;     Date: Sun, 24 Feb 2013 23:16:39 -0500
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 24-02-13 (The Test of Time [7])
;       Id: <1.5.4.16.20130224231527.2aff6252@earthlink.net>
; ---------
; 
; FOTD -- February 24, 2013 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; The expression behind today's image combines 1.96 negative parts 
; of Z^(2.3) with 0.98 parts of Z^(4.6), then adds C on each 
; iteration.  When written as a function, this expression has two 
; critical points, zero and -1.  (I previously had this wrong.)  
; The MandAutoCritInZ formula automatically initializes Z to zero, 
; but Z can be initialized to -1 by entering that value as the 
; real(p4) parameter.
; 
; For some strange reason, the minibrots in the fractal that is 
; produced when initial Z is set to zero are quadratic M-sets, 
; while the minibrots in the fractal with initial Z set to -1 are 
; of order 2.3.  This might be because the value of -1 is a point 
; of inflection on the graph of the function, while the value of 
; zero is the tip of a parabola.  In both cases the derivative is 
; zero and the fractal will therefore be undistorted.  I'm not 
; sure if this is true of all fractas created by expressions with 
; multiple critical points.
; 
; Regardless of the correctness of the math, today's image lies in 
; the fractal that results when Z is initialized to -1.  The 
; minibrot at its center is of order 2.3 as expected.
; 
; The rating of a 7 is perhaps a bit conservative.  I did put a 
; half hour or so of effort into the coloring.
; 
; The calculation time of 8 minutes is slow.  Much time may be 
; saved by viewing the finished image on one or more of the FOTD 
; web sites.
; 
; Check the finished image at the official FOTD web site at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; And the variations at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; Back images are at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; A typical late winter day passed uneventfully here at Fractal 
; Central, with lots of clouds during the morning and a clearing 
; in the afternoon.  The temperature of 37F +3C was right on the 
; mark.  The fractal cat played with his catnip ball until the sun 
; appeared.  Then he stretched out on his shelf in the southwest 
; window.  The humans made it through the day with a minimum of 
; annoyances other than the usual miseries of the flu.
; 
; The next FOTD will be posted when it is ready.  Until whenever, 
; take care, and I hear from Old Fractal Central back in Bodymore 
; Murderland, (as the locals there call Baltimore, Maryland), that 
; the weather forecast there today is partly cloudy with a near 
; 100-percent chance of scattered bullets.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

The_Test_of_Time { ; time=0:08:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=cosxx float=y
  center-mag=+0.102350608821/-0.60041985916/3.4e+008\
  /1/150/0 params=-1.96/2.3/0.98/4.6/0/0/-1/0
  maxiter=5400 inside=0 logmap=365 periodicity=6
  colors=000KMUKMUKMUKMUKMUJMUIMWGOXEQXCSXAUX8WX6X`B\
  YdG`gLbkQfnVjrZnuTrzNvzIxzCzz7pzIczTUmcUcmbWzHvMJn\
  zPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfPxfPwePwe\
  PvePudPWSxBt9JoGQjNXeUc``jWgqRmrTkrVjrXhsZgs`esbds\
  dbteatg_tiZtkXumWuoUuqTurSsnUqkVphWneYlbZk__iXagUb\
  fRcdOebLfaIg_FiYCjX9k`WScY9o_KzIUzJTzJTzKSzKSzLSzM\
  RzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZRzWPqqJp\
  pKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLzfLzeLzdL\
  zdMzlJzrGzzCpzEmuGguIgvKfvMewOewQbsR`pSYmSWjTTfTRc\
  UP`UMYVKVWHRWFOXCLXAIY8FY7JX7NX7QW6UW6XW6`V5cV5gU5\
  jU4nU0zm0zmmzTmzQGSNTT_RVaQXbOZdNaeKdfKhhKizUpkUpl\
  Uomcnocmpcmqcqnhozjnpmmfmmcrm`vmZzmWzmQzmTzmWzkZzm\
  VzmQzmMzmIzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJz\
  cJzcKzcKzXKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWczWczWc\
  zVczVczVmzVmzVmzVmzVmzVzzVzzUzzUzzUzzUzzUzzUzzUzzU\
  zzUzzTzzTzzTzzTzzTzzTzzTz }

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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