FOTD 13-01-10 (A Golden Oldie [6])
FOTD -- January 13, 2010 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image is the same one that gave us yesterday's image. This parent consists of two somewhat distorted Mandelbrot sets, but instead of lying in the East Valley of the eastern set, today's image lies in the East Valley of the western set. Now that the location is straightened out, little remains to be said except that the image rates a 6 and I named it "A Golden Oldie" for some reason that I have since forgotten. The image is an incredibly fast one, calculating in only 25 seconds, which is likely even faster than the brief time and effort required to see the image, already calculated, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday dawned with a fresh 2cm of snow on the ground here at Fractal Central. The rest of the day was typical midwinter stuff -- partly cloudy with a temperature hovering just below freezing. The fractal cats ignored the outside conditions and spent their time keeping warm indoors. My day was average. The next FOTD -- above average to be sure -- will be posted at this same spot in 24 hours or so. Until then, take care, and see you then. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= A_Golden_Oldie { ; time=0:00:24.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.86630327098/0/185328 params=1/2/0.05\ /-2/0/0/0/0 float=y maxiter=850 symmetry=xaxis inside=0 logmap=34 colors=000A9KCAKEDKGFKIHKKJKMLKONKQPKSRKUTKWVKYXKm\ bKjZKgXMdUJaRGZODWKATH7QE4NB1QD3VE5ZG6cH8hJAlKBqMD\ uNEqQFmYFi`KehUakcYsmVuzWtmXrcXqUYpKZo7Zm6_l4`f2``\ 1cY2e_3ha4jc5md6of7rh8tj9vkAseEp_ImUMkOQhIUeCYb6a`\ peapccpbepagp_ipZkpYmohonmnmqmlulkukiujhuiguhfugdt\ fbqe`nc_kbZiaXf_VcZUaYSZWQWVOTUNRSLORJLQIJSHKTHLUH\ LYIIaJFdJDhKAlL7oL5lN4jP3gR3eT2bV2`X1YZ0W`0Tb0Rd0O\ f0Mh0Jj0mCRlFPjJOiNMgRLfUJeYIcaGbeFahEbeGcbId`KdYM\ eWNfTPfRRgOThMUhJWiHYjE_jC`gF_dH_aK__M_XP_UR_RU_PW\ _MZ_J`_Gc_Ee_Bh_Bj_Bl_BgZDcZGZYJVYMRYNSZOS_OT_PT`P\ T`QUaQUaQVbQVbQWcQXcQYcQZbQ_aQ``Qa_QbZQcYWcXacWgcV\ ncUtfZzkbui_qgYmfVidTebRaaOX_MTZJPXzLVzHUzDSzBRzGP\ zNOzUNz`LzgKznJztIzsJzsJzsKzrKzrLzrPzqUzqZzqczohzm\ mzkrzivzgzzezzczzazz_zzYzzWzzUz0Wz0Xz0Yz0_z1`z3az4\ bz5dz7ez8fzAhzBizDjzEkzFlzFmzGnzGozHpzHqzIqzIpzLpz\ OpzRpzTpzWpzZYzUXzVXzWTza } 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=========================================
A question was recently asked in the FractalForums concerning the quantity of midgets found closely clustered together: http://www.fractalforums.com/mandelbrot-and-julia-set/proximity-of-minibrots... I was wondering if anybody had some images readily available for reference purposes?? (I am too tired at the moment to recall where I have seen such renderings.) Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/
Paul N. Lee wrote:
A question was recently asked in the FractalForums concerning the quantity of midgets found closely clustered together:
http://www.fractalforums.com/mandelbrot-and-julia-set/proximity-of-minibrots...
I was wondering if anybody had some images readily available for reference purposes?? (I am too tired at the moment to recall where I have seen such renderings.)
I guess a better view (of larger midgets) could be achieved by panning to the lower right, but still: http://www.abm-enterprises.net/fractals/mandelbrotgalaxywallpaper.html Two quotes from Michael Frame's pages at Yale about fractals: http://classes.yale.edu/fractals/MandelSet/MandelBoundary/Mis.html "The Misiurewicz points are scattered throughout the boundary of M: every circle centered at every boundary point encloses infinitely many Misiurewicz points." and http://classes.yale.edu/fractals/MandelSet/MandelBoundary/2Dim.html "The boundary of the Mandelbrot set is a very complicated place, because in addition to the Misiurewicz points, every circle centered at every boundary point encloses infinitely many centers, hence infinitely many copies of the Mandelbrot set." Since we are talking about circles of any (finite) size, that's quite a complicated structure indeed! As of guessing, computing, whatsoever the number of (roughly) same size midgets in an area, that question is probably best put to someone like, say, Robert Devaney or any other of the mathematicians working in the field. The only thing I know is that midgets "shrink faster than you can look", meaning that if you zoom into an M area by a given factor, the average midget size in view goes down by about the square of that factor. Regards, Gerald
Gerald K. Dobiasovsky wrote:
I guess a better view (of larger midgets) could be achieved by panning to the lower right, but still: http://www.abm-enterprises.net/fractals/mandelbrotgalaxywallpaper.html
Thank you very much, Gerald !!! :-) This was one of the images I had been thinking about, but had forgotten where I had seen it. (I am getting too old to recall everything like I used to.) Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/
participants (3)
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Gerald K. Dobiasovsky -
Jim Muth -
Paul N. Lee