimensional space. Yes, I think I'll soon take a break from the endless stream of midgets, and have some fun with the other things found in the world of fractals. But that break from midgets does not appear in today's image, which is another adventure into the parent fractal of the two most recent FOTD's. I named the image "The African Veldt". I can give no reason for the name other than I think it sounds exciting. I also might have been thinking of an old story by Ray Bradbury named "The Veldt", which as I recall is about a house with animated walls that depict an African grassland scene. I rated today's image at a 6. Combined with the render time of 4 minutes, this gives an overall value of 142. The render time can be changed to a faster download time by visiting Paul's FOTD web site at: Thursday was quite a pleasant day here at Fractal Central. The warm sun, light winds and temperature of 56F 13C made conditions near ideal for an afternoon in the yard. The cats took advantage of the opportunity. This morning is starting sunny, but it is colder, and the wind is high. We'll see what the cats think of this. I'll think more of fractal things once I get the work behind me. Until the next FOTD appears, take care, and see you in the land of fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_African_Veldt { ; time=0:04:14.47--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.31518718326216360/+5.515004364619150\
00/2.11448e+007/1/-17.5/3.45976670992897972e-008
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inside=0 logmap=78 periodicity=10
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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==================================
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