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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image shows a midget of a very low order, located in the fractal that results when the formula Z^(1.075)+C is calculated 175 levels up the complex logarithmic ladder. I named it "How Low Can You Go". I gave it this name because one of my current fractal quests is to see how close to unity I can set the exponent of Z and still find midgets in the resulting fractal. The current record is Z^(1.045), but the midget I found there lacks the quality to be a FOTD. Today's parent fractal, like so many other very-low-order fractals, is little more than an elongated oval surrounded by large areas of sandy fractal chaos. The midget in today's scene, which is located in the chaos of its parent, was found by using the 'fmod' outside option. Without this feature, midgets in such low-order fractals would be impossible to find. I rated the image at a 6, more to show my satisfaction at finding the midget than to comment on the quality of the image. But this does not mean I consider the image to be worthless. It is in fact quite an interesting scene to come from a power of Z so close to a straight line. The calculation time of 8-1/2 minutes is slightly slow for an image that is only a little above average, but relief from the impatience is at hand on the FOTD web site at: The New Year's Day weather was dreary here at Fractal Central. Thick clouds covered the sky all day, with occasional periods of light mist and a temperature of a most un-winter-like 50F 10C. The cats of the fractal variety spent the day looking for trouble but finding little now that the last of their left-over Christmas play things have been cleared away. My day was quite relaxing, but the work today should pick up dramatically. The next FOTD will appear in 24 short hours. Until then, take care, and feel free as a sea gull. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
How_Low_Can_You_Go { ; time=0:08:30.14--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1 logmap=122
center-mag=+0.72919018137204830/+5.829204067242754\
00/150370/1/112.5/-1.98509829407722549e-009 float=y
params=1.075/0/175/525 maxiter=6000 periodicity=10
inside=0
colors=000lUAlVAkWAkXAjYAjZAi_Ai`AhaAhbAgcAfdAeeAd\
fAcgAbh9ai8`j6_j4Zj2Yj3Xi4Wg5Vf6Uc7Sa8PZ9NXALVAJSB\
HQCFNDCLEAIF8GG6DH4BI07G29I4BK6DM8EOAGQCISDJUFLWHN\
YJV_LW`NYbP_dQafSbhUcjWdlYen_fpagrbhsairajrairahr`\
hr`gr`fr`er`er_dr_cr_cr_ar_arZaqZ_qZ_qZZqYZqYZqYYq\
YYqYXqXXqXXqXWqXWqXWqYUoYTmYSkZRjZQhZPfZOd_Nc_La_K\
__JY`IX`HV`GTaFSaEQaDOaBMbALb9Jb8Hb7Fc6Ec5Cc4Ac39U\
DjLMkMKlMJmNInNHoNFpOEqODrOCsPBtP9uP8vQ7wQ6wQ5wP8w\
PAwPCwPFwPHwPJwPMwPOwOQwOTwOVwOXwO_wOawOcwOewQbwR`\
wSZwTXwUVwVTwWRwXPwZMw_Kw`IwaGwbEwcCwdAwe8w_9wUAwO\
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`TuZTtXUsVUrTVqRVpPWoNWnLXmJXlHYkGWmFYkFZjE_hE`gDa\
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sJ5tI4uG4vF5yB4zE4zG4zI4zK4zM4zO4zQ4zS4zU4zW3zZ3z`\
3zb3zd3zf3zh3zj3zl3zn2zo3zp4zp5zp6zp7zp7zp8zq9zqAz\
qBzqCzqCzqDzrEzrFzrGzrHzr }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100, p=real(p2)+PI
q=2*PI*floor(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 PARAMETER FILE=========================================
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times.
