June 25, 2010: Cometary Residue | June
24 |
June 26 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's formula, FinDivBrot-2J, is a new one. Actually it's
simply a Julia version of the FinDivBrot-2 formula. Today's image
is the first one I found with the new formula, and it rates FOTD
status. I cannot recall this ever happening before.
The 'comet' with the long, long tail that streaks across the entire
frame is actually a complete Julia set, one of the most unlikely Julia
sets I have yet stumbled upon. The corresponding Mandelbrot
fractal is a Mandeloid with everything scrunched around toward the main
stem, and the east side of the main bay cut off by a straight
wall. Today's image corresponds to the point where the curving
north shore line meets the straight wall.
The image resembles a comet zooming across the sky. (In fact,
comets do not zoom across the sky except in the movies.) I rated
the image at a 7, which is above average. The colors are quite
smooth, and it has some math interest, all of which add to its worth.
The name "Cometary Residue" came about when I turned the image upside
down. It originally was rotated 180 degrees from its present
orientation.
The coloring smoothness was achieved by rendering the image with the
outside set to 'tdis', which colors the points according to how far
they travel before escaping.
The calculation time of under 2 minutes is not too high a price for the
result.
Partly cloudy skies, a temperature of 88F 31C, lower humidity and a
refreshing breeze made Thursday quite an acceptable day here at Fractal
Central. The fractal cats came out of hiding long enough to get
into a squabble over who would spend the afternoon on the foot stool.
My day was satisfactory, as far as that goes. And if all goes
well, tomorrow will be a repeat. With the drought growing worse
here in Pennsylvania, FL is concerned with her garden, but so far, with
generous watering, the plants appear to be holding up rather
well. The next FOTD will be posted in 24 hours. Until then,
take care, and be satisfied.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
Cometary_Residue { ; time=0:01:50.09-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2J function=recip
center-mag=10.892/-14.7808/0.052083/1/90/0 float=y
params=1/1/10000/0/0.79606/0.19699 periodicity=0
maxiter=5000 inside=255 outside=tdis symmetry=none
colors=000zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzMzzNzzNzzOzzOzzPzzPzzQzzQzzRzzRzzSzzSzzTzzT\
zzUzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzbzzbzzczzczzdzzdzzezzezzfzzfzzgzzgzzhzzizzizzjz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzASsASsBSrBSrBSqCSqCSpCSpDSoDSoDSnDS\
nESmESmESlFSlFSkFSjGSjGSiGSiHShHShHSgHSgISfISfISeJ\
SeJSdJSdKScKScKSbLSaLSaLS`LS`MS_MS_MSZNSZNSYNSYOSX\
OSXOSWPSWPSVPSVPSUQSTQSTQSSRSSRSRRSRSSQSSQSSPTSPTS\
OTSOTSNUSNUSMUSMVSLVSKVSKWSJzzJzzIzzIzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz9zz8zz8zz7zz7\
zz6zz6zzzzzzzzzzzzzzzzzzzzzzzzzzzzz4zz4zz5zz5zz6zz\
6zz7zz7zz8zz8zz9zz9zzAzzBzzBzzCzzzzzzzzzzzzzzzzzzz\
zzzzzzzGzzHzzHzzIzzJzzJzzKzzKzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzTzzUzzUzzVzzVzzWzzWzz\
XzzXzzXzzWzzVzzUzzTzzSzzz }
frm:FinDivBrot-2J { ; Jim Muth
z=pixel, c=(p3), a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }
END PARAMETER FILE=========================================