;     Date: Tue, 20 Jan 2004 10:32:07 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 20-01-04 (The Cubic Trinity [8])
;       Id: <1.5.4.16.20040120103423.29b7dbcc@pop.mindspring.com>
; ---------
; 
; FOTD -- January 20, 2004 (Rating 8)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image is the second consecutive one to rate an 8, though 
; its slower render time cuts its overall value to 59.  I did need 
; to take a slightly liberal view of the image to reach that 
; rating however, but it is still an unusually interesting sample 
; of a midget in an almost-cubic fractal.
; 
; The name I chose for the image, "The Cubic Trinity", has nothing 
; to do with religious belief.  It merely reflects the fact that, 
; in the image, everything comes in powers of 3.
; 
; While yesterday's FOTD image examines the negative real axis of 
; the Z^(2.003)+C Mandeloid as it appears 1040 levels up the 
; spiral, today's image looks at the negative real axis of the 
; Z^(3.003)+C figure at the same level.
; 
; Not unexpectedly, much of the same type of detail appears.  We 
; have the same features resembling skeletal hands, and the same 
; barely noticeable lack of symmetry.  The breaks that do appear 
; are arranged symmetrically around the midget so that they become 
; a regular part of the pattern.  Indeed, it takes a bit of 
; searching to find the places where the symmetry breaks, but a 
; careful search will reveal that all corners of the midget's 
; basin are not quite identical.
; 
; The render time of 13 minutes is slow for an image that might be 
; a bit exaggerated.  That wait may be eliminated by downloading 
; the finished GIF file from:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; With the temperature hovering around 25F -4C all afternoon, the 
; day was far too cold for the delicate whiskers and paws of the 
; fractal cats.  They tested the outdoors only a few minutes 
; before deciding that warmth was better than adventure.  A bit of 
; tuna kept them happy.  Today is starting sunny and just as cold. 
; The cats will likely have a similar day.
; 
; I have a bit of work to finish before starting the search for 
; the next fractal, but I can finish that work with the speed of a 
; photon.  I also have an urge to treat myself to some junk food 
; at the golden arches 1/2 mile down the road.  If I survive, I'll 
; return in 24 hours with the next FOTD image.  Could we possibly 
; have three consecutive images that rate an 8?  Check back here 
; in 24 hours to find out.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

The_Cubic_Trinity { ; time=0:13:28.73--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=mandelbrotbc1 function=floor passes=1
  center-mag=-1.08945153107755200/-0.010540023154615\
  56/4.734514e+012/0.9997/-170.7/0.200745373042978764
  params=3.003/0/1040/0 float=y maxiter=2100
  inside=0 logmap=355 periodicity=10
  colors=000EEKCDJGHMJLPNPRQTUUXWX`Z`d`chchmfmskryou\
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  `kzOszBczJQzQNzPLzNJzMGzL }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(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==================================
;