;     Date: Fri, 13 May 2005 11:48:11 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 13-05-05 (Near a Mandelbrot [5])
;       Id: <1.5.4.16.20050513114931.30afea9c@pop.mindspring.com>
; ---------
; 
; FOTD -- May 13, 2005 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; Today is Friday the 13th, an event that happens once or twice 
; every year.  It is supposed to be a bad luck day, though I doubt 
; that is any unluckier than any other day of the year.  Nothing 
; unusually bad has ever happened to me on a Friday the 13th, so 
; I consider the bad luck thing to be an unfounded superstition, 
; most likely originating long ago, when the decree that ordered 
; the elimination of the Knights Templar was passed on a Friday 
; the 13th.  My view would seem to be confirmed by today's image, 
; which is notably un-notable.
; 
; Today's image is a scene in a fractal that is almost a 
; Mandelbrot set.  What keeps it from being a Mandelbrot set is 
; the exponent of Z in the iterated formula, which is 2.00001.  
; This is a very tiny difference, but to make a big deal of a 
; minor event I examined the fractal 100,000 levels up the complex 
; log hyperspiral, at a level where it has rotated approximately 
; 70 degrees.  At this level the negative real axis cuts through 
; what is normally the S.S.W. shoreline of the M-set.
; 
; At this lofty level, the parent fractal still resembles a 
; classic Mandelbrot set, and the inner detail is basically 
; unchanged.  The one difference is along the negative real axis, 
; where a tiny discontinuity exists.  This break is so small that 
; it does not become visible until the magnitude reaches 500000, 
; but the break still does strange things to the inner detail of 
; the area.
; 
; The name "Near a Mandelbrot" refers to the exponent of Z, which 
; makes the parent fractal nearly but not quite a perfect 
; Mandelbrot set.  The rating of 5 means that I am not unusually 
; impressed by the image.  The render time of almost 17 minutes is 
; slow, making a download of the completed image from:
; 
;      <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; a wise choice.
; 
; The clouds cleared unexpectedly on Thursday afternoon, giving 
; the fractal cats an unexpected great afternoon in the holly 
; thicket.  For 15-year-old cats, a great afternoon means a 
; peaceful uneventful afternoon, and peaceful it was.  When they 
; returned indoors in the evening, a small tuna treat closed their 
; day with a whimper.  Today is starting with sun and clouds.  
; It remains to be seen which will prevail.  For me the work is 
; rather light, which will give extra time for fractals.  The 
; next FOTD will appear in 24 hours.  Until then, take care, and 
; if life serves you an apple, make it a napple.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

Near_a_Mandelbrot { ; time=0:16:54.64--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1
  center-mag=-0.70976131907690630/+0.000002313855428\
  97/3.870999e+007/1/42.5000007756963427/-1.18881678\
  390359014e-007 params=2.00001/0/100000/0 float=y
  maxiter=4000 inside=0 logmap=395 periodicity=10
  colors=000aPTaOUbOVcOWcNXdNYdMZeM_eL`fLafLagK_gKZg\
  KYgKXgJWgJVgJUgJTgJSgIRgIQgIPgIOgINgHMgHLgHKgHJgHI\
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  TauSeuQjuPnuNsuMwtNusOtsPsrQqrRpqSoqTnpUlpVkoWjoXh\
  nYgnZfm_em`clabkbakc_jdZjeYifXigVhhUhiTgjRgkQflPfm\
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  NrxLryLsxKrxJrxJrxIrwHqwHqwGqwGqwFqvEpvEpvDpvCpuCo\
  uBouBouAou9ot9nt8nt7nt7ns6ms6ms5ms4ms4mr3lr2lr2lr1\
  ls0mt0mu0mv0mw0mx0my0mz0m }

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=========================================
; 
;