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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: As even a casual glance reveals, today's fractal, which is the final one for the month of September, has no tiny midget lurking at its center. Most of my time in fractal land is spent tracking those elusive midgets. On the trail of the midgets, I often come upon quite a bit of interesting scenery, which I pass by without recording. In today's fractal, I found no midgets -- the expression being iterated, Z^0.009+C, is too close to linear -- but I did come upon some curious scenery, and this time I did not pass it by. I present it instead as today's FOTD, to show some of the lesser things that exist in the world of fractals, but are too often ignored. The parent fractal is a cucumber-shaped lake with mostly sharp, well-defined edges. One corner of the shoreline however holds an area of chaos. It is in this area of chaos that today's scene is found. Despite its initial chaotic impression, the image is filled with themes -- bits and pieces of order that appear regularly spaced throughout the image. I particularly enjoy the tiny black upside-down triangles scattered about the lower left quadrant. The reason that I named the scene "Sawteeth" is obvious. The reason I rated it at only a 3 is because of its poor composition. It has no focus of attention to prevent the eye from scanning it in a haphazard manner. The 25 minute render time is a bit slow for such a lowly image. This problem can be avoided however by giving Paul and Scott a chance to render and post the image to their web sites, and then picking it up from there. Paul's web site is at: The fractal weather today was a repeat of yesterday, with alternating sunny and overcast periods, and a temperature of 64F 18C. The cats accepted the conditions, though they did not approve of them. I'll have one more philosophy-free day to recharge my batteries. Then it's back to my task of humbly enlightening the world, an oxymoron if there ever was one. We've come to the end of another FOTD. I'm going to do nothing for the rest of the day -- unless I start searching for fractals, that is. Until next time, take care, and it's better to be wise than smart, but it's best to be wise and smart. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Sawteeth { ; time=0:25:39.34--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.54393341766901080/-0.256307459919719\
80/942.2051/1/40 params=1.009/0/-12/1500 float=y
maxiter=5000 inside=255 logmap=366
colors=000tYhsXgrWfqWfpVeoVenUdmTclTckSbjSbiRahQ`g\
Q`fP_eP_dOZcNYbNYaMX`NW_MXZMXYMXXMXWMXVLXULXTLXSLX\
RLXQLXPKXOKXNKXMKWLKVKJUJITIISHIRGHQFHPEHOEFNEFMEF\
LEEKEDKFCKFAKF9KF8KG7KG8KG9KG9KGAKHBKHCKHDKHDKHEKI\
FKIFKIFKIFLJEMJENJEOJEPJEQKERKFSKGTKHUKIVLJWMKXNLX\
OMXPNXQOXRPXSQXTRXUSXVTXWUXXVXYWVZXX_YZ`Z`a_bb`cca\
edbgecifdkgelhfnigpjhrkislhsmhslhslgslgskgskfskfsj\
fsjesjesiesidsidshdshcshcsgcsgbsgbsfbsfbseaseaseas\
dasd`sd`sc`sc`sc_sb_sb_sb_saZsaZsaYs`Zs`Ys`Ys_Ys_Y\
sZXsZXsZXsYXsYWsYWsXWsXWsXVsWVsWVsWVsVUsVUsVUsUTsU\
TsUTsTSsTSsSRsSQsSPsROsRNsRMsQLsQKsQKsPKsPKsPKsOKs\
OKsOKsNKsNKsNKsMKsMKsLKsLKsLKsKKsKKsKKtJKuJKvJKwIK\
xIKyIKzHKzHKzHKzGKzGKzGKzFKzFKzFKzJKzKKzKKzKKzKKzK\
KzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKz\
KKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKKzKK\
zKKzKKzKKzKKzKKzKKzKKzKKz
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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| < a }
END 20.0 PAR-FORMULA FILE==================================
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times.
