;     Date: Thu, 21 Feb 2013 04:25:57 -0500
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 20-02-13 (The Phantom Revealed [7])
;       Id: <1.5.4.16.20130221042441.2ad7cdbe@earthlink.net>
; ---------
; 
; FOTD -- February 20, 2013 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; The FOTD that appeared two days ago on February 18 was named 
; "A Phantom Parent".  In that image it is apparent that another 
; fractal lies buried beneath the surface fractal, but because the 
; surface fractal is critical, that hidden fractal must be forever 
; obscured.  But things are not nearly as bad as they first 
; appear, for in today's image I take away the surface stuff and 
; reveal that phantom fractal in its full glory, which explains 
; the name "The Phantom Revealed".
; 
; The trick lies in choosing the alternate critical value of 
; initial Z.  The generating expression actually has two critical 
; values.  In the previous image, the initial value of Z was 
; automatically set to zero, one of the critical values.  In 
; today's image, I have reset the value of initial Z to -1, the 
; second critical value.  The result of this change is to move the 
; previously buried fractal to the surface, and bury the fractal 
; that was previously on the surface.  Fragments of the previous 
; surface image now appear as the bits of orangish stuff scattered 
; about today's scene.
; 
; Calculating complex critical values is not much fun.  One of 
; these days I might find a formula that can switch the critical 
; values of initial Z automatically, but that day is not in the 
; foreseeable future.  Until then, I will continue to find the 
; alternate critical values with the graphic method.
; 
; The rating of a 7 totally reflects the mathematical value of the 
; image.  The artistic value hardly exists.  But I will dive into 
; today's image and post what I find there as tomorrow's FOTD.  
; Who knows, I might find something worth a higher rating.
; 
; Check the fractal phantom at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; With a deeper analysis at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; And the spooks from the past at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; Typical midwinter weather prevailed at Fractal Central today, 
; with a temperature of 28F -2C and frequent but light flurries of 
; snow.  The fractal cat made a break-out but got caught before he 
; got into trouble, and was soundly scolded for his efforts.  The 
; humans made it through the day with only one spat, which was due 
; to FL's testiness.  My patience, approaching that of Job, kept 
; things under control however.  The next FOTD will be posted in 
; 24 hours.  Until then, take care, and when will the over-zealous 
; technophiles realize that technology cannot solve all of man's 
; problems because it has created many of them itself?
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

ThePhantomRevealed { ; time=0:00:10.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=cosxx float=y
  center-mag=0/0/0.69 params=-2/2.3/1/4.6/-0.02/0/-1/0
  maxiter=750 inside=0 symmetry=xyaxis periodicity=6
  colors=000GSNTT_RVaQXbOZdNaeLdfKhhIliHpkFplEomCnoB\
  mpAmq9mn8mk8kh7if7gc6f`6eZ5dW4cT4bQ3aO3`L2_I2ZG3YK\
  4XO4WR5VV5UYzmazmdzmezmfzmfzmgzmgzmbzmZzmVzmQzmMzm\
  IzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcKzcKz\
  XKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWLzWLzWLzVLzVLzVL\
  zVLzVLzVLzVMzVMzVMzUMzUMzUMzUMzUMzUMzUMzUNzUNzTNzT\
  NzTNzTNzTNzTNzTNzTNzJOzLNzNNzPNzRNzLMzMNzMNzNNzNNz\
  NNzONzONzPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfP\
  xfPwePwePvePudPudPtcPscPrcPrbPqbPpaOpaOoaOn`Om`Om_\
  Ol_Ok_OkZOjZOiYOhYOhYOgXNfXNfWNeWNdWNzVNzVNzUNzUNz\
  UNzTNzTNzBYzCXzDXzDWzEWzFWzFVzGVzHUzHUzIUzJTzJTzKS\
  zKSzLSzMRzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZ\
  RzWPqqJppKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLz\
  fLzeLzdLzdMzcMzbMzbMzaMz`Mz_Mz_MzZMzYNzYNzXNzWNzVN\
  zVNzUNzTNzx`zw_zv_zu_zuZztZzsZzrYzrYzqYzpXroXzoXzn\
  WzmWzlWzlVzkVzjVziUziUzhU }

frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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