;     Date: Mon, 01 Apr 2013 18:27:59 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 01-04-13 (A Rectangular Set [No Rating])
;       Id: <1.5.4.16.20130401172718.2e1f1502@earthlink.net>
; ---------
; 
; FOTD -- April 01, 2013 (No Rating)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image is a new view of a minibrot hole on the main stem 
; of the Mandelbrot set.  The minibrot looks so unusual because it 
; is sliced in the Rectangular orientation, which lies at a right 
; angle to the Mandelbrot orientation and is determined by the 
; imag(z) and imag(c) axes.
; 
; The brilliant green bars slicing diagonally through the open 
; area are actually Mandelbrot valleys viewed at a right angle.  
; The bars are straight edged because regardless of where points 
; in the M-set are initialized, they will eventually settle into 
; the same orbits unless they escape first.
; 
; There is no way I could give a rating to such an overworked 
; theme, but being fascinated by things beyond visualization, I 
; continue returning to the four-dimensional Julibrot for ever new 
; surprises.
; 
; The name "A Rectangular Set" is a bit misleading.  The image is 
; merely a small part of one of an infinity of Rectangular sets.
; 
; The calculation completes in 25 seconds, fast enough to waste no 
; one's time.  The web sites are more convenient but probably no 
; faster.
; 
; When the official FOTD web site is back in operation, it will 
; be found at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; Until then, the finished images may be seen in hi-def at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; The back images are posted at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; The day began pleasant enough here at Fractal Central today, 
; with breaking clouds and a temperature of 50F 10C, but by midday 
; the clouds and rain had returned, and the temperature had 
; dropped to 45F +7C.  The fractal cat observed all this with 
; dis-interest, while the humans made it through another day with 
; no unexpected disasters happening.
; 
; The next FOTD will be posted soon.  Until we find out how long 
; 'soon' is, take care, and when disasters happen, look to the 
; bright side.  But before you look, be sure a bright side 
; actually exists.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

A_Rectangular_Set { ; time=0:00:25.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/10166.07\
  /1.3984/29.6185420924715608/28.9858769262522351
  params=90/90/0/90/-1.690128/0/-1.690128/0/2/0
  float=y maxiter=3200 inside=0
  logmap=28 periodicity=6
  colors=000BamCalD`kE_jFZiGYgHXeIWcJVaIU_ISYHQVHOSG\
  MQGKNFIKFGIDDGBADA89846713940B72E94HC6KF8OHARKCUME\
  YPG_SGbUFdXEf_DiaCkdBmfAlgClhDkiEkjFjkHjlIilJimKhn\
  LhoNgpOgqPfrQfrRhoUjmXlk_nibpgerehtckvanx_qqXlkUgd\
  RbZOYSLTMIONJJOLPWSUpfGoaHnYHmTHlPHkLHgNIcOI_PIWRJ\
  SSJPTJSPGVMEYIC`FAaJDaNGbRJbVMcYOcaRdeUdiXem_epadm\
  bdjbdgbLTRLUQKVQKWQJXPJYPIYPIZPH_OH`OGaOGbNGcNFcNF\
  dMEeMEfMDgMDhLCiLCiLBjKBkKBlKAmJAnJ9oJ9oJ8pI8qI7rI\
  7sH6tH6uH6uH7tI7sI8sJ8rJ9rK9qK9qLApLApMBoMBnNBnNCm\
  OCmODlPDlPDkQEkQEjRFjRFiSFhSGhTGgTHgUHfUHfVIeVIeWJ\
  dWJdXJcXKbYKbYLaZLaZM`_M`_M_`N_`iSVgTVeTVdTVbUV`UV\
  _VVYVVWVVVWUTWURWUQXUOXUMYULYUJYUHZUGZUE_UC_UB_U9`\
  U7`U6`U7aT8bT9bT9cTAcSBdSCdSCeSDfSEfRFgRFgRGhRHhQI\
  iQIjQJjQKkQLkPLlPMlPNmPNmPOnOPoOQoOQpORpNSqNTqNTrN\
  UsNVsMWtMWtMXuMYuLZvLZwL_wL`xLaxKayKbyKczKczKbxLaw\
  L`vM`uM_tNZsNYrNYqOXpOWoP }

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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