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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The world is filled with lost things -- lost files, lost computers, lost chords, and last but not at all least, lost fractals. Today's modest fractal offering is lost. It's simply another view of the East Valley area of the Julibrot figure, but the direction in which the scene has been sliced is one I have yet to write a formula to reach. Yes, I know you're wondering how I produced the image if I have no formula that can draw the rotation. The answer is that I have no formula designed specifically for 4-D rotations that can draw this particular angle. The formula that drew today's image was written many years ago, back when Fractint had only 4 variable parameter entries for type=formula. I wrote it at random, with a now forgotten name, just to see what it would do. When I realized it could draw oblique slices of the Julibrot I changed its name to ObliqueMan. Finally, when the 5th and 6th variable parameters were added to Fractint, I changed the name to ObliqueManPlus. The Julia aspect of the image is evident in the familiar East Valley shape of the outer dark rusty red border. The Mandelbrot aspect appears as the brilliant green wedge within and seemingly behind the outer border. This green wedge is the East Valley itself, and a careful examination will reveal the valley's elephants in various stages of formation and not yet able to find their proper buds. The equal stretching of two dimensions of the hypercylindrical East Valley because of the oblique direction of the slice is something that can happen only in four or more dimensions. In three dimensions only one dimension of a cylindrical object can be stretched by an oblique slice. I named today's image "The Lost Valley" not because the valley itself has been lost, but because this particular aspect of it, with the valley at an oblique angle, has not yet been found with a formula specifically designed for the purpose. I rated the image a 4 because it's only moderately attractive. The image's greatest advantage is its speed. The parameter file renders in only 30 seconds -- that is after the minute or so it takes to change this letter into a Fractint parameter file ready for running. Those who would rather surf the Web can find the image at: Today's fractal weather, (How did weather get to be a part of the FOTD?), was the average summer fare for this part of the world. The temperature of 94F 34.5C, and the high humidity, slowed the fractal cats to a crawl, causing them to spend nearly all the day sleeping. There's no time for me to sleep however, not with air conditioning and a full day's work waiting to be finished. So until next FOTD, take care, and become one with the universe. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Lost_Rotation { ; time=0:00:30.05--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=ObliqueManPlus
center-mag=-0.291733/-0.00378091/1.103753/1/90
params=0.28/0/0.28/0/0.015/0.015 float=y
maxiter=6000 inside=0 logmap=yes periodicity=10
colors=000HHCHGBJEALD9NB8PA8RBCTBFVCIXCLXCOYDRZDU_\
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}
frm:ObliqueManPlus {;Jim Muth
z=p1+pixel, c=p2+(p3*pixel):
z=sqr(z)+c,
|z| <=100
}
END 20.0 PAR-FORMULA FILE==================================
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