;     Date: Mon, 03 May 2004 10:14:10 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 03-05-04 (Fractal Cheating [5])
;       Id: <1.5.4.16.20040503101743.29a7a3a4@pop.mindspring.com>
; ---------
; 
; FOTD -- May 03, 2004 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image is more of a demonstration of a Fractint program 
; feature than a picture of a great fractal scene just discovered. 
; I named the image "Fractal Cheating" because I used the 'decomp' 
; option on yesterday's image to create it, which makes the image 
; more of an intentional creation than a discovery.  Yes, I 
; cheated.  But look at yesterday's FOTD, and you will see why I 
; cheated.  The standard rendering of today's scene makes a really 
; nothing image.  I humbly admitted my guilt by naming the image 
; "Fractal Cheating".
; 
; I also cheated with the formula I used.  To create yesterday's 
; version of the scene, I used the MandelbrotMix3a formula and 
; entered the critical -8.888 by hand.  For today's version, I 
; turned to the MandelbrotMix4 formula, which calculated and 
; entered the initial value of Z automatically.  The benefit is 
; a great increase in speed, though with an image as fast as 
; today's, the difference is not very large.
; 
; Most of my fractals are calculated by iterating a simple 
; function of a complex number, producing another complex number, 
; until either the number exceeds some pre-defined bailout value, 
; or the maxiter is reached.  The pixel corresponding to the 
; starting point is then colored based on the result of that 
; calculation.  The decomp feature turns on another coloring 
; method, in which the points are colored according to which 
; section of the complex plane the final value lies in.  The 
; decomp parameter determines how many sections the complex plane 
; is divided into for this purpose.  In today's image, the plane 
; is divided into the maximum 256 sections.
; 
; I would have rated today's image higher than a 5, but the 
; coloring is less than satisfactory, and I just can't shake the 
; feeling that it is not a real fractal.  Apparently, just as man 
; has philosophically done with the sensory-created mental image 
; of a physical universe, I have arbitrarily created a reality.  I 
; have decided that that the 'outside=iter' method produces the 
; 'real' fractal, and all other rendering methods are mere 
; distortions of the one ultimate fractal reality.  But at least, 
; I am still aware that I myself have created and decided what is 
; fractal reality.
; 
; The rating of 5 equals an overall value of 281 when the 1-3/4 
; minute render time is considered.  The time required to download 
; the image from:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; is roughly the same.
; 
; A warm sunny Sunday here at Fractal Central gave the dynamic duo 
; ample time under the holly trees.  When evening came, they were 
; totally exhausted from doing nothing, and came inside for their 
; evening meal without hesitation.  In the late evening, a severe 
; thunder-storm arose, which brought down a large limb from one of 
; the fractal trees.  But, other than the need to eventually 
; remove the fallen limb, no harm was done, as it fell in the 
; alley beside F.C.  This morning is cloudy, chilly and damp, with 
; occasional rain.  What will the cats do to adapt?
; 
; The most immediate task for me is to put the work that is now in 
; front of me behind me.  Then it's on to the fractals, and maybe 
; that tree limb.  Until next time, take care, and a fractal a day 
; may keep the doctor away, but five hundred a day will bring the 
; doctor running.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Fractal_Cheating { ; time=0:01:46.83--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-22.97767772633961000/+0.06349061612053\
  014/3.426261e+008/1/-152.5/0.000251818031069418746
  params=1/2/0.075/3/0/0 float=y maxiter=300 inside=0
  logmap=34 decomp=256 periodicity=10
  colors=000cmzzzVzzWzzWzyWzxXzwXzvXzuXztWysWxsVwrVv\
  qVuqUtpUspUroTqnTpnTomSnmSmlSlkRkkRjjQijQhiQghPfhP\
  egPdgOdfOceObeNbdNadNacM`bM`bL_aL_aLZ`KZ_KY_KYZJXZ\
  JWYIWXGVXFVWEUVCUVCTUCTUBSTDSSDRSERRFQRGPQHPPIOPJO\
  OKNOLNNMMMNMMOLLPLLPKKPKJPJJPIIPIIPHHPHGPGGPGFPFFP\
  FEPEDPEDPDCPDCPCDPCEPCEPCFPCGPCGPCHPCIPCIPCJPBJPBK\
  PBLPBLPBMPBNPBNNBOLBPJBPHAQFAQDARCASCASCATCAUEAUEA\
  VEAWF9WF9XF9XF9YG9YG9ZG9ZG9_H9_H9`H8_G9aH9`H9aHAaH\
  AaHAbHAbHBcHBcHBcHCdHCdICdICeIDeIDfIDfIDfIEgIEgIEg\
  IFhIFhIFiJFiJGiJGjJGjJGjJHkJHkJHlJIlJIlJImKImKJnKJ\
  nKJnKKoKKoKKoKKpKLpKLqKLqKLqLMrLMrLMrLNsLNsLNtLNtL\
  OtLOuLOuLNvMOuLOtLOsLPsLPrLPqLPpLQpLQoLQnLRmLRmLRl\
  LRkLSkLSjLSiLThLThLTgLTfLUeLUeLUdLVcLVcLVbLVaLW`LW\
  `LW_LXZLXYLXYLXXLYWLYWLYVKZUKZTKZTKZSK_RK_QK_QK`PK\
  `OK`NK`NKaMKaLKaLKbKKbJKbIKbIKcHKcGKcFKdFKdEKdDKdD\
  KeCKeBKeAKfAKf9Kf8Kf7Kg7K }

frm:MandelbrotMix4 {; 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,
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==================================
; 
;