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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: What could be better for the fourth of July than a fractal that rates a 4? Well, perhaps a fractal that rates a 6 or 8 would be better, but we'll ignore those technical details and consider today's image just the thing for our national Independence Day holiday here in the USA. The image was created by Andrew's MandelbrotBC (Branch Cuts) formula, which draws the more remote parts of the fractals with fractional exponents. I wandered a rather considerable distance away from ground level in the Z^2.006+C Mandeloid to find today's midget, which is close to a larger midget. I named today's picture "More than a Midget" because the midget at the center is just a bit more complex than the standard Z^2+C midget. It is quite a bit more complex in fact, for it is split right down the negative tail by one of those branch cuts, as well as surrounded by cut-off bits of filament. A close examination will reveal 8 plus a fraction elements around the midget. This is only to be expected in a fractal with an exponent of 2.006. In fact there are 8.072 (2.006^3) elements circling the midget. The parameter file renders in a relatively fast 3 minutes on a Pentium 200 machine. If this is too slow, the GIF image file may be found ready for downloading at: The day's fractal weather was partly cloudy and humid, with a temperature of 88F (31C) that was perfect for the fractal cats, who enjoyed the afternoon on the porch. After dark a mild thunder-shower passed over, which cooled things down for the night. Until tomorrow, take care, and see you in 22 hours. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
More_than_a_Midget { ; time=0:02:50.98 -- SF5 on a p200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-1.05309114080759600/-0.00068667328146814\
/3.069438e+008/1/-92.5 params=2.006/0/233/0 float=y
maxiter=1000 inside=0 logmap=94 periodicity=10
colors=000JHsODoTEsTFuSNnMVeGbYAkP5qH9lEDfBGZ8KS5OH2\
RA0VI9_QIeXQkdZokfpfgvahqXimSjcNkYIlXDmX8nX4oY5mZ5lY\
6jX6iX6gY7f<3>V8`U9ZT9YS9XaRPthHzz9vwDstGnrK<5>ebcd_\
fbXj<3>YNwa6v<3>MPwIUxEYxAbx6fx<9>8VT8UQ8TN<3>8PB<3>\
Ycddgkjjr<8>_NtZKtYHu<3>U7u<3>Zjm_slVof<3>EcK<3>GfJG\
gJHhI<3>IjI<5>YPb`LecIi<3>m4v<8>ZWZYZWWaT<3>QmJ<5>Xd\
AZc8_a7<3>cX1<3>YNbXKkWIt<3>bgLdnCet4<3>iwIjxMjxP<3>\
jwN<3>XwUWwW<2>Zw`_wa`wbawcbwd<3>fwigwjhwk<9>rwmswnt\
wn<3>xwnywk<3>zwczw`zwZ<3>zwRzw`zwi<3>zwNzwHzwCzw6zw\
1<3>zwZ<5>zw`zwQzwOzwg
}
frm:MandelbrotBC = { ; by Andrew Coppin
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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