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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal discussion will once again have to be short. I spent so much time yesterday mopping up the fractal basement and saying un-nice words (which displeased the fractal lady) that the necessary work fell behind and must be finished today. But even the wet basement and late work could not deter me from my obsessive search for ever more fractals. The search led to the MandelbrotBC1 formula and the parameters that generate the Z^1.9+C Mandeloid. By using the evolver feature, I was able to quickly find an interesting section of this infinite fractal. The parent fractal is a reasonably intact version of the Mandelbrot set rotated about 150 degrees. The greatest distortion appears on the southern shore of East Valley, which at this orientation lies on the negative X-axis and is much broadened. Today's scene is found in one of the chaotic areas extending inland from the shoreline. I named the image "Almost a Minibrot" when I noticed that the skewed central midget is otherwise almost perfect. Only the ragged southern boundary and missing bud prevent midget perfection. The ragged appearance can be eliminated by raising the maxiter of the image to 30,000. At this higher maxiter a vestige of the southern bud does appear, but raising the maxiter this high compresses the colors so close to the midget that they effectively vanish. I rated the image at a 7. This rating, which is a result of serendipity, is due to the striking color palette, which I found basically by accident. I needed to adjust only a few registers before the image was finished. The parameter file renders in under 7 minutes on my 200mhz fractal machine with the noisy fan that often needs to be nudged by hand before it starts running. The GIF image may be found on the internet at: The fractal weather Monday here at Fractal Central was absolutely perfect, with crystal blue skies, a temperature of 66F 19C, and light winds. It was perfect weather for mopping out the fractal basement and spraying to eliminate the musty odor. The day's weather was also exactly the kind that keeps fractal cats happy all day. I'm glad the cats were happy all day -- happy cats are far easier to live with in times of irritation. The current news about cloning human embryos has gotten my philosophical wheels turning, but it's a confusing situation, and it will be a few days yet before I have a definite point of view to write about. And now, I've got the day's tasks to attend to. Something tells me that if I hope to finish, I'd best get started. Until next time, take care, and fractals are far easier to clone than people. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Almost_a_Minibrot { ; time=0:06:47.27--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-0.556651401596578/-0.020121851241034/2\
813591/1/20/-1.46463775899108306e-008 params=1.9/0\
/-34.54/0 float=y maxiter=1800 inside=0 logmap=176
colors=000C00900700A00D00B00J40L70OA1WF4cI6XL7YPA`\
QCcTDfYGiaIjdJmiMplOsoPvsSxvTzyVzzYzz_zz`zzYzxXzrV\
zlSzgQzaPzXMzQLzOMzMJzLIzJFyIDvGAsF9pD6mC4lC1iA0f9\
0c70`60Y40V30S10Q10S70TFAVFFXFFYFF_FF_7D`9CaACcCAc\
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J03G01F00C00A03F06K39P6DU9GZCJcAJhDMmGOrJPwMQzPSzS\
VvVXtYYr`_mc`hfccidclfcogcriculcxmczoczpczrczsczpa\
zmazjaxiaufarcapaam_`jX`gT`dS`aP`_M`YL`_Pa`Sc`VdaY\
fcagcdidgjdjlfomgrogupixrjzsjzulzvlzvmzrmzooylouip\
pfpmcri_rdXsaTsYQuTOuQLvMIvIDxFAxA7y64y31z00z00p30\
gA4_I9QODGQI7SM0UQ0WT0YS0_S0aS0cQ0eQ1gQ3iQ4jP6kP1l\
P0mP0oP0q00s00u01w06w0Aw0Fw0Jw1Ox1Py3Qz3Sz4Tz4Vz6X\
z6Yz7_z3`z7azAczFdzIfzMgzPizSjzTlzTmzTozTpzTrzTszT\
uzTvzTxzTyzTzzTzzTzzTzzTzzTzzTzzTzzTzzTzzTzzTzzTzz\
TzzTzzTzzTzzTzzTzzTzzTzzT
}
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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