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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: It's a fractal survivor that won the honor as the FOTD for February 2 -- the last midget that still existed as the world closed in around them. The midget is a tough little contestant, surrounded by sharp angular discontinuities and harsh colors. To find such a tough midget, I started with the formula Z^1.5+C and gradually lowered the exponent until the midgets vanished. As the exponent of Z is lowered past 1.5, the midgets become increasingly hard to find, until at around Z^1.25, where none are left at all. Today's midget however breaks that rule, since the exponent of Z that draws the parent fractal of today's scene is 1.19. Since it's such a robust little midget that appears in today's picture, I named the image "A Fractal Survivor". The intentionally harsh colors keep the rating at an average 5, though a 6 might have been more appropriate if the conditions had been more normal. As is the case with all midgets in this sub-basement zone of the world of fractals, there is no well-defined shape. Instead, the shape of midgets varies randomly. Today's midget for example is roughly elliptic, with the tiny buds few and far between. Some midgets this low down the exponent ladder have no buds at all, and all midgets appear to have at least one edge with ill-defined borders. But my fascination with this exponent range lies not in the shape of the midgets, but in the challenge of finding them. The parameter file of today's image renders in 11 minutes on an aging Pentium machine running at 200mhz. Yes, I realize that this time is a bit too long to wait to see such an outstanding scene. So to ease the wait, the pre-rendered GIF file will soon be posted to the web at: The fractal weather today was partly sunny, with a temperature of 49F (9.5C), which must have pleased the fractal cats, who spent over an hour in the yard, watching for squirrels and birds. And that's it for tonight. I'm about ready to shut down the fractal shoppe and call it a night, but I'll re-appear tomorrow around this same time. Until then, take care, and may the good fractals prevail. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Fractal_Survivor { ; time=0:11:11.24 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=t
center-mag=-0.86047093804658910/+2.98274963158541900\
/1029.124/1/19.999 params=1.19/0/4/0 float=y
maxiter=30000 inside=0 logmap=65 periodicity=10
colors=000H6UH6U<14>HPkHQmHRnHSoHUqHVr<3>H_wH`xJbyKc\
zLdzMezLdyLcwLbtLbrL`o<3>LYdLYbLW_KVYKUVKUSKSQKRM<3>\
KPCKOAKM7CK0KM5QOBWPG<3>vVczWizYnzZkz_iz`g<3>qeYogVm\
hS<2>ejMckK`mHZnFYoCVqA<3>Lv0Jw0Gx0Fx0Cv0As08q26n55k\
82iB1gE0dG0hH0bJ0WJ0QK<2>47L51M50L<3>70Q71R72S<2>86W\
87Y88YCCV<2>MMOPQLSSKWWHZ_FbbCdeAhi7kk6no4rs1tv0xy0y\
z0zz0vx0qt0kq0<2>Ye4Rc0Sb5Sb8SbCUbGUbKUbP<3>VbcWbgWb\
kWboYbsYbwYbzYbzWYz<2>WMzWJzVEzVAzV6zV2zV0zU4zU7ySBw\
SFtSJrROo<2>QZhQbeRgdRjcRocRsbRx`Rz`UwcWreZm``hhccie\
ZnhUrnPvvPyzSz<3>zKzzHzzGzzEyzByzAyz7xz5xz4xz6vz8szA\
rzCozEnzGkzHjzKhzMgzOdzQczR`zU_zVYzYWz_Uz`SzcQzdPzgM\
zhLzjJzrE<3>zUR<19>zWPzWPzVQzWP
}
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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