;     Date: Mon, 10 Dec 2012 08:49:27 -0500
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 09-12-12 (Broken Hyperspiral [5])
;       Id: <1.5.4.16.20121210084707.29973cda@earthlink.net>
; ---------
; 
; FOTD -- December 09, 2012 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image of a strange spiral is located in the Scepter 
; Valley area of the Z^2+C Julibrot.  It is sliced in a direction 
; halfway between the Oblate and the Rectangular, and has been 
; stretched and skewed to a rather large extent to bring it to a 
; recognizable shape.
; 
; The name "Broken Hyperspiral" refers to the infinitely divided 
; nature of the features in the image.  This unlimited division, 
; known as 'Cantor Dust', is typical of the Julia sets of points 
; outside the Mandelbrot set, but as today's image shows, it also 
; exists in the odd planes and angles.
; 
; The image consists totally of points, with no two points being 
; connected.  A zoom into one of the sub-spirals will reveal a 
; never-ending chain of similar broken spirals, and this series 
; continues all the way to infinity, which is not an end point or 
; a very large number, but an abstract idea that can never be 
; reached.
; 
; The rating of a 5 is pretty pathetic by FOTD standards, but it's 
; all I could give the image, which has little more than a bit of 
; pop-math interest going for it.  More effort on the coloring 
; might have raised the rating a point or two.
; 
; The calculation time of 1-3/4 minutes is about average, but 
; perhaps a bit slow for an image with so little reward.  The 
; situation is resolved on the web sites.
; 
; The completed image is posted for instant viewing at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; with high-definition variations at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; The back images are online at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; Clouds ruled the sky today here at Fractal Central, while the 
; temperature of 45F +7C kept things feeling seasonal.  The 
; forecasted rain held off until sunset however.  Both the cats 
; and humans had a typical uninteresting day.
; 
; The next FOTD will be posted when it is ready.  Until whenever, 
; take care, and if humans ever populate the galaxy, how will they 
; agree on a universal galactic time?  (IMO, we will never 
; populate anything but planet earth, so there is no problem.)
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

Broken_Hyperspiral { ; time=0:01:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1
  center-mag=+0.03264445237728411/+0.172536526663781\
  00/8438.382/0.1402/79.9353442340639617/73.17794208\
  35490413 params=45/90/0/90/-1.25/0/0/0/2/0 float=y
  maxiter=2200 inside=255 logmap=-126 periodicity=6
  colors=000knUknUloUloTmpTmpSmqSmqRmrRmrRmsQmsQmtPm\
  tPmuOmuOmuNmvMmvLkvKiwKhwJfwIdxHcxGaxG_yFZyEXyDVzC\
  ayIcyMeyQgyUiyYky`mydoyhqylpykoyjmygjxdhxafxZcwWaw\
  T_vQXuN`sT_qSZoRYmQWkQViPUgOTdNSbMQ`MPYLOWKNUJMRIK\
  PIJMHIKGHIFGFEEDEGBDI8CK6BM3AO8HQ7MS6RU5WW4`Y3eZ2j\
  Z4kZ6kZ8kZAkZCk_EkaGlbIncKodMqfOseQsdSrcUqbWq`Xp_Y\
  oZYoYYnWZmVZmUZlTZkSZkQ_jP_iO_iN_hL`gK`gJ`fI`eH`eF\
  adEacDacCabAba9ba8b`7b_5cZAbaBcaDdaEdaGeaHfaJgaKga\
  MhaNiaOiaQjaRkaTlaUl`Wm`Xn`Zo`_o``p`bq`cq`er`fs`ht\
  `it`ku`lv`nw_nw_mw`mw`lwalwakwbjwbjwczzczzdzzdzzez\
  zezzfzzfzzgzzgzzhzzhzzizzizzjzzjzzkzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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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