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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I rated today's image a 7 because of how well the colors turned out. Although it has only 256 colors, the bands are almost invisible, resulting in a GIF image as close to the appearance of true-color as one is likely to see. I named the picture "Heads Up Mister Midget" when I noticed that the sqrt(3) midget looks almost like a quadratic midget with its nose in the air. For today's image I once again chose the new MandelbrotBC1 formula and calculated the fractal produced by the square root of 3. But this time I set the function to <ceil>, which unlike the <floor> and <round> functions, draws images different from those drawn by the <trunc> function. The parent of today's image is a Mandeloid shaped almost exactly like the midget in yesterday's "Decorative" FOTD. Today's midget, which is shaped exactly like its parent, lies rather deep in a seahorse tail in the Seahorse Valley area of its parent. The branch-cut discontinuities are quite pronounced in this image, making me wish that some way of eliminating them existed. But of course, the breaks are an unavoidable part of fractals with fractional exponents. After several of very fast parameter file, today's is a slow one, taking over 19 minutes to render on a 200mhz Pentium. For those who cannot spare the computer time, the GIF file of the rendered image will be available in an hour or so on the Web at: The fractal weather today was absolutely perfect. The warm sun, cloudless sky, and temperature of 83F (28C) lured the cats into the yard for a full day of enjoyment. They saw no fox, though a raccoon barely escaped detection. And now I once again see that it's time to shut down the olde fractal shoppe and call this day ended but for the wind-down. I'll return in 24 hours however. Until then, take care, and I hear that an apple used to be known as a napple. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Heads_Up_Mr_Midget { ; time=0:19:07.17--SF5 on a p200
reset=2001 type=formula formulafile=branchct.frm
formulaname=mandelbrotbc1 function=ceil passes=1
center-mag=+0.73481980084589390/+0.136649099636705\
70/1.795448e+007/1/-172.499
params=1.73205080807569/0/0/0 float=y maxiter=25000
inside=0 logmap=411 periodicity=10
colors=000YbMZdN_fO`hPbjQclRdnScoSepSfpShqSiqSkqSl\
rSmrSorSpsSrsSssSusSvsSyrUwsSusQssOqsNosLmsJlsIjsG\
hsEfsDdsBbs9ar8`q9`p9_oA_mA_kBZiBZgCYeCYcDYaDX_EXY\
EWWFXVFYU4ZUF_SR`SPaRObRMcQLdQKePIgPHhOGjOElODnPBp\
QAqR9sS7uT6wT2vU5vW8vYBv_DubGudJugMuiOtlRtnUtqXtsY\
tsZtsZts_ts_ts`ts`tsatsatsbtsbtsctsctqcmpdfme_jfTg\
gMehGeiLfkPhlTkmXmnappesqitrmutfum`qiVlcPhWIdMC_G6\
W90S3jzcfvecrf_ngXjiUgjQckN`mJXnGUoCSpDQpDOmEMjEJf\
EHcFE`FBXG9UG6RC0KG4OK8ROCURGXVK`ZOcaSfeYiicmlhppm\
stpvwrywtuwrrwpownlwliwjfwhcwf`weYwdVwcSwcPrdTmdXh\
d`cdd_dgVdkQdoLdsIfzHdvHcsGaoGblFchFeeEgbEiZDkWDmS\
CmPCmLBmI1mGBmFLmFVmE_m0dmESmRFmd1mt2mq2mo2ml3mj3m\
h3me4mc4m`4mZ5oX5qU5sS6uP6wN6yL8zI9zFAzCBz9Ez8Hz8J\
z8Mz8Oz7Rz7Uz7Wz7Zz6`z6cz6fz6hz5kz5mz5pz5sz4uz4xz4\
zz4zz6zz8zzAzzCzzEzzFzzHzzJzzLzzNzzOzzQzzSzzUzzWzz\
XyzWxzWQzGRzHTzIUzJVzKWzL
}
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.
