;     Date: Mon, 08 Nov 2010 20:17:45 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 09-11-10 (Hourglass Spirals [7])
;       Id: <1.5.4.16.20101108201742.136fd23a@pop.mindspring.com>
; ---------
; 
; FOTD -- November 09, 2010 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image is (no guarantee) the last of the series of near-
; Julia Mandelbrot valley images.  This one shows the valley of 
; the north bud of the large minibrot on the west branch of the 
; filament that extends from the north bud of the Mandelbrot set.
; 
; The effect is much the same as the previous images, though there 
; is more decoration around the almost-Julia set.  The name "Hour-
; glass Spirals" refers to the hourglass-like shape of the two 
; spirals on either side of the center.
; 
; It is tempting to think of these fractal spirals as 3-D things 
; such as short curved lengths of string.  But they are actually 
; 2-D slices of 3-D spaces that curve and twist in 4-D space.  As 
; with all 4-D stuff, the entirety of the spirals is impossible to 
; visualize.  As mere humans, our consciousness is limited to the 
; 3-D experience.
; 
; I decided to give today's image, which is likely the last of the 
; series, a rating of a 7.  We have been mired in this series 
; longer than I had intended, and there are many unusual slices of 
; the Julibrot that we have not yet checked.  Tomorrow's image 
; will begin the exploration of these.
; 
; Today's image calculates in under 7 minutes, not fireball fast, 
; but certainly faster than some FOTD's, which have taken days to 
; complete.
; 
; The last I heard, Paul was still in the hospital, recovering 
; from an infection.  He has enough access to the FOTD web site to 
; post the FOTD discussions.  But since he is using a new-fangled 
; laptop machine running Vista, which panics as the sight of the 
; Fractint program, he cannot run the parameter files.  I am send-
; ing the finished GIF images to him while he is in the hospital, 
; from where he can post them to the FOTD web site.  Hopefully, 
; the web site will be up to date shortly.  As always, the site 
; may be accessed at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; A few too many clouds and a bit too little sunshine here at 
; Fractal central on Monday kept the fractal cats from reaching 
; maximum contentment.  The temperature of 54F 12C was just about 
; normal.  My day was normal also.
; 
; The next FOTD will be posted in 24 hours.  Until then, take 
; care, and I hear that within 25 years everyone will have their 
; own private autogyro for their daily commute.
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE=======================================

Hourglass_Spirals { ; time=0:06:51.18-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=1 center-mag=0/0\
  /11.7/1/87/0 params=89.9/0/89.9/52.5/-0.15436/\
  1.0371225/0/0 float=y maxiter=40000 inside=0
  logmap=8 periodicity=6
  colors=000CKVDLUEMSFNWGOTHPRIQOJRMJSJKTIMUJNVIOWIQ\
  XHTYGVZGY`F_aFabEdcDfeDifCkgCnhBpjAskAul9wm9zlCzlE\
  zlHzlJxlMvlOtlRtlTslWslYsl`rlbrlerlgqljqllqlnokmnj\
  lmikkijjhiifhgdhfegedfcbecadcaccaccabcbacc`cc_ccZc\
  cZccYccXccWccVccUcbUcaYc`acZecXicWmcVqcUpcUpcUpdUp\
  dUpdUpeUpeUoeUofUofUofUogUogUogUnhUnhUnhUniUniUnjU\
  nkUmlUlmUkmUjmUimUhmUhmUgmUfmUemUfmUgmUhmUhmUimUjm\
  UjmUkmUlmUlmUmmUnmUnmUomUpmUpmUpmUqmUrmUsmUtmUumUv\
  mUwmUxmUymUxmUxmUxmTxmSxmRwmQwmPwmOwmNwmMwmLvmKvmJ\
  vmIvmHvmGumFumEumDumCumBuiEteHtaKsYNsUQrSRrQSrOTsM\
  UsKUsIVsGVsEWtCWtAXt8Xt6Yt4Zu2_u0`u0bz0dz0ez0ez0fz\
  0fz0gz0hz0hz0hz0iz1jz3jz4kz5kz7kz8qzArzBrzCszEszFs\
  zHuzIuzKuzLuzMuzOuzPuzRuzSuzSuzUzzVzzWzzXzzYzzZzz`\
  zzazzbzzczzdzzezzgzzhzzizzizzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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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