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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's FOTD fractal we have a picture of a midget. But this is not just any old midget. It is a midget in the fractal that results when the nearly-linear formula (-Z)^(1.09)+C is calculated. This parent fractal has X-axis symmetry as well as an overall resemblance to a Mandelbrot set with all its bays but the large period-2 bay missing. Today's scene is located in the chaos that lines the north shoreline of the parent fractal. Midgets are very hard to find in fractals of such a low order, so I was very lucky to find the little fellow. I was so lucky in fact that I decided to grant the image the honor of being FOTD for a day. With its many intricacies, the midget really is interesting, and unexpectedly attractive as well. I named the picture "Nearly Linear", referring to the exponent of Z, which is quite close to unity. Then I rated it at an 8 to reward myself for the extra effort I put into the coloring. The calculation time of 4 minutes on the P2000 would be increased to around 20 minutes on the P200. The calculation time becomes irrelevant however when the pre-calculated image is viewed on the FOTD web site at: Far too much heat here at Fractal Central on Friday made things unpleasant for those who had to be outdoors. High humidity and a temperature of 93F 34C isn't in the comfort range. The cats, who never go outside, paid no attention to the heat. They were happy taking it easy all afternoon on their scratching posts. By the time a cooling thunder-shower moved in at 9pm, they were asleep. My day was moderately busy. Tomorrow will likely be slower. If it is, the next FOTD will appear in 24 hours. If not, the FOTD might take 25 hours. Until then, take care, and be at ease with things as they are. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Nearly_Linear { ; time=0:04:11.33-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMiN passes=1 float=y inside=0
center-mag=+0.03378299242425540/+1.142571955783682\
00/7.474851e+011/1/-87.4999618587140731/-0.0029595\
3393662999609 periodicity=10 mathtolerance=0.05/1
params=1.09/0/0/0/0/0 maxiter=2800 symmetry=none
logmap=772
colors=000EkpEjpDioDhnCfnCemBdlBblAakA`jA_jBYhBXgC\
WeCUdDTbDSaDQ_EPZEOXFNWFLUFKTGJREHQCGOAFN5EL0CK0BI\
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pgYmdXlbVj_UiYShVRgTQfROeONdMLcJKaHI`EH_CGZ9EY7DX4\
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T3LV4PY4S_4Va4Yd4`f5dh5gk5jm5mo5pm6ok6oi6oh6of6od6\
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uPzuUzuZzvczvhzvmzvrzvvzvzzvzzwzzwzzwzzwzzwzzwzzwz\
zwzzwzzxzzxzzxzzxzzxzzxzzxzzyzzyzzyzzyzzyzzyzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotMiN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=(-z)^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
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times.
