;     Date: Mon, 16 Mar 2015 18:23:29 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 16-03-15 (Fractals-101 [A-6,M-6])
;       Id: <1.5.4.16.20150316172715.2a772730@earthlink.net>
; ---------
; 
; FOTD -- March 16, 2015 (Rating A-6,M-6)
; 
; Fractal visionaries and enthusiasts:
; 
; I have been pretty silent lately but I am certainly still here.  
; Though today's image is nothing new, it shows that between my 
; more artistic efforts I still find time to check into the world 
; of fractals.  And don't give up hope.  Some of my latest efforts 
; should soon be worth posting on the web sites.
; 
; If the Mandelbrot set is the mother of all Z^2+C fractals, then 
; the Julibrot is the grandmother, for it is the four-dimensional 
; superfractal that contains the Mandelbrot set as a single 
; two-dimensional slice.
; 
; Today's image shows an undistorted view of a different slice of 
; this Julibrot, sliced in a totally new orientation, with the 
; vertical direction the imaginary C axis and the horizontal 
; direction the real Z axis.  I call this orientation the Oblate 
; direction, though this is totally unofficial.  The image slices 
; through the M-set at the point -0.8 on the real C axis, just 
; beyond Seahorse Valley.
; 
; I have named the image "Fractals-101" because the 4-D aspect is 
; basic to so many fractals.  I could rate it no higher than a 
; double 6 however because we have been here so often before.  The 
; calculation time is almost instant however, and this is the 
; image's best point.
; 
; The finished image is posted 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 temperature of 54F 12C made up for the limited sun here at 
; Fractal Central today.  Now that the winter to be remembered is 
; winding down, and the snow and ice is quickly disappearing, the 
; three fractal cats are giving more attention to the activity in 
; the outside cat world.  Lida has her eye on a big tough-looking 
; orange tomcat that frequents the area, while Jasmine prefers a 
; tuxedo colored tomcat.  Nicholas simply watches the ladies silly 
; behavior with aloof detachment, while the fractal people watch 
; all three with puzzlement.
; 
; The next FOTD will be posted, that much is certain, but only the 
; invisible shadow knows when, and he's not talking.  So until 
; whenever, take care, and everyone should have at least one crazy 
; conspiracy theory he can believe in without feeling silly.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

Fractals-101 { ; time=very brief SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrotSqr center-mag=0/0/0.86
  params=0/0/90/0/-0.8/0/0/0/0/0 float=y passes=1
  maxiter=750 inside=0 symmetry=xyaxis periodicity=6
  colors=0004Ct5Et6Gt7It8Kr9MrAOrBQqCSqGUpIWpLXoNYnR\
  ZmT_kX`i_`ga`e`adZbdXacQacKabEab8cb7dg6hk5jo4ksDic\
  MgOVe8ZcBaaEe_HhYJkWMoUPrSSuQUwOUwMUwLUwJUwHUwGUwK\
  TwNSwQSwURwXQw_Qw`PwaPwbPwbPwYNwULwPKjOqjOqkPqkPql\
  QqmQqmQqnRqnRqoSqoSqpSqpTqqTqrUqrUqsVqsVqtVqtWquWq\
  vXqvXqwXqwYqxYqxZqyZqz_ryZqyZqyYqyYqyYqyXqyXqyXqyW\
  qxWqxWqxVpxVpxVpxUpxUpxUpxTpwTpwSpwSpwSpwRowRowRow\
  QowQovQovPovPovPovOovOovOovNnvNnuMnuMnuMnuLnuLnuLn\
  uKnuKnuKntJmtJmtJmtImtImtImtHmtHmtHmsGmsGmsFlsFlsF\
  lsElsElsElsDlrDlrDlrClrClrClrBkrBkrBkrAkqAkq9kq9kq\
  9kq8kq8kq8kq7jq7jp7jp6jp6jp6jp5jp5jp5jp4jp4jo0lp4j\
  q7iqAhrEfrHesKdsOctRatU`uY_v`YvcXwgWwjVxmTxqSytRzx\
  PywQxvQxvRwuRvtSvtSusSurTtrTsqUszUrzUqzVqzVpzWpzWo\
  zWnzXnzXmzYmzYlzZkzZkzZjz_iz_iz`hz`hz`gzafzafzbezb\
  ezbdzcczcczdbzdazeaze`ze`zf_zfZzgZzgYzgYzhXzhWziWz\
  iVziUzjUzjTzkTzkSzlRzlRzl }

frm:SliceJulibrotSqr   {; 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*z+c
  |z|< esc }

; END PARAMETER FILE=========================================
; 
; 
; 
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