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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Some broken titles have a certain class. Titles such as 'Broken Blossoms', 'Broken Arrow', or even 'Broken Promises' bear witness to a coming drama. But, 'Broken Doughnut'? What could be classy or dramatic about a broken doughnut unless one drowned in their coffee while dunking it? As for the strange name, something in today's image reminded me of a doughnut. Most likely it was the drab green band surrounding the almost invisible midget at the center. But the reason is unimportant; the fact remains that the image has been named "Broken Doughnut", and that name will be its name forever. After giving the picture its classless name, I rated it a 6, which is just slightly above average on my 0-to-10 scale of fractal worth. The scene of today's FOTD is part of the Z^sqrt(2)+C fractal -- a fractal that has more nooks and crannies and buds and valleys than the earth has ants. Having a fractional exponent, the scene is almost overwhelmed by discontinuities. In fact, the discontinuities are what creates the scene. The parameter file runs in 10 minutes on a worn-out 200mhz Pentium, even faster on a more up-to-date machine. Since I will not be posting the FOTD to ABPF until further notice, the 10 minute run time can be bypassed only by downloading the GIF image file from: The fractal weather today was totally and unabashedly miserable, with a steady rain, raw wind, and a temperature of 39F (4C), which was so obviously unpleasant that the fractal cats were satisfied to remain indoors, gazing from their favorite window. (Windows are a cat's TV.) Since I spent so much time today moving stuff to the new Fractal Central, I found no time to sit and ponder the mysteries of existence. Actually, I need a few new mysteries of existence to ponder. The old ones have gotten stale. So when I get the chance, I'll have to ponder what to ponder. Right now, I'm pondering shutting down the soon-to-be-abandoned old Fractal Central and calling it an evening. Until tomorrow at around the same time, take care, and you may already be a fractal. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Broken_Doughnut { ; time=0:10:03.36 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotBC
center-mag=-1.186109041897596/-0.4223498239916194/80\
27451/1/-32.499 params=1.414213562373/0/24/0 float=y
maxiter=12000 inside=0 logmap=616 periodicity=10
colors=000A0GL0LF0KG0TF0YC0cA1g73l64p36u17y03z07z4Az\
9Fz<3>QTzVXz__y<2>ljxpmxurvyuvzzzzxvxsjuoYplMmg9ic0f\
`0d_0c_0c_0a_4a_9`_D__J__OY_S<2>X_d_```aXacSddOffJgg\
F`g0iiApiPxjcziszjrzlpzmoyoovpmurlrsjpujmvilxgiyfgzf\
dzdczc`zaXzm_zalzJazSSz`Izg7zp0zx1zr4zm6zg9zcCz_DzTG\
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6ig6jg7lg9mg9<2>6Gu07z6GzJOpYXfocXvgIxjMydPz`SzVXzQ_\
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TGDPAFL4GG0IC0M90J90I90F90D90C90990790690390190<3>09\
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2>cdIfiDglAjo6lr3mp7opCopGpoLpoProTsmYsmaumfumjaipJf\
v0cz4`u9_pDYjGXfLTa<2>XPO_SLaVJdXGg_FjaClcAof7ri6uj3\
xm1zp0zr0zu0zx0<2>zz0zx0zs0xm0ri0of0lc0f_0`T0VP0PL0J\
F0
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(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| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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