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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Though it takes over one hour to render, today's fractal was found with little effort. In fact, it was found with perhaps too little effort, which accounts for the inglorious rating of 4. The image shows a midget in a remote valley of a twisted minibrot, lying in the chaos near the western shoreline of a remote part of the Z^2.01+C Mandeloid. I named the image "A Hazy Mandelbrot". The name is fairly descriptive of the hazy appearance of the territory surrounding the center midget, especially when viewed from a distance. The texture of the haze reflects the nature of the chaos in the area of the parent fractal where today's image is located. As I watched the image slowly take shape, I wondered about the infinite logarithmic spiral, of which today's scene is an infinitesimal part. Of what dimension is it? My first guess would be that it is five-dimensional, since every twist is four-dimensional. But I'm not at all sure that my guess is right. In fact, the spiral might be of a fractional dimension. The render time of over one hour almost demands a download of the GIF image. But before going for the download, give Paul and Scott a chance to render and post the GIF image file. That file will be available on the Web at: The fractal weather today was partly cloudy and pleasant. The temperature of 83F (28C) was judged purrfect by the cats, who lounged and purred in the intermittent sun for a good part of the afternoon. BTW, the time is getting closer when the fractal cats' pictures will be available, and perhaps my own as well. For now and until next time, take care, and it's interesting to be interested. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Hazy_Mandelbrot { ; time=1:10:00.30--SF5 on a p200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-1.243321752587454/+0.01558682750444/1.\
717303e+007/1/-67.5 params=2.01/0/-20/0 float=y
maxiter=15000 inside=0 logmap=-1145 periodicity=10
colors=000jgZkeVkcRlbNm`JmZFnXBnV9nW8nX7nX7nY6nZ6n\
Z5n_5n`4n`4ykDvgJtdOraUpZZnVdlSijPohMtfJyeMxdOxcRx\
bTwaWw`Yw_`vZbvYevXguWjuVluUotTqtSttRvtVnvYfwaZydS\
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TE7VI7XL7ZP7`S7bW8dZ8fb8he8ji8ll8mo7hk7ch7_e7Va7RZ\
7MW7IS7DP65G79M7DR8HW8L`9Pe9TjAXoA`tAcy9aa8`F9aE9b\
EAcDAdDAeCBfCBgBChBCiACjADk9Dl9Em8En8Bm6En8Gn9JnBL\
nCOnDQnFTnGVnHYnJ_nKbnLdnNgnOhrNinPijQifSibTiZViWW\
jSXjOZjK_jGajCbl6bj9ciCchFdgIdfLeeOedRfcUfbXga_g`a\
g_`hZ`hY_hY_hX_iWZiWZiVZiUYjUYjTXjSXjSXkRWkQWkQWkS\
ZeTa_VcUWfOYhIZkCcp6_m7Wj8Sg9Od9LaAHZBDWB9TC5QD0G1\
2OD4WP6c`8kl9sw8pr8mn8jj7ge7da7aY7ZU6WP6TL6QH5NC5K\
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DIwDJuGHsJFqMDoOBmR9kU7hX1jW5kW8lVBmVFnUIpULqTOrTS\
sSVtSYvR`wRdxQgyQjzQmvdWssFeTAdXGd_LdbRcbXdeWegVei\
VfkUgmTeyMgoTif_kXf`b_iib
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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times.
