FOTD -- April 20, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today we take a break from the lumbering elephants and turn instead to a fractal fantasy land created by the JulibrotMulti2 formula, which does things too complicated to describe in less than a long paragraph. But how we got here does not matter. The fact is that here we are and we have found an image unusual enough to be declared FOTD for April 20. The image is almost but not quite a Julia set, since it is double rotated 1.5,1.5 degrees from the true Julia orientation. It is also barely an image at all, with both its inside and outside parts rendered with the 'FMOD' option. I named the image "Springtime Blues" because of the time of year in the Northern Hemisphere and the somber moody colors of the scene. In the Southern Hemisphere the name should be changed to "Autumnal Blues", which better matches the mood of the image. The rating of a 7-1/2 includes a half-point bonus for the coloring. The bonus is pretty much a gift however. The F8 key did most of the work. Luckily, the image is a reasonably fast one that finishes in about 40 seconds on most machines, even with the single-pass option in effect. The unusually small magnitude of 0.18 is mostly responsible for the speed. Calculation may be avoided totally by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The entire FOTD history is online at: <http://www.Nahee.com/FOTD/> Today was a beauty here at Fractal central, with lots of sun, enough clouds to make things interesting, and a temperature of 75F 24C. The fractal cats must have caught spring fever; they slept through most of the afternoon. The humans spent the day getting things caught up. When we finally did get caught up, FL somehow had energy to spare, which she exhausted working in this year's garden. With no energy to spare, I fell asleep watching the news. The next FOTD will be posted in 24 hours. Until then, take care, and in an effort to explain the quantum world, scientists have invented the various mental models known as the QM interpretations. In an effort to explain the mystical world, holy men have invented the various mental models known as the world's religions. To me, the message is that both scientists and holy men face the same difficulty, and in all likelihood, are investigating and trying to explain and communicate the same incomprehensible reality. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Springtime_Blues { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti2 function=recip passes=1 center-mag=0.278046/0/0.1816027/1/90/0 maxiter=1500 params=-3/25/88.8/0/88.8/0/0.75/0/0/0 inside=fmod float=y proximity=1.5 outside=fmod periodicity=0 colors=000`jNajMaiMbiMbhMchMcgMdgLdgLdfLefLeeLfeKf\ dKgdKgdKhcKhcJibJibJjaJjaJicGjbHjaIjaJj`Kj_Lj_MjZN\ jYOjYPjXQjWRjWSjVTkUUkUVkTWkSXkSYkRZkQ_kQ`kPakObkO\ ckNdjJgkLfkNekPdkRckSbkUakW`kY_kZZk`YkbXkdWkfVkgUv\ zzuzztzzsyzrxzqwzpvzouzntzmszlrzkqzjpzioyhnxgmwflu\ eksdjqdjocimchkbgibggafeaec`db`ca_b`Za_Z`ZY_YYZXXY\ WXXVWWUWVUVUUUTUUSUTRUTQUSPUSOUROURNUQMUQLUPKTOJSO\ IRNHQNGPMFOMENLEMLDLKCKJBJJAII9HI8GH7FH6EG5DG4CF3B\ F3AF49F48F48F58F59F59F6AF6AF6AF7BF7BF7CF8CF8DF8DF9\ EF9EF9EFAFFAFFAGFBGFBHFBHFCIFCIFCIFDJFDJFDKFEKFELF\ ELFFMFFMFFMFGNFGNFGOFGOFGPFGPGGOFGPFGPFGQFGQFGRFGR\ FGSFGSFGTFGTEGUEGUEGVEGVEGWEGWEFXEFXEFXEFYEEYDEZDE\ ZDE_DE_DE`DD`DDaDDaDDbDDbCDcCDcCCdCCdCCdCCeCCeCCfC\ BfCBgCBgCBhCBhCBiCBiCAjCAjCAkCAkCAlCAlCBjCAkCAkCAk\ CAlD9lE9lF9lG9mH8mI8mJ8mK8nL8nM7nO7nP7oQ7oR6oS6pT6\ pU6pW6pX5qY5qZ5q_5q`4ra4r } frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================