Fractal of the Day
by Jim Muth
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FOTD -- February 19, 2010 (Rating 7.5)
Fractal visionaries and enthusiasts:
Today's image is named "A Slipped Disk". This does not refer to a medical condition; it refers to the Siegel disks in the fractal, which have suffered some kind of slippage.
Actually, there are no Siegel disks at all in the image. Siegel disks are purely Julia objects, while today's image, which is rotated 0.02,0.02 degrees from the Julia orientation, comes close but wins no cigar. In this case, the tiny rotation makes a world of difference.
Actually, I have never had a clear idea of exactly what makes a Siegel disk. I know the disks appear in the Julia sets of points on the edge of the Mandelbrot set, but just what parts of these Julia sets are called Siegel disks?
Well, I guess it really doesn't matter. As today's image shows, not-quite-Siegel disks can make interesting images, especially when they are rendered with the inside set to 'bof61'.
The rating of 7.5 includes a small bonus for the coloring. The calculation time of 30 seconds will pass in a flash, as fast in fact as the trip to view the finished image on the FOTD web site at:
Thursday featured partly cloudy skies and a temperature of 39F +4C here at Fractal Central. The fractal cats, who dislike partly cloudy weather with its on-and-off sunshine, spent only a few minutes on their sun-shelf before seeking the artificial heat of the large radiator in the hallway.
My day was close to normal; tomorrow should be the same. The next FOTD will be posted in 24 hours. Until then, take care, and speak with some wisdom.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
A_Slipped_Disk { ; time=0:00:29.86-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm float=y
formulaname=SliceJulibrot4 symmetry=none periodicity=6
center-mag=0/0/0.94 logmap=yes maxiter=500 inside=bof61
params=89.98/0/89.98/0/-0.390541/-0.586788/0/0/2/0
colors=000hkNjlRlmUmnYoo`qpcrqgtrjvsmwtqyutzvwzzzw\
wwuuuyrhyodylayhYydUy`RyXNyRJyPGsTHnXIh_JccKYfLTjM\
OmMGfK8_I0UG6SMCQRHOXNMaTKgYIlcGrhEweCrbAn`8jaAgbC\
dbEacFZcHWdJUdLReMOfOLfQIgSGgTDhVAhX7iZ4i_2gb8edDc\
gIaiN_lSZnYXqbVsgTvlRxqQzvMowIdxEUyAKzDLsFMmHNgJOa\
aazbZxbWwbTvbQubNtbLsbIqbFpbCob9nb6mb4l`5k_6kZ7kY7\
kX8kW9kV9kUAjTBjSCjRCjQDjPEjOEjSHiVKiYNiaQidShgVhk\
Yhn`hqbhq`fqZeqXdqVcqUaqS`qQ_qOZqNYmO_jO`gOacOc`Pd\
YPeUPgRPhOQiKQkHQlEQmLcXSqGUkMVeRW`WYVaZPf_KkVIiRG\
hNEfJDeFBcB9b78a9UlBnvEnsHnqJnoMnmOnkRniTngWneZnc`\
nacn_enYhnWjnUmnSonQppSpqTprUqsVqtXquYrvZrw_rx`mwY\
ivWeuTatRYsOUsMQrKMqHIpFEoCAnA6n87oD8pI8qN9rS9rWKh\
TV_QeQNoHKkNNhTQdZTadWYjZVo`RpZNpYJqXFqWBqU7rT3rS0\
rR7kSEdTKYURRVYKWcDXj6Yp0Zq6_qC_rH_rN`rS`sY`sb`sha\
tmatsatxaikZZ_WONTEBQA8N75L42J10z8hzF`cGVzHPcIJzJD\
cK7zK2cfezTMbF2z2vzKmzV0m }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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