;     Date: Mon, 20 Dec 2004 09:06:15 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 20-12-04 (Fractal Flight [5])
;       Id: <1.5.4.16.20041220090808.29d757b6@pop.mindspring.com>
; ---------
; 
; FOTD -- December 20, 2004 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; For today's fractal we break out the MandelbrotBC2 formula, 
; which takes advantage of the multi-valued nature of the complex 
; 'log' function, and gets an infinity of fractals from formulas 
; that would seem limited to only one.
; 
; The additional fractals are especially interesting when the 
; exponent of Z is set to a value between 1 and 2.  Today's image 
; uses a value of 1.1 -- a value in the lower part of that range, 
; where the images explode in size as we travel up the logarithmic 
; spiral and the changes are the greatest.
; 
; The parent fractal is an oversized thing resembling a dead bird 
; lying on its back, with its pointed bill facing upward.  Today's 
; scene is located in the valley that forms the lower edge of the 
; bird's bill.  Not wanting to make allusions to a dead bird in 
; the name of the image, I decided to name it "Fractal Flight".
; 
; The question of whether fractals can fly is moot.  Fractals are 
; abstractions, and abstractions can do anything we wish them to,
; though usually they do nothing.
;   
; In today's image I saw a flight of fractal somethings taking off 
; into a blue sky and vanishing beyond the upper left corner of 
; the frame.  Perhaps they have been frightened by approaching 
; danger.  (It is hard to imagine how a fractal could come to harm 
; however.)
; 
; The 'objects' (if that's what they are) share a curious similar-
; ity.  In some ways they are alike; in other ways, each has a 
; character of its own.  Even the larger groups of objects share 
; this partial similarity.  The image is a true fractal.  In it, 
; the same pattern is repeated again and again at the deeper 
; levels.  Of course, the deeper we explore, the slower the calcu-
; lation becomes.
; 
; With nothing really exceptional to raise its rating, the scene 
; could be rated no higher than an average 5.  Its render time of 
; almost 23 minutes gives it an overall worth of only 22.  It is 
; still an interesting image to see however, and well worth the 
; small effort of downloading it from the FOTD web site at:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; Heavy clouds, a chilly temperature of 36F 2C, and a cold rain 
; kept the duo indoors for the entire day on Sunday.  Their moods 
; were surprisingly good considering their confinement.  As night 
; fell, the rain changed to snow, which soon froze solid, making 
; for tricky walking and worse driving.  When the duo saw the bad 
; conditions, they actually seemed glad to be indoors, where a 
; generous serving of tuna was available to assure their content-
; ment.  This morning is starting sunny, but with a temperature of 
; only +7F -14C and a wind of 20mph 30kph, I doubt that the duo 
; will want to go outside.
; 
; The work is still heavy in my department, but I hope to squeeze 
; in a fractal or two before the day ends.  The best of what I 
; find will appear as tomorrow's FOTD.  Until then, take care, and 
; keep your cool when the snow falls.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

Fractal_Flight { ; time=0:22:55.83--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1
  center-mag=+0.77134655541610010/+0.189518755374709\
  60/3732.587/1/-12.5/-1.07880579469643578e-011
  params=1.1/0/23.8/0 float=y maxiter=3000
  inside=255 logmap=304 periodicity=10
  colors=000HHUJIULJTNKSPLRSMRVOQXPPZQO`RNbSNdTMfULh\
  VKjWKlXJoYIrZHs_Fr_Hp_Jn_Kl_Mi_Og_Pd_Rb_SZ_UX_WV_X\
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  udvuevvewvexveyveyvfurfqofmmfmmgmmgmmgmmgmmhmmhmmh\
  mmhmmhmmgmmfmmfmmemmemmdmmdmmcmmbmmbmmammamm`mm`mm\
  _mmZmmZmmYmmYmmXmmXomWqmWrmXqmYqmZqmZqm_qm`pm`pmap\
  mbpmbpmcomdomeomeomfomgnmgnmhnminminmjmmkmmlmmlmmm\
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  ikrhkshktgjugjvfjzfjxejydjzdjzcjzckzblzbmzanzaoz`p\
  z`qz_rzZszZtzNuzNuzNuzOuzOuzOuzOuzPuzPuzPuzQuzQuzQ\
  uzRuzRuzRuzSwzRvzRuzRtzRszRszQrzQqzQpzQpzQozPnzPmz\
  PmzPmzPmzOmzOmzQmzOmzLmzJmzHmzFmzDmzAmz8mz6mz4mz2m\
  z0mz3mz5mz7mz9mzBmzDmzFmz }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*floor(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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