FOTD -- December 12, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image shows an odd slice of a midget that lies in the East Valley area of the prominent midget on the main stem of the M-set. At this angle, the tiny open area at the center of the image cannot be said to be a midget -- Julibrot holes appear as midgets only when they are sliced in the Mandelbrot orientation along a critical plane. The orientation of the entire image is so far removed from both the Julia and Mandelbrot directions that the hole at its center appears as a mere slit. Much of the distortion of the hole is caused by the extreme stretching and skewing that was necessary to remove the inherent distortion from the surrounding pattern. The world of the odd slices of the 4-D Julibrot is unlike the world of the M-sets or the J-sets. In the odd slices, the features twist, turn and stretch in an unpredictable manner, and must be unstretched to make reasonable pictures of them. So the stretching that went into today's image is actually an unstretching -- a stretching in the opposite direction. I named the final result "Fractal Trinity". The brilliant white triangle around the center slit reminds me of a religious symbol that might be used to represent the Divine Trinity. I'm not trying to promote religion, but I have always wondered whether fractals have a far deeper significance than mere candy for the eyes and ears. After all, fractals resemble the quantum world of the very small, in that they both can be properly comprehen- ded only by the math that describes them. And like fractals, the world at the quantum level does not really come into exis- tence until we make a measurement (iterate a formula) and force it to do something that we can comprehend. Despite (or because of) its religious connotations, I could rate today's image no higher than an average 5. These distorted Julibrot slices have a certain feeling of stress about them that does not make for totally enjoyable viewing. The render time of just under 4 minutes is reasonable enough, but a download of the completed image, which may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even more reasonable. The sun was strong on Sunday, but the high winds and tempera- tures barely above freezing (33F 0.5C) kept the dynamic cats indoors all day. Their moods were surprisingly pleasant however as they chased the patches of sunlight streaming through the windows. Since they have never figured out which way the sun- light will move, they were only partly successful in keeping themselves in the warm rays. As for me, I know which way the sun will move, but I'm not sure how the day's work will move, so I'd best take some action to see that it moves in the right direction. I'll return in 24 hours, more or less, still in the third dimension but talking about the fourth. Until then, take care, and follow the sun. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Trinity { ; time=0:03:56.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=-0.00000000000111381/-0.000000000000085\ 77/3.48225e+011/0.02201/173.968599844493554/-76.31\ 6192842800163 params=125.45/-71.48/2/0/-1.74910112\ 6619117/0.0003477184884611/-1.749101126619117/0.00\ 03477184884611 float=y maxiter=2500 inside=0 logmap=426 symmetry=none periodicity=10 colors=000ZCBWBDUBFSBGQAIOAJMALKAMN9LQ9LT9KV9PY9U`\ 9Zb9ce9hh9kj9nmItpKrsMppOomPmjRkgTjdUh`WfYYeY_cY`a\ Yb`YdZYeYWa_UYaSVbQRdOOfMKgKHiIDkHAlNDjSGhXJgaMefP\ ckSbpV`uYZz`YnRUbIQR9MF0IKEJORKSXLWYLCYpBZnA_m9_k8\ `j8`i7ag6af5bd5bc4cb3c`2d_2dZHcRVcKibDwb6Xa_V`YT_X\ SZWQYUPYTNXSMWQKVPJVOHUMGTLESKDSJEQMEOPFMSFKUGIXGG\ _HEbHCdIAgI8jJ6mJ5oL7mN9lOBkQCiREhTGgVIfWJdYLcZNb`\ PabQ_cSZeUYfVXkYHh_IeaIbcI_eIXgJUiJSjJPlJMnKJpKGrK\ DtKBuK8jV6_d4Po2FyBKrJPkRUe_ZZgcTohUwlcwnoxqzyszzq\ uxokvnbsmbqlYmj`mjbmjdmjfmjimjkmjmmjominkineimaimX\ ilTilPhlKhkGhkBhj7hj3hj8jfDlbInZNpVSrRXtNavJewGhqM\ klSnfYqactWiwRoyMtmVhacYQkNL`RHRVDHYCI_CJ`CKbBKcBL\ dBMfAMgANiAOj9Ok9Pm9Qn9Qo9Tj9Vf9Xa9_Y9aT9cP9eL8eK8\ gJ8iI8kH8mG8oG7qF7sE7uD7wC7yB7zBOz9cz8sz7pz8mz8kz8\ hz8ez8cz8`z8Yz8Wz8Tz8Qz8Oz8Nz9Mz9NzlOzlQzkRzjTziUz\ hVzhEzAKzKQzUVzc`zmezwazZ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================