FOTD -- September 13, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image in the Mandelbrot set lies within the range of conventional math, yet it rates an 8.5. This shows that the more accessible shallow parts of the M-set are not quite as thoroughly explored as some might assume. The image is located in the debris-filled radical of a remote bud on the northwest shore line of the main bay of the M-set. The name "A Siegel Connection" refers to the resemblance of the basins in the image to the so-called Siegel Disks of the siegel- disk fractals, the Julia sets with a C-value of -0.390541,+-0.586788i. Actually, I am not sure what is so special about Siegel Disk fractals. I assume the corresponding Mandelbrot points of the official Siegel Disks are on the exact edge of the M-set, yet an infinity of other points are also on the edge. Why then should these particular points be so special? As is usually the case with fractional ratings, the extra half- point is a reward for my coloring, which is the greater part of the image. The extremely brief calculation time of 45 seconds can be attributed to the relatively shallow magnitude of 3*(10^11), which is within the range of the high-speed conventional math routine. For the convenience of those who do not calculate fractals, the image is posted already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A near perfect day prevailed here at Fractal Central on Tuesday. The blue skies, puffy clouds, gentle breezes and temperature of 84F 29C were just what the fractal cats ordered. They spent the day in their window, wishing they could go out and be a part of the world. The humans passed the day just being human, which is sometimes not as easy as it appears. The next FOTD will be posted in 24 hours. For all I know, it might make it. Until then, take care, and are fractals animal, vegetable or mineral? Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= A_SiegelConnection { ; time=0:00:45.15-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.3031762780813\ 251/+0.6219200633096369/3.178477e+011/1/72.5/0 params=0/0 float=y maxiter=300000 bailout=9 inside=0 logmap=1442 periodicity=6 colors=000DmdEneIodMpdQqeUrfYshatieukivmmwoqxqtyru\ yquypuypvyowyoxynyymwzmwzmwzrwzvwzzwzzwzzwzzwzzwzz\ wzzzzzzzzzzzzzzzzzvzzrvzmrvhmrchmZchUZcUUZUUWUUTUU\ SUUSUURUURUUQUUQoNhudztfvtgsshpsjlrkirlfrmcqo_qpXp\ qUpsQotNouKovHluKjtNhtQfsSdsVarY_q_YqbWpeUpgPfcLX_\ HNWDDS93O82R82U82X72_72a72d62g62j62l97jCBiFFgIJfKI\ hLIiMHjNHkPGmQGnRGoSFpUFrVEsWEtXEuWHsVKqVNoUQmTTkT\ WiSZgRaeRdcQgaPj_PmYOpWOsUGZV9KWBANDAEEA6FDAFCDFBH\ FBKFANF9RF8UG8YG7`G6cG5gc0mG4nG3qG3tH5sI6sJ7rK9rLA\ qMBqMCpNEpOFoPGoQInRJnSKmSLmQNlOOkNQkLRjJTiIUiGWhF\ XhL`fRcdWfbai`flZloXqrWspSunPwlMyjJziHziGziFziEziD\ zhBzhAzh9zh8zh7zg5zg4zg3zg2zg1vg0rh5mhAhhFchKZhPUh\ UPfSLdQKbOJaNI_LHYJGWIFUGDRECQDBNBAL99J88H67E46D35\ F45H45J44K44M44O43R43T43X42Z42bU2cU1dU1fZ1gZ1hZ2eZ\ 3cZ3aZAaZG`ZM`ZS`ZZ`Zd`Zj`sp`urYntWhvTbwRXoV_gZb`b\ dTfgMjiEnl7rnCsl8pGAoLBnQ } END PARAMETER FILE=========================================