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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal features the next midget in an apparently endless series of midgets, which is reason enough to name the picture "The Next Midget". Yes, I realize that a name such as "The Final Midget" or "Dancing Midget" would be more poetic, but I was not trying to be a poet. I was simply trying to name a fractal. The bluish-gray picture, with its metallic appearance and broad, intricate filaments, rates a 6, which is a little above average. I gave the image just the slightest boost in a graphic program. The graphic boost is included in the parameter file. The expression behind the image, Z^(-14)+2.5Z^(-1.45)+(1/C), is simple enough, and thanks to the wonder-formula MandelbrotMix4, it produces a fractal filled with midgets. BTW, I call the M-Mix4 a wonder-formula because I wonder why it sometimes works and other times fails to draw a fractal with midgets. The MandelbrotMix4 formula has an interesting history, which I may tell in one of these C-FOTD's. But today is not the day. It's Saturday evening and the time is near for my weekly excursion into the world of junk TV. With the parameter file having a render time of 1-1/2 minutes, it's a toss-up whether to run the parameter file or to run to Usenet at: The fractal weather today was cloudy with a few tiny drops of rain. The temperature of 67F (19.5C) was un-notable. The cats failed to note it as they frolicked in the yard. There's no philosophy today, but it's coming, so keep in touch. You wouldn't want to miss out on the action when the philosophy breaks. Until next time, take care, and enjoy today's image. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Next_Midget { ; time=0:01:29.75 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip
center-mag=-1.778683555482173/-0.5422446532818447/23\
5454.1/1/-49.999 params=1/-14/2.5/-1.45/0/0 float=y
maxiter=1200 inside=0 logmap=17 periodicity=10
colors=000RQ_UTaWVdZYe`_gcajedlgfmjhplkrmmshhmeeha`d\
ZY_VTVRPPOKKKHGHCAD86C99AAC9CG8CI7DL7EO6GQ5GU3HW2I_1\
Ja1Jd<4>0PZ0QY0RY<3>0WT0YR0ZQ0ZQ5_RA_RH`RL`RRaRYaRaa\
RgcRleRrgTxjTzkTwoUqrVkuWexW_zYUzZPzZKx`HqcDje9cf5Vh\
1Ok0Hm09o0Gj3Ke<2>HZRLcI<3>cvegzkkzqgwvepyahz_azWVzU\
OzQHzO9zK2zI0zH8zHKz<2>GuzGzzKzzOxzTuzWqz<3>lczq_zuW\
z<2>IJz<2>W1z_0zV0zQ1z<3>7Cz2Ez0Hz0Jz2HzAEzJDzRAz<2>\
o6z<3>sAzsCzuDz<3>xIzyJzzKzzKz<8>eVzcWz`Yz<2>U`zRazQ\
`z<2>PZzOYzOWzNWzNVzLUzLUz<3>rTz<3>e_za`z_azWdzUez<3\
>HkzDmzAoz7pz5qz9oz<7>aezedzhcz<3>wZzaRzHKz0Ez0Lz1Tz\
<2>8mzAuzCzzJszQkzWczcVzjNzpGzhHzcIzYJzRKzLLzGNz9Oz3\
Pz0PzEYzVdzkkzzrz<2>zNzzKz<2>zGzETzEQzGPzGNzHKzHJzIH\
zIGz<2>POz
}
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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