;     Date: Wed, 27 Oct 2010 19:06:56 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 28-10-10 (Curious Coincidence [No Rating])
;       Id: <1.5.4.16.20101027190656.12c7e5ba@pop.mindspring.com>
; ---------
; 
; FOTD -- October 28, 2010 (No Rating)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image gets no rating.  Why?  Because it's a virtual 
; repeat of yesterday's image.  The difference is that, while 
; yesterday's image was sliced in the Oblate direction, today's 
; is sliced in the Rectangular direction, which consists of the 
; imag(Z) and imag(C) axes of the Julibrot.
; 
; IMO, what made yesterday's scene so curious is the fact that the 
; fractal terminates on the left and right at values of plus and 
; minus 1.618...., (the golden ratio), while the large valleys 
; meet at plus and minus 0.618...., the reciprocal of the golden 
; ratio).
; 
; This is curious enough, but when I checked the horizontal 
; terminal points of today's image, I found a value of plus and 
; minus 0.78615....  What an incredible coincidence it is that 
; this is the reciprocal of the square root of the golden ratio.  
; (The two large valleys in today's image meet at plus and minus 
; 0.521555...., though I have yet to find anything significant in 
; this value.)
; 
; Mathematical interest aside, today's image is simply a variation 
; on yesterday's image, with the same color palette.  Those who 
; enjoyed yesterday's will enjoy today's almost as much.  Those 
; who thought yesterday's image was boring will be no more 
; impressed by today's.
; 
; The name "Curious Coincidence" refers to the mathematical aspect 
; of the image.
; 
; The calculation time of only 3 seconds is mercifully brief.  The 
; best way to view the image is to enjoy it already calculated on 
; the FOTD web site at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; Wednesday began with clouds here at Fractal Central.  But the 
; clouds broke up by midday, leading to a sunny afternoon with a 
; temperature of 72F 22C.  These conditions were perfect for the 
; fractal cats, who spent several hours in the sun that streamed 
; in the southwest window.  My day was average; FL had a similar 
; day.  The next FOTD will be posted in 24 hours, and is likely to 
; be another mathematical curiositiy, though one with far more 
; artistic impact.  Until then, take care, and why does the number 
; epsilon equal minus one when it is raised to the power of 
; imag(PI)?
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE=======================================

CuriousCoincidence { ; time=0:00:03.35-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/1.398/1/\
  90/0 params=90/0/0/90/-1/0/0/0/2/0 float=y inside=0
  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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