;     Date: Thu, 22 Sep 2005 10:18:55 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 22-09-05 (The Fourth Root [7])
;       Id: <1.5.4.16.20050922102125.3907718a@pop.mindspring.com>
; ---------
; 
; FOTD -- February 22, 2005 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; In the northern hemisphere today is the first day of autumn.  
; In the southern hemisphere it is the first day of spring.  At 
; 2223 GMT the sun stands directly over the equator somewhere not 
; too far south of Hawaii.  For a brief moment, everything is in 
; balance, the great world fractal is motionless, and it is said 
; an egg will balance on its end.
; 
; This might be true in some parts of the world, but not here at 
; Fractal Central.  The only way I can make an egg stand upright 
; is to place it on a flat surface and prop it up with a few 
; grains of salt.  The big question would seem to be how the story 
; got started.  It is also said that the entire universe might be 
; a fractal, which would mean that eggs are fractals also.  But 
; there is nothing egg-like in today's striking image.
; 
; Today's fractal is part of the larger fractal that results when 
; the formula Z^(1.1892)+C is iterated at ground zero level of the 
; logarithmic spiral.  Actually, I should say 3.14159 levels down 
; the complex logarithmic hyperspiral spiral, for the number pi is 
; actually best considered ground level of the spiral.  (I might 
; write another formula, one that correctly sets ground level.)
; 
; The exponent of Z in today's image is 1.1892, and it is no acci-
; dent that this number is the fourth root of 2.  I chose this 
; value because the midgets are easier to find in fractals whose Z 
; exponents are roots of 2.  I really did not need to choose a 
; root of 2 however, for I have discovered a simple method of 
; finding those elusive hidden midgets in fractals with exponents 
; of Z between 1 and 2.
; 
; After giving today's image full consideration, I rated it at a 
; 7.  This is about the 6th consecutive rating of a 7, which is a 
; sign that, at least in my opinion, I am on a fractal roll.  The 
; name "The Fourth Root" is a simple description of the exponent 
; of Z.  The render time of 2 minutes is thankfully brief.  And as 
; for those with Fractint-deprived machines -- they can see the 
; image by downloading it from the FOTD web site at:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; An absolutely perfect day (we sure have been having a lot of 
; them lately) here at Fractal Central on Wednesday kept the 
; fractal cats contented.  Finishing the work early and finding a 
; good fractal kept me contented also.  Today is starting sunny 
; and only the slightest bit cooler.  It seems another good day 
; is coming up.  The next FOTD will appear in 24 hours.  Until 
; then, take care, and don't ignore the minutiae.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE=======================================

The_Fourth_Root { ; time=0:02:05.01--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1 periodicity=10
  center-mag=+1.99538087334197200/+1.392766250999284\
  00/37712.73/1/-17.5/2.84751282275675e-009 logmap=55
  params=1.1892/0/0/0 float=y maxiter=1500 inside=0
  colors=000VTVTQTQOQOMTMKRKEOI7LH0HB0HD0OB7UHMZX_fl\
  nnzzttlzlXzdHzX2zQ0zvazzzizzizzinqiaeiQViFKiXMvlOz\
  zQzzTzzOzzMdqKHtIDvH9xH5xF2zF0zD0zD0zM2xXBveMtoXqz\
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  zzQzzTzzTzzKzzDzz7zz0zz0zz0zz2zzFzzTzzzzztzznzzgzz\
  azz3zz0zzlzzezzazzXzzTzzOzzIzzFzzBzzHzzKzzIzzIzzIz\
  zlzzzzzlzzKzzQzzV0zY3zaBzgKzlTzo_ztQzxIzzBzz3zz0zz\
  0zz0zz0za0z00z30z90zD0zI0zM0zBBz0Tz0iz00zT0zK0zD0z\
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  2zo3zz0zz0zz0zz0zz0zz_zzgzznzttzdzzOzzBzzDxzDtzFoz\
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  z29z0zzXzzXzz0vz0ez0Oz39zF0zQ0za0zF0z07z0Kz0Yz3lzI\
  zz_zzozzazzOzzBzz0zz2zz5zz9zzDzzHzzKzzOzz_vzioztgz\
  zazzXzzVzzVzzVzzvzYozYizY }

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