FOTD -- December 31, 2013 (Rating A-6,M-8) Fractal visionaries and enthusiasts: Strange rectangles appear in the Julia sets of the Z^(2.003)+C Mandeloid corresponding to the area on the X-axis just east of the large, split apart minibrot. Not surprisingly, rectangles are also found around the Mandel minibrots in this area. But totally surprisingly, when the Julia sets of these Mandelbrot rectangles are checked, they turn out to be not rectangles, but concave octagons. And even more surprisingly, when the julia sets of the edges of these Mandelbrot rectangles are checked, we find not rectangles, nor octagons, but pentagons, two of which appear in today's image. I named the image "Pentagon Paradise" because of the two pentagons sitting blissfully at the center of the scene, enjoying the inevitable boredom of their eternal rest. The art aspect of the scene is worth only a 6. We have seen similar scenes many times before. The math aspect however rates a quite honorable 8, at least for those who are into fractal math. The image calculates in an average 2 minutes. This is fast enough to prevent impatience yet slow enough for a bit of anticipation to build. The web sites will avoid all anxiety. The happiness usually found only in paradise may be enjoyed by viewing the finished image on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The day here at Fractal Central began with heavy clouds and light snow. After leaving a dusting on the sidewalk, the snow moved out, and by afternoon the sun appeared. The high temperature of freezing was right on the mark. The fractal cats watched the snowflakes fall for an hour or so, then began playing with each other until Nico grew tired and retired under a chair cover. Jasmine soon retired to the chair in her room. The humans, who are doing absolutely nothing special this year, had little trouble preparing for the new year's arrival. The next FOTD will be posted next year. Until then, take care, and what will the good people do when they grow bored with the eternal peace of heaven and want a little action? Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Pentagon_Paradise { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0\ /40000/1/-177.5/0 params=90/0/90/0/-1.743377131101\ 082/7.467157179206152e-007/0/0/2.003/0 float=y maxiter=750 inside=0 logmap=289 periodicity=6 colors=000TPNIRNcV`aUZ_TWZSUXRSVQPTPNROLPNINMGMMEK\ NGIOHGPIEQKCRLASM8TN6UP4VQ2WR0XS0WQ0VO0VM0UK0UJ5_H\ 9eGDkEHpDFdGDTJBHMA6OA9RABUADXAF_AHbAJeALhANkAPnAR\ qATs9Sq8So8Rn7Ql6Pk6Pi5Oh5Of4Nd3Mc3Ma2L`1KZ1KY0JW0\ JV3LQ6NM9PHBRDCUFDWHEZJF`KGcMHeOIgQJjRKlTLoVMqXMsY\ NtXOuWPuVQvURvTSwSTwRUxQVxPWyOXyNYzMZzMcuOgpQlkSpg\ UqiXrk_rmasodsqftsitukuwnuyprzAfwKVuTJsa8qj6coBckG\ cgLccQh`RhbRmcRmdRmeRmfQhbRhhRhiRcjRckXc8hzzhzzhzz\ hzzhzzhzzhzzhzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzQzmRzmRzlRzlF\ zvIztKzrNzpPznBzGDzJEzMGzPHzSJzVKzYMz`NzcPzfQzioz_\ kzahzcezdbzf_zhXziUzk`zO_zQZzRZzSYzUYzVXzWXzYWzZWz\ _VzaVzbUzcUzeTzfTzgSziSzjRzkJzsMzpPznzzptzonznhznb\ zmXzlozlmzllzlkzljzlizlgzlfzlezldzlczlazl`zl_zlZzl\ YzlWzlVzlUzlTzlSzl`zF_zHZzJZzLYzNYzOXzQXzSWzUWzWVz\ XVzZUz`UzbTzdTzeSzgSziRzk } 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=========================================