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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's spectacular but mis-shapen little midget exists in the fractal that results from iterating the formula Z^1.2+C. It's a lively scene, reminiscent of the heaving earth at the time the planet was still molten, though instead of fiery reds the scene boasts an incongruous palette of serene deep blues. As I examined the picture, I had the impression of a great thing happening. I decided that the midget, or perhaps the earth itself, was just being born. I named the picture "A Fractal Birthing". The exponent of Z in today's scene is 1.2. As exponents of Z fall farther below 2, the midgets in the Mandeloids become progressively more difficult to find, not only because they become much smaller, but also because they are not surrounded by the symmetrical features that point to pure quadratic midgets. By the time the exponent drops to 1.5, the midgets are nearly impossible to locate, so finding a Mandel midget in the fractal created by an exponent of 1.2 is a real achievement. Actually, the only midget I could find was the one on the negative tail. Yes, I realize that the Z^1.2+C Mandeloid has no negative tail, but this is only when the ground floor of the infinite spiral is examined. The MandelbrotBC formula, which I used to calculate today's scene, draws the more remote parts of the spiral, and it is in these remote parts of the spiral that a kind of tail exists. Since the tail zig-zags off in a northeast direction, it would be more appropriate to call it a positive tail. But regardless of what it is called, the tail has one very prominent midget on it. This midget appears in today's FOTD, which I rated a 7. The parameter file's render time of 15 minutes is nearly totally expended on calculating the shoreline of the high-maxiter midget. The unusually high maxiter of 250,000 is needed to sharply define the edges of the midget, which become quite diffuse at a lower maxiter. The image file has been posted as always to Usenet at: The fractal weather today here at fractal central was once again perfect, with totally clear skies and a temperature of 68F (20C). The fractal cats approved of the conditions by spending nearly an hour lounging in the yard. With much work and housebound cats, I had no time to write philosophy today. But the time of the revelation draws ever closer, so keep checking for imminent enlightenment. (IMO of course.) For this evening, the fractal shoppe is now closing. But it will open again tomorrow, with another FOTD and at least a few words about the image. Until then, take much care, and two fractals at bedtime guarantee a good night's sleep. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Fractal_Birthing { ; time=0:15:10.94 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC center-mag=+0.0809888879629\
3256/+9.393661595475319/101.5492/1/7.499
params=1.2/0/7.06/0 float=y maxiter=250000 inside=0
logmap=24 periodicity=10
colors=00090D70D<3>20J10L00M00O10P<2>90UC0VE2XH4ZL5`\
M6aM7cO9dOAePCgPDhREjREkRGmTHoTJpULrUMsWOuWPwWPwYUuY\
_uYdsYisYoqYuqYzqYysYyuYwwYwyYwyTzsOznJzgGzfDzdAzd9z\
b6zb4z`1z`0z_0z_0zY0zY0yW0wW0wW0uW0uW0sU0qU0qU0oU0oU\
0nT0lT0lT0iT0iT5gPAfMFfLKdHPbEUbDZ`Ac`9h_6mY4rY2wW0z\
W0wY0rY0mY0h_1<3>P`2L`2O`2R`2UcHXfK<4>kuKmwPmzLmzGgz\
C_z7Wz4Tz0Pz0Mz0Oz0Pz1<3>WzHYzM_zR`zW<3>gzqizwizzgzs\
gzngzgfzbfzYfzRdzMdzHdzDbz9bz4bz0`z0`z0`z0bz0bz2bz9b\
zGdzPXzY<2>ezy<2>nzPqzGtz6wz0zz0zz0zz0zz2zz6zzA<3>zz\
TzzYzzbzzW<2>zzDzz7zz2zz0<9>zz0zz0zz0<2>zz0zz0zz2<2>\
zzJ<3>zzlzzszzzzznzz`zzPzzEzz5zz0<13>zz0<3>zz0zz1zz5\
zz7zzCzzEzzJzzMzzRzzUzz_zzb<3>zzuzzzzzozzdzzUzzLzz7<\
5>zzL
}
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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times.
