FOTD -- October 28, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is unusual enough to rate an 8. Its generating expression is (Z^3)-0.355(Z^4)+C, which creates a parent fractal consisting of a small Mandelbrot set rotated 180 degrees and surrounded by holes. Just beyond the main spike, which points east, lies a large butterfly-shaped hole partly filled with something resembling the East Valley of a much larger but mostly hidden Mandelbrot set. Curiously, this area of the parent is extremely sensitive to small changes in the real(p2) parameter. Today's image lies just north of the X-axis, rather deep in this phantom East Valley. The image strikes me as an unusually well-defined circular ring of pink clouds surrounding an orange minibrot, spectacular enough to rate an 8. But perhaps the most unusual feature of today's image is not in the frame at all. It is the phantom East Valley of the parent fractal in which today's image lies. The larger minibrots in this phantom valley come in all shapes and sizes, as well as in all orders from quadratic to quintic. Many of the minibrots are of a never-before seen, random variety. I might feature a few of these weird semi-critical minibrots in the FOTD's over the next week or so. The actual name I gave the image is "Ring Around the Minibrot". This name did not fit into the allotted space in the parameter file however, so I cut off the 'brot' part. The calculation time on the inactive 2000mhz machine would have been an estimated 52 seconds, quite a bargain considering the quality of the image. The image is posted for instant viewing on the questionably 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 original, now venerable, FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Lots of sun prevailed here at Fractal Central today, but later in the afternoon, clouds started moving in, preparing for the major snowfall expected tomorrow. The temperature of 45F +7C was cold for the season, causing the fractal cats to seek extra warmth. The humans had a typical day. I spent a half hour or so lining up the snow removal tools, though it remains to be seen if they will be needed -- at least for this storm. The next FOTD is not in doubt however. It will be posted in 24 hours. Until then, take care, and I must have over-estimated the number of working brain cells remaining in the general population. When I commented this morning on the quality of today's popular music, the immediate reply was, "what's wrong with it? It's great." I shook my head and thought, it's great for the brain-dead. I guess this makes me an old fuddy-duddy. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= RingAroundTheMini { ; time=0:00:52.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=+0.49827164808178630/-0.000969928530694\ 85/6.81019e+011/1/165/0 params=1/3/-0.355/4/0/0/0/0 float=y maxiter=1000 logmap=131 mathtolerance=.05/1 colors=000A0cA1cA4aA7_A7YA7WA7UF7RG9MLBLQGDVH7_H3z\ zzzpzzjxtcopZdhTZZHKPAAH20EGCAVO6i_2wl9siFpgKkfQgd\ YfkcemefmhfnjfqofuifxkfzHwdfZNzB5sCGfEQVEaQHZOLWKO\ UHSQFVO9d_4pj6gd9__BUVELPGEKJ7FFFCCLAAU97_64f41n20\ u00z02z09z0Fz0Kz0Qz0Xz0cz0iz0az2VxCOrNHmXBhg5cs0_z\ 1Uw4Oq5Hl7CfA6_B1VE0PF0KJ0LNANQKOUVOXdPapQczQimVmb\ XsSawGcz6gz0jx0iq2ii6ib9iWBgOFgHHgBKgOlzFNtHFVALZ2\ Qb0Wd6XbGZ_Q_XaaVlaSdUX_LaVFdO7jJ0nE0s0jB0ab9Sz6Px\ 4Nt1Kn0Hj0Fd0Ca0BX0AS09N07H27E569754A40B40C70CA0EE\ 0EG0EK0FN0FQ0FU0GS6GSFGSOHSXHSfHSpHSzFZwCcuAjt9pq6\ wp4zn2zmW0da2cdAbiHbmPaqX_ud_zmZzuZzxVzzQzzOzzKzzG\ zzEzzAzz7zx9znAzdBzWCxNEwEFu5Gt0Gp0Jm0Kj0Ng0Od0Qb0\ SW00_00c60gE1kK4oS6sZ7wjEzuKzjAza1zS0z0gz7ZzOQzUQz\ XQz_KzaEzc7zd1zg0zi0zd1zbCz_NzXZzVizSuzPzzWzzauzfp\ zllzcjzXizQgzKfzEdz7cz1bzcbzcXzFSzOOzZJziEzsAzdNzS\ ZzFlz2xzBzzJzzQzz_zzgzzpz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================