;     Date: Mon, 01 Jan 2007 23:22:22 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 02-01-07 (How Low Can You Go [6])
;       Id: <1.5.4.16.20070101232440.29a7797c@pop.mindspring.com>
; ---------
; 
; FOTD -- January 02, 2007 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's image shows a midget of a very low order, located in the 
; fractal that results when the formula Z^(1.075)+C is calculated 
; 175 levels up the complex logarithmic ladder.  I named it "How 
; Low Can You Go".  I gave it this name because one of my current 
; fractal quests is to see how close to unity I can set the expo-
; nent of Z and still find midgets in the resulting fractal.  The 
; current record is Z^(1.045), but the midget I found there lacks 
; the quality to be a FOTD.
; 
; Today's parent fractal, like so many other very-low-order frac-
; tals, is little more than an elongated oval surrounded by large 
; areas of sandy fractal chaos.  The midget in today's scene, 
; which is located in the chaos of its parent, was found by using 
; the 'fmod' outside option.  Without this feature, midgets in 
; such low-order fractals would be impossible to find.
; 
; I rated the image at a 6, more to show my satisfaction at find-
; ing the midget than to comment on the quality of the image.  But 
; this does not mean I consider the image to be worthless.  It is 
; in fact quite an interesting scene to come from a power of Z so 
; close to a straight line.
; 
; The calculation time of 8-1/2 minutes is slightly slow for an 
; image that is only a little above average, but relief from the 
; impatience is at hand on the FOTD web site at:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; where the image has been calculated and posted for instant easy 
; viewing.
; 
; The New Year's Day weather was dreary here at Fractal Central.  
; Thick clouds covered the sky all day, with occasional periods of 
; light mist and a temperature of a most un-winter-like 50F 10C.  
; The cats of the fractal variety spent the day looking for 
; trouble but finding little now that the last of their left-over 
; Christmas play things have been cleared away.  My day was quite 
; relaxing, but the work today should pick up dramatically.  The 
; next FOTD will appear in 24 short hours.  Until then, take care, 
; and feel free as a sea gull.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

How_Low_Can_You_Go { ; time=0:08:30.14--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1
  center-mag=+0.72919018137204830/+5.829204067242754\
  00/150370/1/112.5/-1.98509829407722549e-009
  params=1.075/0/175/525 float=y maxiter=6000
  inside=0 logmap=122 periodicity=10
  colors=000lUAlVAkWAkXAjYAjZAi_Ai`AhaAhbAgcAfdAeeAd\
  fAcgAbh9ai8`j6_j4Zj2Yj3Xi4Wg5Vf6Uc7Sa8PZ9NXALVAJSB\
  HQCFNDCLEAIF8GG6DH4BI07G29I4BK6DM8EOAGQCISDJUFLWHN\
  YJV_LW`NYbP_dQafSbhUcjWdlYen_fpagrbhsairajrairahr`\
  hr`gr`fr`er`er_dr_cr_cr_ar_arZaqZ_qZ_qZZqYZqYZqYYq\
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  qBzqCzqCzqDzrEzrFzrGzrHzr }

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