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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's fractal we once again turn to the MandelbrotMix4 formula, and the unusual images to be found therein. The exact expression that was iterated to create today's picture is Z^(-0.9)-Z^(1.1)+C, another deceivingly simple one, which promises nothing but delivers everything. I named the picture "The Laciest Midget", not because it is the laciest fractal I have ever seen, but rather because it is an unusually delicate image, giving the impression of an evaporating universe. Indeed, when studying the image, trying to think of a suitable name, I was reminded of the Veil Nebula in the constellation Cygnus, which is the remnant of an ancient supernova. I was tempted to name the picture "Life" because the elements from which life developed were created in ancient supernovae, but the connection seemed a bit too remote, and I decided on the present name. At first, I considered rating the image a 7. But then I noticed that due to too low a maxiter, the midget is not fully defined. I settled on the present rating of 6. The parameter file renders in 10 minutes. Unless the internet is jammed, the GIF image downloads from: The fractal weather today was once again perfect, and the fractal cats took full advantage of the perfection, lounging on the porch and in the grass from late morning until 6pm. The temperature of 72F (22C) was perfect for any activity either indoor or outdoor. I finished my long philosophical article this afternoon. For those curious to see the article that took a week to refine, it will be posted as a separate article to the Philofractal list immediately following this FOTD. The article is a little hard on science, but it is hard in a way intended as helpful. And now I'm going to call it an evening, feed the cats, and settle into my favorite chair, where I try to watch TV but usually doze off. Until tomorrow, take care, and keep your fractals sealed tightly, or they might evaporate. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Laciest_Midget { ; time=0:10:06.38 -- SF5 on a P200
; Version 2000 Patchlevel 15
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-3.567904787630714/-1.163843669311012/552\
1.075/1/70 params=1/-0.9/-1/1.1/0/0 float=y
maxiter=1200 inside=0 logmap=137 periodicity=10
colors=000S00Q10P40O60M93MC6LD9JGCIJFILIGOLFPODSQCVT\
CXYA_`9ac7cf7fi6gl4jo3mr1ou1rx0uz0vz0yz0zz0yz1xz3vz6\
uz7sz9rzApzDozFmzGlzIjzLizMgzOfzPdySdyTcxVaxX`x__v`Y\
vaXucVufTsgSsiQsjPrmOroMppLpuMsrLppLooJmmJllJijIgiIf\
gIdfGccG`aF_`FY_FXYDT<2>TCPSCOPALOAJMAIL9GJ9DI9CG7AF\
79930C64D77FAAGCDIDGLGLMIOOJQPMTQOXSP_VScXTfYVi_Yl`_\
oa`rdcvfdygfziizjjzipzjozjmzllzljzlizmgzmgzofz<2>paz\
p`zr`z<3>sVzsTzuTz<2>vPzvOzxMzxMy<3>zGxzFxzFxyDuyDsy\
DryDpyDmyClyCjyCiyCfyCdyAc<4>y9Vy9Ty9Qy9Py9Oy7My7Jy7\
Iy7Gy7Fy6C<2>y67z10z43y66<2>pAGlFLiMOfTQc`V`gYMgoQgi\
TgdYg``gXcgQggSjgTigTjg4lg9mgDogGpgLrgPsfSuaXu_`vVdx\
QgyMlzJpzFszAxz6zz4zz3zz3zz1z<3>z0zz0zz0yz0xz0xz0vz0\
vz0uz0sz0sz0r<3>z0xz0yz0z<6>z0zz0zz0z<2>z1zz1zz3z<3>\
z9zzAzzCzzDzzFz<3>zFz
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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times.
