;     Date: Mon, 10 Sep 2012 08:52:20 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 08-09-12 (Truncated Rectangle [8])
;       Id: <1.5.4.16.20120910085607.38ffd7f0@earthlink.net>
; ---------
; 
; FOTD -- September 08, 2012 (Rating 8)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image is part of the Julia set of a rectangle in the 
; Z^(2.003)+C Mandelbrot set.  Surprisingly, there is no rectangle 
; at the center of the image, but rather an octagon with in-curved 
; sides.  The Julia set of a rectangle would normally be expected 
; to be another rectangle, but fractals, like so many theories of 
; modern physics, do not always do the intuitive things.  For some 
; reason, objects that appear as rectangles in their Mandelbrot 
; aspect appear as octagons when viewed in their broader Julia 
; aspects.
; 
; This Julia doubling is not actually so surprising, considering 
; that the Julia sets of the Mandelbrot radical 'stars' have 
; double the number of arms as the Mandelbrot stars themselves.  
; Thus, the Julia set of the two-branched star located around 
; -1.543 on the main spike of the M-set has four main branches.
; 
; The name "Truncated Rectangle" is another way of describing an 
; "Octagon", which to be more precise, is a truncated square.
; 
; I rated the image at an 8, due mostly to the coloring, which is 
; a combination of my efforts and a random shot of the Fractint 
; program.
; 
; The calculation time of 4 minutes borders on slowness, but at 
; least IMO, the image is worth the effort.  And the web sites can 
; remove even most of that effort.
; 
; So take life easy.  View the finished image at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; And experience the thrill of high definition at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; Finally, check the past at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; The pleasant late summer weather took a break here at Fractal 
; Central today, when heavy clouds moved in, followed by lively 
; thunder-showers.  The temperature of 84F 29C felt warmer than 
; usual due to the high humidity.  The fractal cats got into a bit 
; of a spat when they both wanted to lie on the table beside my 
; favorite chair, but reason finally prevailed and they agreed to 
; share the space with tails thrashing in unison.  The next FOTD 
; is soon to be posted.  Until whenever that might be, take care, 
; and if we only go around once in life, as conventional wisdom 
; says, then when do we get to use the lessons we have struggled 
; so hard to learn during our time on earth?
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

TruncatedRectangle { ; time=0:04:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=-0.000021470\
  16991775/+0.00000106606499224/269396.1/1/-12.5/0
  params=90/0/90/0/-1.743492647282116/2.074078440319\
  529e-008/0/0/2.003/0 float=y maxiter=3200 inside=0
  logmap=994 periodicity=6 mathtolerance=0.05/1
  colors=000BBCFFHIINLMSOR`RWfUZmW`wYdz`gzcjzfmzirzm\
  vzrzzmszhmzccpZUfVKUSJKPJPMIVJI_GHeDHjccEYgOTjXOmf\
  JpoLiiNbdOW_QQURJPTCKU6FfDScLO`TLY`HVhESpAQw7cVMp3\
  `bVfQvkPqlOmlNimNemQhlSkkUnjWhfXcbYZZ_UV`PRaKNZLKW\
  LHTMERMBON8LN5IO2GO0HL9IIIJFRKC_LAhXDihGjsJkmPhhVf\
  c`dZfbnLPkQUhVYf_acce`hjZmnWrrUvvdbmoJdkIXgIPcIH_I\
  AWNHSRNPWTL_ZIddEhjBlpLngVoZdpQmqInkGofFpaEqXDrRBs\
  MAtH9uC8zSgzVbzYYz`TzcPzfKziFzkBzfAzaAzXAzSAzNAzJA\
  zSHz`NgiUfr__iSTaLMTEGL7KJEOHKRGRVEXYDb`9fc6if3mh0\
  pnXHmbPlgXlldkqlkvthuuftvcswarxZqyXqyUrwSsuQtsOuqM\
  voKwnNsoQppTmqVirYfs`ctb`ucdqdgmejifnegqahtYiwUakP\
  U_LUOKECC618G4AP7BZ9DgCEpEFfMUXUhN`wO`rO`nO`jO`fO`\
  bPaZQbWRcSScPUvN`xcfzs`uzWqpRmoLinGemBal6YkFxrLpqQ\
  ipVao_VndNmiGln8ks1kt3kt4ku6ku7ktDhsJesPcrV`r`ZqfW\
  qlUhiY`gaSeeKciBam3_p7XoAUnDRmGOmJLlMIkPFjSDjTAfU7\
  bV5ZW2VW0SX4VGJV5PK8JEBE8 }

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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