FOTD -- December 29, 2012 (Rating 7) Fractal visionaries and enthusiasts: On its surface, the Z^(-2)+C Mandeloid is not much to look at -- little more than a triangle consisting of flat overlapping disks. The disks can be made larger or smaller by changing the escape radius, but this has little effect on the worth of the fractal. All is not lost however. When the entire Julibrot is sliced in different directions, it shows some aspects that are more interesting. In today's image I have double rotated the slice 66 and 66 degrees toward the Julia orientation, and rendered it with the outside parts set to 'real'. In the image, we see that the flat disks have become organized into more attractive semi- chaotic spirals. (The parent fractal actually has buds, but this is a story for another day.) I named the image "Faerie Fantasyland". The odd spelling is kind of a trendy pseudo-magical way of spelling the word 'fairy', which is used by those who are into new-age stuff. The rating of a 7 includes a full point for the smooth GIF coloring, which I really did put an hour or so of effort into. Without the coloring, the underlying scene would rate only a 6. The image is very fast. It finishes in under one minute on all but the oldest and slowest units. The image may be viewed without the inconvenience of setting up and running the included parameter file. Simply surf over to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and view it there. High-definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted to the venerable FOTD web site at <http://www.Nahee.com/FOTD/> Snow fell all day here at Fractal Central today, while the light winds and relatively mild temperature of 30F -1C actually made the snow enjoyable. At post time about 5 inches or 12cm had piled up, but it was still falling. I'll give a final report in the next FOTD. The fractal cat alternated between stretching out on the radiator and hunching on the shelf in the southwest window, watching the snowflakes drift down. The humans took it as easy as possible, but I am concerned with the sidewalk that will eventually need to be cleared. The next FOTD will be posted when it is ready, most likely in 24 hours. Until whenever, take care, and I see that two people have been pushed in front of subway trains within a month. These trains are dangerous. We must do something about the needless deaths caused by misused subway trains. We must pass tighter train-control laws to keep subway trains from the hands of those who would misuse them. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Faerie_Fantasyland { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+1.49344425/\ +0.22623503/210/1/-90/0 params=66/0/66/0/0/0/0/0/\ -2/0 float=y maxiter=1500 inside=0 outside=real periodicity=6 colors=000CbFCcGDcGEcGEcHFcHGcHGcIHcIIcIIcJJcJKdJK\ eKLfKMgKMhLNiLOjLOkNPlNQmOQmPRmQSnQSnSToUUoWUoYVo_\ WoaWocVoeUogToiSokRomQnoQnqRnsRnuRmvQlwRkwRjvRitRg\ sSfqSdoSbnSalT_jTZiTXgTVeTUdUSbUR`UP_UNYVMWVKVVJTV\ IRVJQWJRXJSYKTZLUZMV_NV`OWaPXaQYbSZcT_dU_dV`eWafXb\ gYchZch_di`ejbfkcgkdhlehmfingjnhkoilpjlqkmrmnrnoso\ ptpquqqurrvsswttxuuxvuvututttstsrtrqtqpsposonsnmsm\ lslksjjriirhhrggrffreerddqccqbbqaaq``q__qYZpXYpWXp\ VWpUVpTUpSToRSoQRoPQoOPoNQrNOoNNmNMkNLiNKgNJeNHbNG\ `NFZNEXNDVNCTNAQN9ON8MN7KN6IN5GN4EM6HL8KKAMJCPJESI\ GUHIXGKZGLaFNdEPfDRiCTkCVnBXqAZs9`v9ax9cu9ds9ep9fn\ 9gk9hi9if9jd9ka9l_9mY9nV9oT9pQ9qO9rL9sJ9tG9uE8u99v\ CAvFBvIBvKCvNDvQDvSEvVFvYFvYHtYIrYJpYKnYMlYNjYOiZP\ g_Re`ScaTabU_cVZdXXeYVeZTf_RfaPfbNgcMgdKhfIhgGhhEi\ hCig9lgBifDfcFc_H`WJYTLVPNSMPPIRMETJBVG7XD4YB5ZC6Z\ C6_D7_D8`D8`E9aEAaEAaFBbF } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================