; Date: Sat, 05 Mar 2005 10:28:19 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 05-03-05 (Oblate Miniature [6]) ; Id: <1.5.4.16.20050305102852.2b2f760e@pop.mindspring.com> ; --------- ; ; FOTD -- March 05, 2005 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; The Mandelbrot set is filled with miniature versions of itself. ; All these miniature M-sets are of the same basic shape, though ; some are distorted to a certain degree. It is the different ; surroundings of the miniatures that create most of the interest. ; ; The Julia sets of the miniature Mandelbrot sets are filled with ; miniature Julia sets, but these Julia sets, as well as their ; surroundings are all alike, so there is no great reason to ; explore them. But then there are what I call Oblate miniatures. ; ; The word miniatures is not quite correct, for, unlike Mandelbrot ; and Julia miniatures, the holes that appear in the Oblate slices ; of the Julibrot bear little resemblance to the shape of their ; parent fractals, and in fact often are unpredictable and ; unexpected. Today's image shows an Oblate miniature associated ; with a point near where the negative stem of the M-set joins the ; main body of the set itself. (This explains the name "Oblate ; Miniature".) ; ; Oblate miniatures can be of almost any shape except the familiar ; Mandelbrot shape. They frequently have perfectly straight ; edges, something that is never seen in either Mandelbrot or ; Julia miniatures. At other times, as in today's image, they ; resemble miniature Julia sets. When they do resemble Julia ; miniatures, these miniatures are not all alike. They will vary ; throughout the parent fractal. ; ; Finding Oblate miniatures is made more challenging by the fact ; that the parent fractals are sometimes stretched to a large ; degree, and must be unstretched and sometimes skewed before any ; sense can be made of the scene. ; ; Today's image needed only a small amount of stretching, though ; considerable skewing was required to bring it to an undistorted ; shape. The object it pictures is more like a 'Siegel Disk' ; Julia miniature than anything else. It has no open center, ; though the stuff filling the center is of extremely high ; iteration, and slows the calculation to nearly an hour. ; ; The rating of a 6 includes the mathematical interest. The ; artistic rating is closer to a 5. The slow rendering may be ; avoided by downloading the finished image from the FOTD web site ; at: ; ; ; ; Friday was a little warmer here at Fractal Central, but 39F 4C ; is still not balmy, and the fractal cats demand balmy, so extra ; tuna was needed to keep the complaints at a minimum. Today is ; starting with some sun, but I see possible snow mentioned for ; later today. It looks like another questionable day for the duo. ; ; In my department the situation appears settled. The commercial ; work is about caught up and the fractals are coming along on ; schedule. The next FOTD will appear in 24 hours. Until then, ; take care, and look to the light. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Oblate_Miniature { ; time=0:54:21.47--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0.00001661999961360/+0.000003\ 43572018929/1.324138e+010/1.1184/-22.9825910406299\ 059/5.63619786054203864 params=0/90/2/0/1.401863/0\ /-1.401863/0 float=y maxiter=250000 inside=255 logmap=332 symmetry=none periodicity=10 colors=000ptzpszprzpqzppzpozpnzpmzplzpkypjypiwphwp\ gupfupetpdtrcrrbrtapt`pu_nuZmwYkwXhyWfyVdzUbzTZzSY\ zRWzQUzPQzOOzNMzMKzLHzKFzJDzIBzHDzGFzFHwEIuDKrCMpD\ OmHQkMShQUfUWbZYZbZYh`UkbSpdOtfMyhIziHzkDzmBzm9zi9\ zh9zf9zd9zb9z`9zZ9zW9yU9wS9uQ9tO9rM9pK9nI9mF9kD9iB\ Bh9Df7Fd5Hb3I`7KZ0MY0OW0QU0SS0UQ0WO0YM0ZK0YI0WI0SM\ 0QQ0MU0KU0IU0HQ0FM0DI7BHF9DK79S55Y33d00i00p00u00y0\ 0z00z00y00w07u0Bt0Fr0Ip0Mn0Km0Ik0Ii0Hh0Ff0Fd0Db0D`\ 3BZ39Y59W57U55S75Q73O93M90KB0KB0MD0MD0MF0OF0OF0OI0\ UK5YO9`QFfSIiWOmYSr`Yub`ydfzhizinznyzkrzhkzdfz`ZzY\ SzUMzQFzO5zM9zKBzIDzHFzFHzDIzBKz9Oz7Qz5Sz3Uz0Wz0Yz\ 0Zz0bz0dz0fz0hz0iz0kz0mz0mz0nz0pz0pz0rz0rz0tz0tz3u\ z5uz7wzBwzDyzHyzIzzKzyOzwQzuUzuWztYzr`zpbzndznbzm`\ zkZyiYuhWtfUpdSnbQk`Qi`OfZMbYK`WIYUHWSFSQDQOBMMBKM\ FMOIOQMQQQQSSSSWUUZUUbWWdYWhYYkZYn`Zr``tb`wdbzdbzf\ dzhdzhfzifzkhzkhzkhzkhzkh } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ; ;