Fractal visionaries and enthusiasts: 

The name of today's image, "The Ultimate Zexpe", is more a wish than a fact.  It took two days to find a Zexpe fractal that qualified for the status of ultimate, and even after finding it, I'm not so sure how ultimate it is.  If ultimate is taken to mean 'the best', its supremacy is quite doubtful, but if ultimate is taken to mean 'final', then today's image certainly is the last, at least in the present series.  Tomorrow's FOTD will feature the first in a similar series of 'Zexpi' (exponent PI) fractals.  (You ain't seen nothing yet.)

Today's parent double-Zexpe came about when I calculated Z^(epsilon) at a level of epsilon steps up the hyperladder with no function applied.  I omitted the function for the sake of simplicity.  This parent has both main buds on the same side (the northeast side) of the single main bay.  The scene lies in a minor valley on the west side of the main bay.  (I often choose to explore valleys because they emphasize the mathematical characteristics of the particular area in which they lie.)

The first impression of today's image is its brilliance, which earns it the rating of an 8.  The calculation time of 3 minutes is slower than I would have preferred, but still well within reason.  The web sites take the effort from viewing the image.

A near perfect summer day was fully appreciated here at Fractal Central today.  The temperature of 81F 27C, low humidity and Photoshop blue skies decorated with puffy white clouds were just what the fractal cats ordered.  They spent a good bit of time gazing out the window, wishing they could get outside to explore that big forbidden room.

The humans had too many other things to do to appreciate the weather.  (By the time humans have enough free time to enjoy good weather, it's too late in life to enjoy very much of anything [except fractals]).  The next FOTD will be posted in a proper amount of time.  Until whenever, take care, and make that big decision today.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

The_Ultimate_Zexpe { ; time=0:03:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident float=y
  center-mag=-0.332850274478/+0.147018580443/5e+007\
  /1/-172.5/0 params=2.718281828459/0/2.718281828459\
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  zrTzsQztNzuKzvHzwFzxCzy9zz6zz3zzVzzXzzZzz`zzazzczz\
  ezzgzzizzjzzlzznzzpzztzzq }

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=========================================