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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal formula, the 'mandel4', is nearly as simple as the classic Mandelbrot formula. In fact, it *is* the Mandelbrot formula, with Z raised to the power of 4 rather than 2. Since 2 times 2 equal 4, I named the image "Mandy Times Mandy". Unlike the classic Mandelbrot set, which has one large lobe, the Z^4+C mandeloid has three main lobes, and is shaped very like an equilateral triangle. In keeping with the parent fractal, the midgets are shaped like triangles and the buds and sub-buds have three lobes. The inner details are very much like the details of the M-set, with slightly fancier seahorse tails in the valleys leading to the main buds and extra elephants in the valleys jutting into the main bay. Perhaps the main difference is that in the Z^4 set the elements around the midgets branch repeatedly into 4 smaller elements rather than into 2 as they approach the edge of the midget. But the Z^4 set has one thing that the classic M-set does not -- valleys that separate the lobes in the buds, and it is in these areas that most of the interest lies in the fractal. With a magnitude of almost 2x10^12, today's image lies near a larger midget very deep in one of these new valleys. The extreme magnitude requires the 'mathtolerance' entry in the parameter file to assure that the image renders at the correct magnitude. I rated the image at a 5. There is really little in it worth a higher rating. But with a render time of only 7 minutes, the image is worth a look. The rating and render time combine to give an overall worth of 54. Those who feel that an image rating a 5 is not worth waiting over 9 minutes to see may see it quicker by downloading it from the FOTD web site at: Chilly winds, too little sun, and a temperature of only 48F 9C made life difficult for the fractal duo here at Fractal Central on Monday. They in turn made life difficult for me -- difficult that is until I filled their food bowls with tuna and salmon. Then they became the happy cats we have known and loved for 14 years. Today is starting sunny, but the temperature is hovering around freezing. More tuna may be needed before the day ends. I will need no tuna to make me happy. Only a small bit of work lies before me waiting to be done. By 2pm I will have finished and the sailing will be smooth to Fractal Land. The fractal I find there will appear as tomorrow's FOTD. Until then, take care, and don't be a gloomster. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandy_Times_Mandy { ; time=0:09:18.21--SF5 on a P200
reset=2003 type=mandel4 passes=1
center-mag=+0.03915334545225174/+0.796786825682308\
70/1.84718e+012/1/-22.5/-0.000748740511517090312
params=0/0 float=y maxiter=16000 bailout=9 inside=0
periodicity=10 mathtolerance=/1
colors=000niipilogjnehmcglael_dkYbjWaiU_iTZhUXhUWh\
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`IMYKKVLJUNHTPGSQESSDRTBQVAPX8NY7L_5K`4Na8PbBSbEUc\
HWdLZdO`eRbfUefXgg`ihclhf }
END PARAMETER FILE=========================================
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