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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For many years I have searched for the perfect fractal, one which I could rate an honest 10. I wrote and discarded one formula after another in my fruitless search, but the perfection I sought always eluded me. It eluded me that is until one day recently, when I realized that I had the perfect fractal on the screen before me. I now offer this perfect fractal to the world in its full 10-rated glory as the FOTD for 10-10-00. The parameter file of this perfect fractal is the fastest of all time, requiring only an incredible 3 seconds to render. The quickness of the parameter file however takes nothing from the worthiness of the image it creates. I named the picture "The Perfect Fractal" because that's what it is. Of course, there is but one perfect fractal, and that fractal is the parent fractal of all fractals -- the simple yet infinitely complex fractal -- the Mandelbrot set. To give the image a little something extra, I rendered the M-set using Fractint's continuous potential coloring method, which produces images as close to true-color as is possible with a mere 256 colors. Since we have the Mandelbrot set already on the screen, this is the perfect time to describe and give the names of its various features. The names I have given to the features are mostly based on common usage, though some names are of my own invention. The Mandelbrot set appears on the screen in its 'normal' orientation. Just as is the case with terrestrial maps, North is up, South is down, West is left, and East is right. The largest open area, which has a vague heart shape, is known as the Main Cardioid. This cardioid is surrounded by roughly circular shapes known as buds. The buds are separated from the Main Cardioid by cusps known as Valleys. The large bud on the west side of the Main Cardioid is West Bud. North Bud and South Bud lie at the north and south edges of the cardioid respectively. Northwest, Northeast, Southwest, and Southeast buds are located on the corresponding sides of the cardioid. The Main Cardioid is cleaved on its east side by East Valley, sometimes called Elephant Valley because of the elephant-like features that appear to be parading out of the valley. The double valley separating the West bud from the Main Cardioid is known as Seahorse Valley. It has been named after the spirals shaped like seahorse tails, which are so prominent in this area. The next valley to the west is known as Seahorse Valley West, or Scepter Valley, because of the scepter-like features found there. The next valley west is Double Scepter Valley, then comes Triple Scepter Valley, and so on to infinity. At the north edge of the cardioid lies North Valley or Triple Spiral Valley. 45 degrees clockwise lies Northeast Valley or Quad Spiral Valley. Northwest Valley lies approximately 45 degrees counterclockwise from North Valley. A similar arrangement of buds and valleys lies along the southern border of the cardioid. The buds, along with all their associated filaments and midgets are known as radicals. The long straight spike shooting out westward to a coordinate of -2 is known as the negative tail. The prominent midget on the negative tail is known as the main midget. As I stated above, these names are the particular names I use. As far as I know, official names have yet to be given to the features of the Mandelbrot set. The classic Mandelbrot set renders in just over 3 seconds from the parameter file. It downloads in a period of time that is many times as long. But for those who choose the download, the GIF image file may be found on Usenet at the binary group: The fractal weather today was downright chilly, with variable clouds and even a few drops of rain. The temperature of 49F (9.5C) was too much for the fractal cats, who asked to come back indoors only 3 minutes after I let them out. Then they scolded me because it was too chilly for them to enjoy the outdoors. Barring an unexpected rush, the fractal philosophy will continue tomorrow, as I investigate something known as the Zexpe fractal in a way you've never seen before. Then I've got all those odd orientations in the Julibrot to describe. Until tomorrow then, take care, and when boredom strikes, rush to your computer to create a fractal. Jim Muth jamth@mindspring.com |
START PARAMETER FILE=======================================
The_PerfectFractal { ; time=0:00:03.32 -- SF5 on a P200
reset=2001 type=mandel passes=1
center-mag=-0.606416/2.22045e-016/0.8503401
params=0/0 float=y maxiter=260 inside=0 logmap=yes
potential=255/260/260 periodicity=10
colors=000000dmLdoLcrM<20>iU9jT9jS8kR7kQ7<3>lK4lJ4mI\
3mH3mG2nE0<47>7Zl6Zm5_n<2>2`q1`s2`r<59>Q7dR7cR6cS6cR\
5bS4cS5bS5bS5aS5bT6aT6`T6a<36>_CJ_CJ`CI_CI<3>aEGaCFa\
EFaEEaEEaDFbEF<9>`LD`MD_MD<10>YXBYYBXZB<3>XbAXcAXdAX\
eAXfA<3>hjAkkWrmzzoz
}
END PARAMETER FILE=========================================
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