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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: Distracted as I was by Tippy, the fractal cat, my finger paused a bit too long on the <1> key as I was entering the parameters for today's fractal, causing me to inadvertently enter 111111.... instead of the 11 I had intended as the value of imag(p2). "What the heck," I mumbled as I saw the string of ones. "Let's see what these parameters will do." Substituting a decimal point for the third digit, I let the formula do its thing. As expected, I found that the extra digits have almost no effect on the appearance of the parent fractal. On a whim I set real(p3) to 0.3. The formula then created a grossly oversized and nearly indescribable fractal with grossly underestimated potential. A bit of searching revealed things in the fractal that looked like a space alien's antenna with a bulb on the end. I investigated one of these antenna bulbs. As I went deeper into the bulb, I came to an area of sickle-shaped elements, and soon I found the two symmetrical features that usually mean a midget is hiding there. As today's picture shows, I was once again right. With its star-like coloring and delicate filaments, today's fractal looks pleasing from both near and far, easily deserving its above-average rating of 7. When I saw the eight-pointed star effect, I named the picture "Octagonal Star". Coincidentally, the time the parameter file takes to render on a P200 machine is almost exactly 7 minutes. Yes, I realize that fractalists are sometimes very busy people, so I have mercifully posted the JPEG image file to: The fractal weather today was dry but cloudy and quite cool, with a raw east wind and a temperature of 61F (16C) that kept all but the hardiest picnickers safely indoors. It was a day more typical of those in the Pacific Northwest than those on the Mid-Atlantic coast. The raw weather also kept the fractal cats indoors, where they passed the day eating and sleeping. And now for the bad news . . . yes, I once again failed to philosophize. My humblest apologies to the disappointed and my sincerest empathies to the relieved. But all is not lost, for the longer the philosophy takes to ripen, the better it will be when it's finally ready. So brace yourself for imminent and unexpected enlightenment. But until that time when light shines, take care and keep those fractals coming. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Octagonal_Star { ; time=0:07:03.15 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-15.17590216673625/-56.06011507835237/3.8\
61277e+007/1/142.499 params=1/1.1/1/11.1111111111111\
1/0.3/0 float=y maxiter=1200 bailout=25 inside=0
logmap=136 symmetry=none periodicity=10
colors=00009D<2>07A079268<3>A45C44E33G33<9>_S5aU5cW5\
<2>ic5ke5kg5<4>UOSRKWNG`<3>A0q<5>VTXYYUaaQ<3>ntDnuDn\
vDmvDowD<2>wxDzyDzyD<3>zvEzuEytExtF<3>qqFopFnoF<6>gk\
HfjHeiH<2>cgHbfHbfIbeI<12>XXKXWKXWKWVKWUKWUK<12>EISC\
HSBGT<3>5CVABW<4>ZQMcTN<2>raVsdYtg`ujbtmatpasqa<26>j\
_Yi_XiZX<3>hWXgWYgVZ<3>fTbfScgRd<3>iOhjOimJjjNkkMl<2\
>lKmmJmkOmiNmgNm<7>iMuiMviMwiMxiLy<9>kKzlKzlKz<3>mJz\
<2>ZJzUPz<3>AOz<11>RMzTLzULz<3>_KzeAzdAz
}
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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