;     Date: Tue, 26 Oct 2010 22:17:28 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 27-10-10 (A Golden Slice [5])
;       Id: <1.5.4.16.20101026221723.1327ec74@pop.mindspring.com>
; ---------
; 
; FOTD -- October 27, 2010 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; The formula behind today's image is Z^2+C, the same formula that 
; creates the Mandelbrot set and all its associated Julia sets.  
; But today's image is obviously not the M-set, nor is it any 
; recognizable Julia set.  It is something I call an Oblate set, 
; a hybrid set half-Mandelbrot and half-Julia.
; 
; The X-axis of the image is the real(Z) axis of the Julibrot, 
; while the Y-axis is the imag(C) axis.  The image has a Mandel-
; brot nature in its vertical direction and a Julia nature in its 
; horizontal direction.  The center of the image is the center of 
; the large period-2 bud of the M-set.  No shape manipulation such 
; as stretching or skewing was done in the creation of the image, 
; though I did add a bit of life by rendering it with the outside 
; set to 'real'.
; 
; A most curious relation exists in the location of the elements 
; along the X-axis of the image.  The fractal terminates on the 
; left and right at the points plus and minus 1.61803398875.... 
; which of course is the Golden Ratio, while the two major valleys 
; closest to the center meet at plus and minus 0.61803398875.... 
; which is the reciprocal of the Golden Ratio.  There must be a 
; logical reason why this is so, though I have not been able to 
; find it.
; 
; I rated the image at a 7, a good part of which is due to the 
; mathematical interest.  Artistically, the image rates a 5 or 6.  
; I named the image "A Golden Slice" because of the appearance of 
; the Golden Ratio in it.
; 
; Despite all the golden glitter, the image is blazingly fast, 
; finishing on my machine in under 3 seconds, almost as fast as 
; the display can switch to super-VGA mode.  The trip to see the 
; finished image on the FOTD web site at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; may not be quite as fast, but it will involve much less set-up 
; work.
; 
; Rain fell most all Monday night here at Fractal Central.  The 
; remaining clouds blocked the sun on Tuesday, but the temperature 
; of 70F 21C was mild enough that the lack of sun was never 
; noticed.  The fractal cats spent an hour chasing a mechanical 
; toy mouse we picked up Monday evening.  Nicholas finally killed 
; it when its battery went flat.  The rest of the day was occupied 
; with routine work.
; 
; Remembering yesterday, I dared not ask FL what was happening on 
; the Spanish channel.  The next FOTD will be posted in 24 hours.  
; It should be no surprise if another odd slice of the Z^2+C 
; Julibrot shows up.  Until then, take care, and let your negative 
; side shine through.
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE=======================================

A_Golden_Slice { ; time=0:00:02.85-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/0.7544715
  params=0/0/90/0/-1/0/0/0/2/0 float=y maxiter=300
  inside=0 outside=real periodicity=6
  colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\
  HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\
  vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\
  OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\
  zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  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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