FOTD -- October 13, 2005 (Rating NONE) Fractal visionaries and enthusiasts: I gave today's image no rating. I could not rate it because I made no effort at all to color it. The image's color palette is the Fractint default palette, which was designed for technical but not artistic value. I chose this default palette because the entire point of today's image is mathematical. Today's formula, which is named "MytestAGnew", has nothing to do with a former governor of Maryland and U.S. vice-president. It is a newer version of the 'MytestAG' formula. Of course, its newness is a relative term, since it was written quite a few years ago. The newer version adds two changeable and basically useless parameters to the earlier version. It turned out that the additional parameters do nothing that could not have been done with the two parameters of the earlier version, so the newer version fell into immediate neglect. But I resurrected it today to create a most unusual variation of the Mandelbrot set. I named today's image "Mandel Variation-2", since it is the second variation of the series. The image multiplies the imaginary square root of 2 by itself to come up, not surprisingly, with real 2. The result, also not surprisingly, is the Mandelbrot set. I'm not really sure where the extra stuff comes from. Most likely it is the result of mathematical imprecision. In yesterday's FOTD I stated that today's image would be most unusual. So what is so unusual about a Mandelbrot set with a few extra circular disks scattered about? It is the nature of those disks. Every disk has a dot at its center. But those dots are not simple dots, they are the Julia sets of the area of the M-set in which they lie. And even more unusual, those Julia sets are filled with disks with dots at the center, and those smaller dots also turn out to be Julia sets with disks at their centers. Like the holy hermit on the mountaintop said to the seeker of truth, it's disks all the way down. As if this were not enough, the borders between the iteration bands have broadened into narrow open lanes, with bits and pieces of something else showing through. The closer to the M-set itself we search, the more detailed the stuff showing through the cracks becomes. It is especially detailed around the mini Julia sets at the centers of the disks. There almost seems to be another fractal hidden below the surface M-set, but there also seems to be no way to bring this second fractal to the surface. All we can do is see hints of the buried fractal and say, oh my! There can be no complaints about the 4-second time required to render today's image. The only complaints might come from those with new-fangled computers that can zip around the internet in the wink of an eye but cannot run a simple DOS-based fractal generating program. But these complaints can be eliminated by a quick visit to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted ready for download. A bit of sun managed to break through in the middle of the day, on Wednesday here at Fractal Central, making the yard just pleasant enough for the cats to venture outdoors for an hour or so. They ended the day peacefully if not satisfied. But it rained overnight, and this morning is starting chilly, cloudy and drizzly. The cats usually complain about this kind of weather. For me, the day coming up appears to be about average. The next FOTD will appear on schedule in 24 hours. Until then, take care, and look to the fractal side of things. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Mandel_Variation-2 { ; time=0:00:04.67--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=MytestAGnew center-mag=-0.5/0/0.7 params=1.414213562373/1/1/1.414213562373 float=y maxiter=100 inside=0 logmap=yes symmetry=xaxis colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:MytestAGnew {; Jim Muth z=c=pixel, a=flip(real(p1)), b=flip(imag(p1)), d=real(p2), f=imag(p2): z=(d*(z^a))^(f*(-b))+c, |z|<=100 } END PARAMETER FILE=========================================