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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image takes us to the bottom of the barrel, way down to the land of Z^(1.009)+C. At this abysmal depth, the sand-like fractal material has reached such a high maxiter that it is effectively beyond reach. But the areas of extreme discontinuities continue to multiply, and though still of a very high maxiter, are within reach for those with patience. The 'recip' function was an accident. The 'floor' function works best with this formula, but the image is good, and who's complaining. In today's fractal, the coloring makes the picture. A very broad palette is necessary to add definition to an otherwise featureless image, but when this is done, a series of feathery curving arms appears. I have named the image "This is How Low" because its exponent of Z is about as close to unity as it is possible to come and still get something other than an empty, featureless circle. I have rated the image at an average 5, more for mathematical interest than for artistic worth. If it were not for the render time of over 2 hours on my machine, the image might have rated a 6. But don't be put off by the slowness of the image. Give Paul and Scott a couple hours to render the image, then visit their web sites to download the completed image. Paul's site is: The rain held off on Sunday here at Fractal Central. Despite a temperature that never reached 70F 21C, the fractal cats had a good day. When the cats are happy, I'm happy also, so I also had a good day. Today is actually starting with some sun, and no rain is forecast, making another good day near certain. Once the day's work is behind me, assuming the cats are happy, my day should once again be good. Tomorrow's FOTD might launch out in a new direction, or it might be a return to the MandelbrotMix4 formula and the midgets it draws. To see what happens, check back in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
This_is_How_Low { ; time=2:05:42.24--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=mandelbrotbc1 function=recip passes=1
center-mag=+0.07536313779841985/+0.000859404003554\
35/8654862/1/51/-1.76329913170736319e-009
params=1.009/0/-182/1000 float=y maxiter=12000
inside=255 logmap=3216 periodicity=10
colors=000zlPzmQzmQzmQzmQzmRzmRymRymRymRymSxmSxmSx\
mSxmUwmTwmSwmSwmRvmRvmQvmQvmPumPumOumOumNtmNtmMtmM\
tmLslKskKsjJsiJrhIsgItfHueHvfGwfGxgFygFwhEwhEwiDwj\
CziDziDzhDzhDzgEzgEzfEzfEyeExeFwdFvdFucFtcGsbGrbGq\
aGpaGo`Hn`Hm_Hm_HmZIlZIlYIlYIlXIlXJlXJlWJlWJkVJkVK\
kUKkUKkTKkTLkSLkSLjRLjRLjQMjQMjPMjPMjONjONiNNiNNiM\
NiMOiLOiLOiKOiKPhJPhJPhJPhIPhIQhHQhHQhGQgGQgFRgFRg\
ERgERgDSgDSgCSfCSfBSfBTfATfATf9Tf9Uf8Ue8Ue7Ue7Ue6V\
e6Ve5Ve5Vg3Wf4Ve5Ve5Vd6Ud6Uc7Uc7Tb8Ta8Ta9S`AS`AS_B\
R_BRZCRYCQYDQXDQXEPWFPWFPVGOUGOUHOTHNTINSINSJMRJMQ\
KMQLLPLLPMLOMKONKNNKMOJMOJLPJLQIKQIKRIJRHISHISHHTG\
HTGGUGGVFFVFEWFEWEDXEDXECYDCYDBZD9YCBZDC_DD_DE`EF`\
EGaEHaEIbFJbFKcFLcGMdGNdGOeGQeHRfHSfHTgHUgIVhIWhIX\
iJYiJZjJ_jJ`kKakKblKclKclJblJalJalJ`lI_mI_mIZmIYmH\
YmHXmHXmHWmGVmGVmGUmGTmFTmFSnFRnFRnEQnEPnEPnEOnDNn\
DNnDMnDLnCLnCKnCJoCJoBIoB }
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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