;     Date: Thu, 19 Aug 2010 20:19:37 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 20-08-10 (From Epsilon to PI [7])
;       Id: <1.5.4.16.20100819201933.11774ed2@pop.mindspring.com>
; ---------
; 
; FOTD -- August 20, 2010 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; On Thursday I was occupied with the 'Zexpe' series of formulas 
; (formulae is the plural word for the over-educated) and tried 
; one of my own.  Using the MandelbrotBC3 formula, I checked to 
; see what the Zexpe fractal looks like at a level of PI steps up 
; the complex logarithmic hyperladder.
; 
; The parent fractal that I found there looks pretty much like the 
; minibrot at the center of today's image, though it is rotated 
; 180 degrees, and as today's image shows, it is quite interesting 
; in its depths.
; 
; Today's scene lies in a valley of its parent that corresponds to 
; the small valley near the center of the eastern shore line of 
; the main bay of the minibrot at the center of the image.
; 
; The rating of a 7 means I consider today's image to be a bit 
; better than yesterday's, yet nothing to get over-excited about.
; 
; The name "From Epsilon to PI" fairly describes the math behind 
; the image.
; 
; The calculation time of 1-1/2 minutes is fast by any standards.  
; But viewing the finished image on the FOTD web site at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; is less work and more fun.
; 
; Perfect weather prevailed here at Fractal Central on Thursday -- 
; sunny skies, low humidity and a temperature of 84F 29C.  The 
; fractal cats had a thrill when a very loud fight broke out 
; between two cats in the yard next door, but they seemed a bit 
; disappointed when one cat, presumably the loser, made a cautious 
; retreat before the dispute could escalate to physical violence.  
; My day was slow, which gave more time to waste before searching 
; for fractals.
; 
; The next FOTD will be posted in 24 hours.  Until then, take 
; care, and I found a mind lying on the basement stairs.  Did 
; anyone lose theirs?
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

From_Epsilon_to_PI { ; time=0:01:28.70-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-0.1738289076076641/+0.3463464790189864\
  /9.098551e+008/1/152.5/0 params=2.71828182845905/0\
  /3.14159265358979/0 float=y maxiter=3600 inside=0
  logmap=129 periodicity=6
  colors=000E28F3BG4EH5HI6KJ7NK8QL9TMAWNBZOCaPDcQEcR\
  FcSGcTGcUGcRGcOIcKJcIJdGJeEJfCKgAKh8Kk6Kn7Lq8Nt9Qw\
  HTzRVzZ_ybcxgfxlgzoiqshkvddwVZmNScHLU6F4sbBpVHmONj\
  HTgAZd3`jBcoJmuRzzY4EA5FG5GM6HS6HY7Ic7Ji8Ko8KuAYoC\
  kiEydKs`QmYWgVcaRjWOrRLkPHdOEYNAQM7JL4EI3AG2JFBSEK\
  aDTjDagHZeKXcNUaQSZUQXXNV_LTbJQdLOeNMgPKhRIiTGkVEl\
  XCmZAo`8pb6qd4sf2th0uj3rk5pk8nkAlkCjkFhkHfkJdkMalO\
  _lRYlTWlVUlYSl_QlaOlcPjdQieRggSfhTeiUcjVblV`mW_nXZ\
  oYXqZWr_Us`Tt`StZPtXNtVLtTJtRHtPEtNCtLAtJ8tH6jE7aB\
  7T87J57A271070039yy8tt7pp7kk6gg5bb5ZZ4VV3QQ3MM2HH1\
  DD188044PYuNVpLTlJQhHOdGL`EJXCHTAEO8CK79G57C348124\
  3oS2bL1QE0D7upgpkckg_fbXaZTXUPTQMOMIJHEEDB987443w1\
  mw0hw0cx0Zx0Ux0Px0Ky0Fy0Ay05yI5zC3z6zzEszCzzBhzAzz\
  8Zz7zz6Pz0zzE9zDzzDAzDzzDCzCzzCEzUzzCFzUzzKCzUzzR9\
  zUzzY7zUzzk9zUzzbIzUzzTRzUzzNSzMzzLMzKzzIHzHzzGBzF\
  zzJGzNzzMTzLzzLdzKzzJpzJz }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-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=========================================
; 
; 
; 
; 
; _______________________________________________
; Fractint mailing list
; Fractint@mailman.xmission.com
; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
;