;     Date: Tue, 31 Dec 2013 18:22:05 -0500
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 31-12-13 (Pentagon Paradise [A-6,M-8])
;       Id: <1.5.4.16.20131231182225.38e75fca@earthlink.net>
; ---------
; 
; 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=========================================
; 
; 
; 
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