;     Date: Mon, 15 Nov 2010 20:59:56 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 16-11-10 (Expect the Unexpected [6!])
;       Id: <1.5.4.16.20101115205952.10df21f6@pop.mindspring.com>
; ---------
; 
; FOTD -- November 16, 2010 (Rating 6!)
; 
; Fractal visionaries and enthusiasts:
; 
; One should always be prepared for the unexpected, even when it 
; seems impossible.  Today's slice through the Julibrot is a good 
; example.
; 
; The slice is centered on East Valley of the Mandelbrot set, and 
; oriented 0.1 degree from the Oblate direction, which means the 
; Mandelbrot stuff is stretched about 573 times its normal extent 
; in one direction.
; 
; In the image that I found before today's, I unstretched the 
; Mandelbrot parts, but in so doing, I stretched the Julia parts 
; about 573 times.  The grossly stretched Julia stuff is visible 
; near two corners of today's image.  When I did this stretching, 
; I had almost no hopes of finding any of the Mandelbrot stuff 
; that I had presumedly returned to its normal proportions, but 
; much to my surprise, I found one tiny open spot lurking in the 
; upper left corner.
; 
; When I closed in on the tiny spot, I found the better part of 
; one of the twisted minibrots that fill East valley.  At first I 
; could not believe that any Mandelbrot features at all could 
; remain when the Julibrot is sliced 89.9 degrees from the Mandel-
; brot orientation.  But pictures do not lie, (unless they have 
; been manipulated on a computer), and the twisted object at the 
; center of today's image is most certainly the remains of an East 
; Valley minibrot.
; 
; The rating of a 6! means that almost all the interest lies in 
; the mathematical aspect of the image.  The artistic worth is 
; minimal, though not entirely absent, and the features surround-
; ing the chopped-off minibrot certainly are curious.
; 
; The name "Expect the Unexpected" relates my adventures on the 
; way to finding today's image.
; 
; The calculation time of 21 seconds takes almost all the work out 
; of running the included parameter file.  The calculation work 
; can be eliminated entirely by viewing the finished image on the 
; FOTD web site at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; The sun departed and the clouds moved in here at Fractal Central 
; on Monday, while the temperature hovered around a mild 55F 13C.  
; The fractal cats took it all in stride, concerned only about 
; their next food treat.  My day was uneventful.  Until next time, 
; take care, and beware of global warming -- it's got me worried.  
; How long will it be before we wake up one morning up to our 
; knees in the rising seas, and find polar bears extinct?
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE=======================================

ExpectTheUnexpectd { ; time=0:00:21.31-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 center-mag=-0.023260073\
  46855092/-0.00735188243689156/2294.688/0.002601/\
  -179.929980454595068/89.7871683432740895
  params=0/0/89.9/0/0.277/0/0/0 float=y maxiter=2400
  inside=0 logmap=22 periodicity=6
  colors=000A0OA0PA0QA0RA0SA2TA4UA6WA8YAA_ACaAEcAGeA\
  IgAKiAMkAOmAQoASqAUsAWuAYwA_xAayAczAdvAcrAZm9Uh8Pc\
  6KjNFiRFPYCK`CFcAAe85d70a90Y90R60L40720xy1tu0pq0lm\
  0hi0de0aa0YY0UV0QR0MN0JJ0FF0BB0770330KmNHeJEZGBSD8\
  L95E6273USSPOOLKKHGGCCC888444PUvGKb8AJyfVnZPdSKVLF\
  KEAA752Tg1JT09E8yM7rJ6kH5dE4YC3R92K71D4062jcxdZq_V\
  jVQcQMXKHRFDKA8D546amLYhJVdHS`FPXEMTC_oGbeIeXJhOLj\
  FMeFOaFPYFQUFSQFTLFUHFVDFX9FY5FZ1F_4M`6Sa9ZbBdcEkd\
  GqdEpfDogCniAmj9ll8km7kn9loAlpBlpDmqEmqFmrHmsInsJn\
  tLntMnuNovPovQowRowUkuXgsZcqa`odXmfTkiPilMgnIeqEct\
  Aav7`uAYuCVtETtGQtJNsLLsNIsPGiRD`TBSU9NV8IW7EW79X6\
  4Y50Y56bABgEGkILpMQtQQuSQvUQwWQxYQy_cz`czbczdczfcz\
  hcziczgczemzcmzamz_mzYmzWmzUmzSmzzmzzmzzmzzmzzrzzv\
  zzzzzzzzzzzzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzznzzkzzgzzczz_zzXzzTzzPzz\
  MzzLzzKzzJzzIzzHzzHzzFzzE }

frm:SliceJulibrot2   {; draws most 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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