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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================