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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I am occasionally asked why I set the periodicity to 10 when I use Fractint, when such a setting slows the calculation noticeably. Today's image shows the reason. With periodicity set to 10, as it is in the parameter file, the image renders in 4-1/2 minutes. With periodicity turned off, the image takes 5 full minutes to render. With maximum periodicity checking, (a setting of 1), the image renders in only 4 minutes, but the midget is distorted because the program thinks it sees periodic behavior where none exists, and stops calculating. Through trial and error I found that a periodicity setting of 10 gives the best compromise between time saved and correct rendering. Therefore, I use 10 as the default periodicity setting. Today's image is a dark somber thing with a ring of small and brilliant but shattered cylinders surrounding the midget. I pondered the image a few minutes before noticing that the small red cylinders resemble exploding firecrackers. Once I noticed this, I had my name -- "Firecracker Fractal". Rating the image gave me more reason to ponder. Several minutes of doing other things passed, while the image sat idly on the screen, before I decided that it was worth a 7, a rating that might be a bit liberal. The rather gloomy image was created by iterating the formula -0.6(Z^(-1.3))-0.006(Z^(-3))+(1/Z). The 4-1/2 minute render time can be reduced to one minute or less by giving Paul and Scott a chance to render the image and post it to their web sites at: The fractal weather today was partly sunny with a temperature of 86F (30C) and a few rumbles of thunder in the evening from a small thunder-shower that passed just north of Fractal Central. The fractal cats had an uneventful day, displaying moods of neutrality as they slept peacefully. I had a day of deeper than usual meditation as I pondered the rightness or wrongness of inflicting the death penalty. It's now around 10:30am -- past the time to get busy. So I'll have to cut things short. But I'll return within 24 hours with the next in the unending series of fractals. Until then, take care, and keep those iterations up. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
FirecrackerFractal { ; time=0:04:33.04--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+9.688449083063871/-16.01010465889809/1\
.588386e+008/1/40 params=-0.6/-1.3/-0.006/-3/0/1200
float=y maxiter=1500 inside=0
logmap=66 periodicity=10
colors=000I0XI0bK0fM0iN0nP0sR0vSMtUftM9aXcsIMgN`qI\
VqFShDIZAAP9EQ53M30020000F0Cd0Iz0Fy0Dv0Cq0An0Uz05f\
03m02Z05UA6PK9KfAHdCCvO6zX3zcCzAKr3Sc0`D0h30p00x00\
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ddSfiRhmPiqNktMkxMmyZmykmzxmzznyzpxzqvzstytsvvqtxp\
qynpzmmzkkzihzhfzfczdbzcZzbXzXRqUKhPDZM9PH2FD05A0M\
HzRMzURzXUz`Zzcczffzcnzbvp`zcZzPXzCfv6p`2yD0z00z00\
z09z0Hz3Pz6XzAczDkzHszKzzNzzRzvSzsUzpWzkWzhXzdZzb`\
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vmptiqsdssbsqZtqUvpRvpNpnUin`dnfZmmSmsNmxRqzStzWyz\
Xzz`zzbzz`zy`zmZz`ZzMXz9Xz0Xz0izN`z0bz0cz0dz0fz0hz\
2iz5kz9mzCnzFpzIqzMszPtzSvzWczzdzzfzzhzzizzizzkzzm\
zynzvnztpzqqznszkszhtzdvzbxzZkzzmzznzzpzzpzxqztszp\
tzmtzhvzdxz`zzizzhzzfzzfzzdzzdzzczzczzbzz`zz`zzZyz\
ZxzX0z0Cz0Pz5`zFzzPzzS0z0
}
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.
