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Fractal of the Day
by Jim Muth
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FOTD -- December 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows what happens when a fractal with a positive exponent of Z (in this case 2) starts to change into a fractal with a negative exponent of Z (in this case minus 15). As the real(p2) parameter of 0.0000001 shows, a very small departure from zero makes a great change in the appearance of the resulting fractal. Curiously, the image is also quite sensitive to the bailout radius. The original Mandelbrot set is still present at the center of the image, but the 16 points of the minus 15 Mandeloid are already fully formed, symmetrically surrounding the Z2 figure. I named the image "Two Into Fifteen" because it shows a Mandelbrot set already well on the way to being a Z^(-15) Mandeloid. There are almost certainly many interesting minibrots deep in today's image, which is actually its own parent fractal. I might search out a few of them in upcoming FOTD's. As for a rating, I decided on a 6. I really put too little effort into the coloring to rate the image higher. Even with the passes set to 1, the image is extremely fast, finishing in a mere 15 seconds. The already finished image is posted to the FOTD web site at: Friday dawned with wet snow falling here at Fractal Central, but with the temperature around 34F +1C, it melted almost as fast as it fell. A little sun peeked through the breaking clouds in the afternoon, too little too late to make the fractal cats happy. My day was rather busy, though not as hectic as it would have been if problems had come up. The next FOTD is due to be posted in 24 hours. A lot of graphics work remains to be finished however, so there is no guarantee that the FOTD will appear as scheduled. Until next time, take care, and shun disappointment. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Two_Into_Fifteen { ; time=0:00:15.42-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=DivideBrot6 passes=1 float=y logmap=yes
center-mag=-0.03296/0/0.295 inside=0 periodicity=10
params=-15/19/1e-007/17 maxiter=1000 symmetry=xaxis
colors=000FoctThhKzmx0hzzHcdHUYHKSJMPKONLQLNSIOUGP\
WEQYCMUKIQREMYAIdFKZKMUPOPUPKZRFcTAgU5hTMhTahTqiOs\
jJukEzl9zl4zk7zj9ziBzhDzgFzfHzeJzeLziWzmezqoztyzrQ\
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p2z2Rz8SzETzKTzQUzWVzaVzgWzlWzAdzEezHezKezNezQezOX\
zNOzK_zIkzGwzSpzcizoczHUzKOzNJzQDzT8zNizRhzzhfzhhz\
hjzhkzdez``zXWzVOzTGzUUzTSzTQzTOzTNzTLzTJzSIzSGzSE\
zSDzSBzS9zbNzXFzXgzUQzSezSbzS_zSYzSVzSSzSQzSNzSLzS\
IzSFzSDzSAzUdzkgzfazaWzXQzSKzNEzI8zE2zF3zG4zH5zI6z\
J7zK8zK9zIAzGAzEAzCBzABz8Bz6BzCQzHczMqzQjzKazETz8K\
zTebmzYntUonPqhLscNudOweQxfRygSzgzzezzdzzczzbzzazz\
`zzazzbzzczzczzdzzezzfzzfzzgzzizzjzzkzzkzzkzzkzzkz\
zkzzkzzkzzkzzkzzkzzkzzkzzkzzkizkkzjlzjmziozipzhqzh\
rqhozdmzakzZizWjzXjzXjzXkzYkzYkzYkzYlzZlzZlzZlzZmz\
_mz_mz_mz_izTfzNczHczGbz7 }
frm:DivideBrot6 { ; Jim Muth
z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2,
d=real(p2)+0.00000000000000000001, f=imag(p2)+16:
z=z^(a)/(z^(-b)+d)+c
|z| < f }
END PARAMETER FILE=========================================
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times.
