;     Date: Mon, 10 Sep 2012 08:52:22 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 09-09-12 (Oblate Rectangle [7.5])
;       Id: <1.5.4.16.20120910085609.37073ee0@earthlink.net>
; ---------
; 
; FOTD -- September 09, 2012 (Rating 7.5)
; 
; Fractal visionaries and enthusiasts:
; 
; We have found the strange Z^(2.003)+C rectangle in the Julia 
; sets and in the Mandelbrot set.  But what about the four 
; remaining perpendicular directions through the Julibrot?  Well, 
; as today's image shows, the rectangle also appears in the Oblate 
; orientation, where, with the proper stretching and skewing, it 
; makes quite a striking appearance.
; 
; At first glance the image appears to have origin symmetry, but a 
; close inspection will reveal that the symmetry is only apparent, 
; and not exact.
; 
; I named the image "Oblate Rectangle" for the obvious reason.  
; The rating of a 7-1/2 includes the usual bonus for my coloring 
; work, which creates a good part of the overall effect.
; 
; The calculation time of 3-1/2 minutes might seem slow to those 
; who are growing bored with rectangles.  The web sites bring 
; total relief from boredom however.
; 
; The next three FOTD's will feature the rectangle in its 
; remaining three aspects.  Then we'll move on to other fractal 
; wonders.
; 
; The completed image is online at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; A high-definition rendering is at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; The back images are at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; A near perfect day prevailed here at Fractal Central today, with 
; a temperature of 75F 24C and a Photoshop (aka Kodachrome) blue 
; sky dotted with small, puffy white, chamber-of-commerce cumulus 
; clouds.  The fractal cats enjoyed the outside conditions from 
; inside, spending much time on the shelf in the southwest window, 
; where the sun, at its lower angle, is again starting to come in.
; 
; The humans made it through the day without incident.  The next 
; FOTD image will be posted in 24 hours.  Until then, take care, 
; and, if the world is a dream, then the evidence that it is a 
; dream is also a dream.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

Oblate_Rectangle { ; time=0:03:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/3620/\
  0.01375/0/-77.0000000000000995 params=0/0/90/0/\
  -1.7435/0/0.000175/0.073883/2.003/0 float=y
  maxiter=72000 inside=0 logmap=54 periodicity=6
  colors=000K8aKAcKCeKEgKGiKIkKKmKMoIOqGPsEQuBQwDRvE\
  RuGSuHStJTuKTvLTwNUxOUyQVzRVzSVzUWzVWzXXzYXz_Yz`Yz\
  aYzc_zd`zfbzgcziezhezhdzgbzgazg_zfZzfZzeXzeWzeVzdU\
  zdSzdRzcRzcQzbPzbQzbSzaUzaWzaYxc_ve`tgaribpkcnmdmj\
  ehgfdeg_bhW`iSYjN_kJblEemAho6kqMnsaquVtwPwyJzzDwwK\
  tuQqsknqWkoihmwekubis_gqXeo_crRanI_k9`g0if1gd1eb2d\
  `2bZ3aY3_W4ZU4XS5VQ5UP6SN6RL7PJ9RH7SI6NJ4JK0EL3KL5\
  QL7QL9RLBRLDSLFSLHTLJULIVKHWJGZIFaHEdGEgFFfIGfKHfM\
  HeOIeQJeSJeUKdXLdZLd`MdbNcdNcfOchPbkPbmQboRbqRasSa\
  uTawTayDczCczCczCczCczBczBczBczBczAczmZzmZzmZzmZzm\
  ZzmZzmZzmZzmZzmZzmYzmXzmWzmVzmUzmUzhPNkPOnPPpPPmOM\
  mOKmNImNFmMDmMBmL8mL6mK4mK2mJ6mI9mHDmGGmFKmENmERmD\
  UmCYmB`mAdm9gm6km9jmBimDimGhmIhzKgzMgzPfzRfzTezVez\
  Ydz_czaczdbzfbzhazjazm`zo`zq_zuZzs_zq_zo`zn`zl`zja\
  ziazgbzebzdbzbcz`czZdzYdzWdzUezTezRfzPfzSfzRgzQizP\
  jzNkzMmzLnzKozIqzHrzGszDs }

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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